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        <title>爱幻想的Ren</title>
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            <title><![CDATA[2024年终总结]]></title>
            <link>https://fantasy-ren.tech//article/2024-review</link>
            <guid>https://fantasy-ren.tech//article/2024-review</guid>
            <pubDate>Tue, 31 Dec 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[2024结束了，作为对过去工作展开的总结与回顾，我希望不仅能为我未来某刻回忆这一年时提供一些可追溯的碎片，也能激励我向前看，未来才是应该努力的方向]]></description>
            <content:encoded><![CDATA[<div id="notion-article" class="mx-auto overflow-hidden "><main class="notion light-mode notion-page notion-block-16d002488f2d80c2ad1bf96ded9b5941"><div class="notion-viewport"></div><div class="notion-collection-page-properties"></div><blockquote class="notion-quote notion-block-16d002488f2d818394a3d6e917c691e1"><div>Work Hard, Play Hard. 
这是我对我的2024这一年的一个总结。</div></blockquote><div class="notion-text notion-block-16d002488f2d81658077e0b122ad25fb">我的2024年开始于佛罗伦萨的一间青年旅馆，彼时，正值英国研究生第一学期的圣诞节假期阶段，我和女友刚启程了意大利+西班牙之旅，为我今年四处旅行拉开序幕；此时，在年末已经游历了十多个国家之后，我正在上海租住的小公寓内写下这篇2024年终总结，以此来对我过往一年的经历进行整理。</div><div class="notion-blank notion-block-16d002488f2d80398dc5fb3c0041a82f"> </div><div class="notion-text notion-block-16d002488f2d804a9f8feeac7937279b">整体来说，2024年对我而言是一个不断移动的时期。最让我有感触的是11月刚到上海实习时，我因不知能否通过实习试用而暂住在一家青旅，第一晚躺在床上思考时，竟突然因为忘记了自己在哪、自己正在做什么而感到短暂的恐慌。现在细细想来这一年走过的路干过的事，也觉得挺了不起的，当然也有一些遗憾，例如确实在UCL上课时间不够长、最后在伦敦的日子没有好好珍惜，只不过在和更重要的事情进行权衡以及考量最后所实现的目标后，大致我认为还是满意的。</div><div class="notion-blank notion-block-277002488f2d8054abbce82bbec3790a"> </div><div class="notion-text notion-block-277002488f2d80c49e9aeab424a70596">按照惯例，还是先对每个月发生的大事纪做一个梳理吧。（想跳过的朋友可以一键收起）</div><details class="notion-toggle notion-block-277002488f2d807ca613e56e9180c8d8"><summary><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-277002488f2d807ca613e56e9180c8d8" data-id="277002488f2d807ca613e56e9180c8d8"><span><div id="277002488f2d807ca613e56e9180c8d8" class="notion-header-anchor"></div><span class="notion-h-title">月度梳理</span></span></h2></summary><div><h3 class="notion-h notion-h2 notion-block-16d002488f2d805ca471f280430269b1" data-id="16d002488f2d805ca471f280430269b1"><span><div id="16d002488f2d805ca471f280430269b1" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16d002488f2d805ca471f280430269b1" title="一月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">一月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16d002488f2d80f3a3e4e55e363b0a23" style="list-style-type:decimal"><li>重访了佛罗伦萨、威尼斯和巴塞罗那，并且终于自驾开进了心心念念的意大利多洛米蒂山区，看到了日照金山和夜晚银河并且滑了雪。然而这次租车也是我唯一一次把车擦伤，并且收到了停车未缴费的罚单，但所幸提前买好了保险。</li></ol><div class="notion-row notion-block-16d002488f2d80988576c1f9f406f4c9"><div class="notion-column notion-block-16d002488f2d8003bf1cfd852ff74c22" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d809fad20fcf4a377835f"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F9c791d38-6156-4d90-b1d4-cd464848b3fa%2FA6237C65-E736-42BF-BB37-C6357CB185AC_1_105_c.jpeg?table=block&amp;id=16d00248-8f2d-809f-ad20-fcf4a377835f&amp;t=16d00248-8f2d-809f-ad20-fcf4a377835f&amp;width=288&amp;cache=v2" alt="多洛米蒂的夜空" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">多洛米蒂的夜空</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16d002488f2d8011ac4dc62e41ee42b8" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d8085b631c86c9c2cd980"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F5527b400-4bc0-415b-8892-f0042c450e63%2F732A55E6-4A26-44C6-A969-B057D7E52B34_1_105_c.jpeg?table=block&amp;id=16d00248-8f2d-8085-b631-c86c9c2cd980&amp;t=16d00248-8f2d-8085-b631-c86c9c2cd980&amp;width=336&amp;cache=v2" alt="巴塞罗那的晚霞" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">巴塞罗那的晚霞</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="2" class="notion-list notion-list-numbered notion-block-16d002488f2d80cc9875c6076b00054b" style="list-style-type:decimal"><li>在伦敦观看了周杰伦的演唱会（感谢npy请我看）</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16d002488f2d8093b0bec09124339839" style="list-style-type:decimal"><li>特种兵旅游了德国科隆和柏林，第一次纯背包旅行，第一次尝试过夜大巴和胶囊旅店</li><ol class="notion-list notion-list-numbered notion-block-16d002488f2d8093b0bec09124339839" style="list-style-type:lower-alpha"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d80b28c1ee05277e3c2e0"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:480px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fe3c02abc-296a-4568-ae64-0fe29c5b23e8%2F3F013E52-5847-4CEF-AC4D-D9339DC9B092_1_105_c.jpeg?table=block&amp;id=16d00248-8f2d-80b2-8c1e-e05277e3c2e0&amp;t=16d00248-8f2d-80b2-8c1e-e05277e3c2e0&amp;width=480&amp;cache=v2" alt="刚从科隆坐了7、8个小时的大巴到达柏林，在车站看到的朝阳" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">刚从科隆坐了7、8个小时的大巴到达柏林，在车站看到的朝阳</figcaption></div></figure></ol></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16d002488f2d80bd956cd093c418f078" style="list-style-type:decimal"><li>来到埃及，看到了金字塔、人面狮身像，并且体验了红海潜水</li></ol><div class="notion-row notion-block-16d002488f2d80acace3e533a52be4ae"><div class="notion-column notion-block-16d002488f2d801e8218f2d1da80ced2" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d80eb9d4fcb0dfaed6510"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F561d7b8b-b972-4819-904d-9c8575012949%2FB119A11D-5F2F-4554-8CDE-DE276E696A65_1_201_a.jpeg?table=block&amp;id=16d00248-8f2d-80eb-9d4f-cb0dfaed6510&amp;t=16d00248-8f2d-80eb-9d4f-cb0dfaed6510&amp;width=336&amp;cache=v2" alt="红海海底的鱼群" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">红海海底的鱼群</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16d002488f2d8069b88dd3dc1948a544" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d8009b792dc82a4982044"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fdc9472ca-039b-42e3-b3e8-17f44dfb0106%2FC4269609-B933-4848-A326-13F4E1F0B1C3_1_105_c.jpeg?table=block&amp;id=16d00248-8f2d-8009-b792-dc82a4982044&amp;t=16d00248-8f2d-8009-b792-dc82a4982044&amp;width=336&amp;cache=v2" alt="远看金字塔" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">远看金字塔</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="5" class="notion-list notion-list-numbered notion-block-16d002488f2d81bea5edc3e19d25dbd8" style="list-style-type:decimal"><li>小结：由于有部份圣诞假期以及第一学期的考试不放在第二学期开始，因此这个月有更多的时间去探索世界</li></ol><div class="notion-blank notion-block-16d002488f2d80128cfdc815aeba8fca"> </div><h3 class="notion-h notion-h2 notion-block-16d002488f2d80db8e26dadc34e1e3f4" data-id="16d002488f2d80db8e26dadc34e1e3f4"><span><div id="16d002488f2d80db8e26dadc34e1e3f4" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16d002488f2d80db8e26dadc34e1e3f4" title="二月（春节）："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">二月（春节）：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16d002488f2d80388be4fd3b692d01a7" style="list-style-type:decimal"><li>第一次和家人一起在国外旅游，在老爸全程驾车的环境下，与爸爸妈妈和弟弟一起游历了法国、瑞士和意大利。参见<span class="notion-link-mention"><a href="https://fantasy-ren.tech/article/travel_fr_sw_it" target="_blank" rel="noopener noreferrer" class="notion-link-mention-link"><img class="notion-link-mention-icon" src="https://avatars.githubusercontent.com/u/77408244?s=400&amp;u=0ca3d10c0c09fadcc266416c876ebca5d5eb2afa&amp;v=4" alt="一家人的春节法意瑞自驾游 | 爱幻想的Ren"/><span class="notion-link-mention-provider">一家人的春节法意瑞自驾游 | 爱幻想的Ren</span><span class="notion-link-mention-title">一家人的春节法意瑞自驾游 | 爱幻想的Ren</span></a><div class="notion-link-mention-preview"><article class="notion-link-mention-card"><img class="notion-link-mention-preview-thumbnail" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F394431e4-a36e-4025-b638-5791ba40614f%2F1AE61F35-D530-48EB-91F5-7AFDED51CBF0_1_105_c.jpeg?table=block&amp;id=b9f6c5bc-d4e9-4dc1-b3f2-d400ae969c6f&amp;t=b9f6c5bc-d4e9-4dc1-b3f2-d400ae969c6f&amp;width=800&amp;cache=v2" alt="一家人的春节法意瑞自驾游 | 爱幻想的Ren" referrerPolicy="same-origin"/><div class="notion-link-mention-preview-content"><p class="notion-link-mention-preview-title">一家人的春节法意瑞自驾游 | 爱幻想的Ren</p><p class="notion-link-mention-preview-description">谨以此来记录2024年春节假期和家人在法意瑞的自驾之旅</p><div class="notion-link-mention-preview-footer"><img class="notion-link-mention-preview-icon" src="https://avatars.githubusercontent.com/u/77408244?s=400&amp;u=0ca3d10c0c09fadcc266416c876ebca5d5eb2afa&amp;v=4" alt="一家人的春节法意瑞自驾游 | 爱幻想的Ren" referrerPolicy="same-origin"/><span class="notion-link-mention-preview-provider">一家人的春节法意瑞自驾游 | 爱幻想的Ren</span></div></div></article></div></span></li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16d002488f2d8048982fc0fe6c4a94e3" style="list-style-type:decimal"><li>下半个月紧锣密鼓的组织学习计划，在自己整个MSc项目中最想选的课程Algorithmic Trading和Advanced ML in Finance中钻研</li></ol><div class="notion-row notion-block-16d002488f2d80aa8df4cb736a7976b0"><div class="notion-column notion-block-16d002488f2d80dd9be1f0d95afd52e6" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.375)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d80209188f803ac447c63"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:1182px"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Ff5252c3f-9330-4f06-97b9-c876af92f1d9%2F1427A66C-0F9F-4A80-8A2D-117430CAA6F7_1_105_c.jpeg?table=block&amp;id=16d00248-8f2d-8020-9188-f803ac447c63&amp;t=16d00248-8f2d-8020-9188-f803ac447c63&amp;width=288&amp;cache=v2" alt="正在做金融数据时序分析的coursework，最后拿了高分" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">正在做金融数据时序分析的coursework，最后拿了高分</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16d002488f2d809e8b09ec5af04f8f71" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.625)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16d002488f2d80e28224ed44cf579d18"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F7bec5391-468d-4583-b6c9-c61e3fb05172%2Fimage.png?table=block&amp;id=16d00248-8f2d-80e2-8224-ed44cf579d18&amp;t=16d00248-8f2d-80e2-8224-ed44cf579d18&amp;width=432&amp;cache=v2" alt="成功说服意向导师监督我的summer project！" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">成功说服意向导师监督我的summer project！</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="3" class="notion-list notion-list-numbered notion-block-16d002488f2d805b9a8bd90d9a6f381f" style="list-style-type:decimal"><li>为Summer Project做准备，确定了以Research为导向，寻找合适的导师并且沟通申请他当我的supervisor。在经过几次沟通后，成功说服意向导师。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16d002488f2d8019a3b6c72314e9984b" style="list-style-type:decimal"><li>开始了美股的致富（韭菜）之旅。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16d002488f2d8182ad7bfa176a1d3eeb" style="list-style-type:decimal"><li>小结：在和家人旅行过后，本月开始将重心放在学业上，并且取得了一定进展。</li></ol><div class="notion-blank notion-block-16d002488f2d809e8a33f11f2974aaf6"> </div><h3 class="notion-h notion-h2 notion-block-16d002488f2d8087b452c6c123d52849" data-id="16d002488f2d8087b452c6c123d52849"><span><div id="16d002488f2d8087b452c6c123d52849" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16d002488f2d8087b452c6c123d52849" title="三月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">三月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16d002488f2d801a8b88d5793c744195" style="list-style-type:decimal"><li>高中百年校庆，受班主任邀请录制祝福视频</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d8050a34ff561a898cd64" style="list-style-type:decimal"><li>继续上课，并且开始准备暑期实习申请，尝试了很多行业</li></ol><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80c18c09ca14fb13f24b"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:240px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A6163f348-f4bb-4087-a6cc-5624ccae5698%3Aimage.png?table=block&amp;id=27700248-8f2d-80c1-8c09-ca14fb13f24b&amp;t=27700248-8f2d-80c1-8c09-ca14fb13f24b" alt="第一次来到汕头" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">第一次来到汕头</figcaption></div></figure><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d80a5b1ecdafa6c1516bc" style="list-style-type:decimal"><li>放复活节假，准备回国一个月。回广州当天又赶从广州东到汕头的高铁找npy过生日，然后回郑州。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80babe29da4a9bdd2633" style="list-style-type:decimal"><li>小结：这个月大部分时间还是在上课和做coursework，同时也开始为暑期实习做准备，到处投递简历并且面试。同时这个月也迎来了23岁生日。</li></ol><div class="notion-blank notion-block-16e002488f2d80ef8a1ec5b0946d44bc"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d808da01fff673ca12a95" data-id="16e002488f2d808da01fff673ca12a95"><span><div id="16e002488f2d808da01fff673ca12a95" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d808da01fff673ca12a95" title="四月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">四月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16e002488f2d8062b938d2ada9ec1181" style="list-style-type:decimal"><li>清明节回南阳老家给爷爷奶奶上坟。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d804384b4f06691315351" style="list-style-type:decimal"><li>去北京参加上交所笔试，见了很久没见的高中室友。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d802295e3f8856a371419" style="list-style-type:decimal"><li>线上参加了第一次群面，体验感极好并且发挥出色。</li></ol><div class="notion-row notion-block-16e002488f2d80178414cd65dc86a1ee"><div class="notion-column notion-block-16e002488f2d8068aa9cd708240eb0dc" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80cf8b84ff572b9679a8"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:336px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F5cef95eb-b54c-4883-8994-34c038d47925%2F85C92786-EF06-4A00-8813-808C490FA761_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-80cf-8b84-ff572b9679a8&amp;t=16e00248-8f2d-80cf-8b84-ff572b9679a8&amp;width=336&amp;cache=v2" alt="调皮的拉夫拆院子" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">调皮的拉夫拆院子</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d80abab26eb22dcbe85cc" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80ef9869d2bf6cafeee4"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F6784db1f-c44d-4c53-82ae-7259e82797e0%2F5660F4A5-82D9-4D33-B328-14B1DAA84B62_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-80ef-9869-d2bf6cafeee4&amp;t=16e00248-8f2d-80ef-9869-d2bf6cafeee4&amp;width=336&amp;cache=v2" alt="每次来广州都喜欢坐在这个位置看夜景" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">每次来广州都喜欢坐在这个位置看夜景</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d80b3a6a9fb044531056f" style="list-style-type:decimal"><li>和npy去福州、泉州还有厦门旅游，也是第一次来福建旅游。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80eba833cfb97ccd355d" style="list-style-type:decimal"><li>第一次一个人体验坐卧铺火车从郑州到广州，和老爸一起参加广交会，不过这次更多的是以观察者的身份来参观学习，实际没有帮上什么忙。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d807e8206ed9c18567b4f" style="list-style-type:decimal"><li>同一天上午在深圳参加一场面试，下午在广州参加一场面试，非常奔波，期间也顺带去了华强北参观。</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d8062b65ee5ae27e2c5bb" style="list-style-type:decimal"><li>小结：这个月回国内做了一些以前很难接触到的事情，也开始和国内找工作环境接轨，同时也开始参加了一些父母的工作。</li></ol><div class="notion-blank notion-block-16e002488f2d80b78376dc18d1a9d9a5"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d8014b3e9e7286c57854b" data-id="16e002488f2d8014b3e9e7286c57854b"><span><div id="16e002488f2d8014b3e9e7286c57854b" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d8014b3e9e7286c57854b" title="五月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">五月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16e002488f2d80b18b7acffd1ec9f483" style="list-style-type:decimal"><li>1号返回伦敦，开始准备学期末考试，但是感觉三阳了，复习时很难专注，遂开始在伦敦的公寓附近闲逛，意外找到几个公共篮球场。同时因为没有时间做饭，这段时间经常做一锅炒饭然后吃四顿。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d805eba89c6fba91ea062" style="list-style-type:decimal"><li>在ExCel参加学生时代最后一场考试。</li></ol><div class="notion-row notion-block-16e002488f2d8092b8b9e11a7547fc68"><div class="notion-column notion-block-16e002488f2d80a28bb8ef2fd9738ad3" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d801497b7de7449b7b320"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F00d1eca4-1903-495b-9f21-32e339b9037b%2F3E2C4623-4C4C-4239-9E39-1FB114CC42A8_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-8014-97b7-de7449b7b320&amp;t=16e00248-8f2d-8014-97b7-de7449b7b320&amp;width=690&amp;cache=v2" alt="UCL的超大考场" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">UCL的超大考场</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d8068afcfc1f1e7b7938a"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F610c9408-722f-4f1d-a9d7-501a03e794ba%2F4CB04028-3428-4836-B97B-E20B85400B7A_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-8068-afcf-c1f1e7b7938a&amp;t=16e00248-8f2d-8068-afcf-c1f1e7b7938a&amp;width=316&amp;cache=v2" alt="和朋友晴天伦敦City Walk" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">和朋友晴天伦敦City Walk</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d80dc8451f1b1e0ca701f" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d801086efca35a7d34e56"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fd692f5cc-b907-497b-a562-96a654903e89%2F545F2026-F34A-43FC-84A2-9350F68172B4_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-8010-86ef-ca35a7d34e56&amp;t=16e00248-8f2d-8010-86ef-ca35a7d34e56&amp;width=315.9921875&amp;cache=v2" alt="和朋友在晴天打球" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">和朋友在晴天打球</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d8005a9e3e83ee252b035" style="list-style-type:decimal"><li>参加UCL的MSc项目酒会，并且参加Summer Project的启动会，与导师开始线下沟通细节</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80beb024e807a24e4c2a" style="list-style-type:decimal"><li>参观维多利亚和阿尔伯特博物馆，周末去Folkestone小镇挖化石</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d804a872ddaee9bca4dab" style="list-style-type:decimal"><li>拿到深圳某家头部大公募基金的暑期实习offer，岗位是人工智能实验室，听起来非常有趣！同时也收到了杭州一个金融科技中厂的offer，但由于面试体验不够好且压力更大，最终选择了深圳的公募。</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d8076b40df56e35e65c77" style="list-style-type:decimal"><li>终于开通了个人网站，并发出了第一篇个人技术博客，实现了本科期间就一直有的规划。</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-16e002488f2d805e8fa4fe14aa27e367" style="list-style-type:decimal"><li>小结：本月部分性的结束了学生时代，并且花了更多时间享受了和朋友们在伦敦的生活。伦敦作为从小我的梦中之城，这种状态是稀缺可贵的。此外这个月也幸运的收到了实习offer，为了能提高个人竞争力且提早感受金融行业工作氛围，这个月做了决定在六月底回国实习（虽然五月才刚回伦敦）。</li></ol><div class="notion-blank notion-block-16e002488f2d80a1a599cebf71915f80"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d809ab03df70cbdc09fa7" data-id="16e002488f2d809ab03df70cbdc09fa7"><span><div id="16e002488f2d809ab03df70cbdc09fa7" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d809ab03df70cbdc09fa7" title="六月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">六月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16e002488f2d80fc8d7eee5ff8d0a685" style="list-style-type:decimal"><li>女朋友又来到伦敦找我，一起感受伦敦的夏天，去了伦敦周边的动物园</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80c09a5aecd0c3015007" style="list-style-type:decimal"><li>在去冰岛的路途前，先经过了瑞典的哥德堡和斯德哥尔摩</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d806dbf26f6e677524a56" style="list-style-type:decimal"><li>在冰岛开启了为期一周的露营车环岛旅行</li></ol><div class="notion-row notion-block-16e002488f2d80e09f89fd83a76c2d85"><div class="notion-column notion-block-16e002488f2d80129b6be3c92c397c64" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d8081ae69e3e6de1e4f77"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fac22abbd-4da5-4110-8bd0-93e051a59f53%2FD2E10C31-8729-43E1-A97D-0A49B81F92D5_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-8081-ae69-e3e6de1e4f77&amp;t=16e00248-8f2d-8081-ae69-e3e6de1e4f77&amp;width=678&amp;cache=v2" alt="第一次在车里过夜，此时车停在露营区，并且正值极昼" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">第一次在车里过夜，此时车停在露营区，并且正值极昼</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d80f3bca5ff575ecfcca3" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d807b9ba2d07138eb3280"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F7e3cb10a-e008-4a7b-a561-c9e014b4db73%2F08CCB531-3DCF-439F-A4F7-AB36FCEE22F8_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-807b-9ba2-d07138eb3280&amp;t=16e00248-8f2d-807b-9ba2-d07138eb3280&amp;width=316&amp;cache=v2" alt="遇到好看的风景就停下，然后躺在车里打开车门看" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">遇到好看的风景就停下，然后躺在车里打开车门看</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d807a90a2ce64e35837fe" style="list-style-type:decimal"><li>在冰岛期间定了Summer Project的主题</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d802bad60f09466aa230d" style="list-style-type:decimal"><li>看了传说中的Magic Mike秀</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d803fbc54dfd6c2d41221" style="list-style-type:decimal"><li>旅行结束后，开始回到深圳实习，在这期间也和来香港读研的本科同学重逢</li></ol><div class="notion-row notion-block-16e002488f2d80d8aeb7d41c566d3256"><div class="notion-column notion-block-16e002488f2d80c6982cff6d6f384bc5" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.375)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80bf9c3bfd04fceb9d8d"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:240px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F037ca08c-f43a-47de-917f-05f046f7f981%2F5D102808-E787-4476-BD98-918CEC082703_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-80bf-9c3b-fd04fceb9d8d&amp;t=16e00248-8f2d-80bf-9c3b-fd04fceb9d8d&amp;width=240&amp;cache=v2" alt="实习的基金大厦" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">实习的基金大厦</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d80e8bf35ec63e74650c3" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.625)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d803fa7bdc29bf57eecb0"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:336px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fce9ea1e6-6990-48b8-a349-cef83773d815%2F79082C1A-BDE6-462C-BE4C-270F2C1ACBE0_1_102_o.jpeg?table=block&amp;id=16e00248-8f2d-803f-a7bd-c29bf57eecb0&amp;t=16e00248-8f2d-803f-a7bd-c29bf57eecb0&amp;width=336&amp;cache=v2" alt="南山区天际线" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">南山区天际线</figcaption></div></figure><div class="notion-blank notion-block-16e002488f2d8096acf8e0ca186cc119"> </div></div><div class="notion-spacer"></div></div><ol start="6" class="notion-list notion-list-numbered notion-block-16e002488f2d80d6b4fddb2540fbe3a6" style="list-style-type:decimal"><li>与UCL的supervisor每周线上开会，汇报结果</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d806d81d9dcf0aae1f695" style="list-style-type:decimal"><li>小结：这个月完成了一个人生目标，并且开启了国内工作的第一幕，并且学术研究也开始有了目标。</li></ol><div class="notion-blank notion-block-16e002488f2d8057ae34c1cb9ba99282"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d8088a075fc65cf34683f" data-id="16e002488f2d8088a075fc65cf34683f"><span><div id="16e002488f2d8088a075fc65cf34683f" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d8088a075fc65cf34683f" title="七月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">七月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16e002488f2d806ab525fe39ed4cb72c" style="list-style-type:decimal"><li>继续实习工作，继续完成暑期学术研究项目。实习工作稳定推进，但学术研究遇到过瓶颈，但最终解决了。</li></ol><div class="notion-row notion-block-16e002488f2d80789c4ad67ffebe757f"><div class="notion-column notion-block-16e002488f2d80fa8e17cb80ade96876" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80498e73cdbbe1e545e2"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F5b7ab4d4-048a-4271-9779-19bf921420c6%2FE3647EAC-C60F-4DC2-B426-B849A45F0206_1_102_o.jpeg?table=block&amp;id=16e00248-8f2d-8049-8e73-cdbbe1e545e2&amp;t=16e00248-8f2d-8049-8e73-cdbbe1e545e2&amp;width=678&amp;cache=v2" alt="在公司加班到21点" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">在公司加班到21点</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d801ba1bdf458a9b64bc6" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80ec8ec9f9c856416d39"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F50c655f2-21bc-4311-b35d-518d2c59da6e%2FBB350D29-9767-42DB-A5D4-563068195743_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-80ec-8ec9-f9c856416d39&amp;t=16e00248-8f2d-80ec-8ec9-f9c856416d39&amp;width=315.9921875&amp;cache=v2" alt="找了家24h自习室继续学校研究" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">找了家24h自习室继续学校研究</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80039175df6950339fd2" style="list-style-type:decimal"><li>开启澳洲PhD的申请计划，并且进行了多位导师的套瓷和面试，较为明确了未来的方向。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80f1b40bc1990130c5b0" style="list-style-type:decimal"><li>拥有第一篇放在arXiv的论文，来自我本科的毕业论文。</li><ol class="notion-list notion-list-numbered notion-block-16e002488f2d80f1b40bc1990130c5b0" style="list-style-type:lower-alpha"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d8005b66ff441ad424bb7"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fa1488181-97f4-43fe-be26-a12d71061019%2F4A882CA3-4198-4817-AA07-FF281AA7F02D_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-8005-b66f-f441ad424bb7&amp;t=16e00248-8f2d-8005-b66f-f441ad424bb7&amp;width=649.984375&amp;cache=v2" alt="终于放在arXiv的论文，可算是占坑了" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">终于放在arXiv的论文，可算是占坑了</figcaption></div></figure></ol></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d804b8f09d2c7d45e07e4" style="list-style-type:decimal"><li>小结：本月是今年第一个整月没有在天上飞翔的月份，可见重心都在工作和科研上了。同时之前的科研结果也有了好的消息。最重要的是，确立了申请PhD的规划，也确立了去澳洲读博的心愿。</li></ol><div class="notion-blank notion-block-16e002488f2d80e69de0d6a4687e2db0"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d80a7811bf2b228da43bf" data-id="16e002488f2d80a7811bf2b228da43bf"><span><div id="16e002488f2d80a7811bf2b228da43bf" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d80a7811bf2b228da43bf" title="八月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">八月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16e002488f2d80ab9d00f2437f535154" style="list-style-type:decimal"><li>和npy在周末的凌晨熬夜去了深圳湾看日出。</li></ol><div class="notion-row notion-block-16e002488f2d8015b7d6caeffee7e050"><div class="notion-column notion-block-16e002488f2d8066beebf70232c6558d" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d805a93e3dce3eab39fef"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fd7fa10b5-982b-4136-9671-196e6db8a23d%2F1E1EC830-F90C-4182-B861-596E7693F836_1_102_o.jpeg?table=block&amp;id=16e00248-8f2d-805a-93e3-dce3eab39fef&amp;t=16e00248-8f2d-805a-93e3-dce3eab39fef&amp;width=649.984375&amp;cache=v2" alt="深圳湾日出剧院" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">深圳湾日出剧院</figcaption></div></figure><div class="notion-blank notion-block-277002488f2d807e8567dcf20c866018"> </div></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d8078ada8c83328c5ae58" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d804597b6c31e22fd3dff"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F2fc8699f-01bf-48f4-bb1e-144e07ccd2d1%2FD502FCDE-0C91-490A-B62C-C7A7D9BCC7F1_1_102_o.jpeg?table=block&amp;id=16e00248-8f2d-8045-97b6-c31e22fd3dff&amp;t=16e00248-8f2d-8045-97b6-c31e22fd3dff&amp;width=318&amp;cache=v2" alt="维多利亚港湾" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">维多利亚港湾</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80889c66d604de1d9a74" style="list-style-type:decimal"><li>之前申请的香港高才计划通过，终于这个月去香港办理身份证，顺便也用了自己的工资给妈妈买了礼物，一条罗意威的围巾🧣。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80439c02e1b9d7575839" style="list-style-type:decimal"><li>两个月的深圳实习结束，家里人一起来深圳短暂玩耍了几天，但我感觉四阳了状态很差，然后一起回郑州。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d8080bb22d55041dfe5de" style="list-style-type:decimal"><li>又回伦敦了，但这可能是最后一次学生身份飞英国了，也是第一次选择从郑州直飞伦敦。</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-16e002488f2d80d8906fdd68bd10e0fc" style="list-style-type:decimal"><li><b>天塌了</b>，回深圳前不小心把伦敦公寓的冰箱的电断了，里面变得非常可怕。忍痛连夜从小红书找了保洁阿姨帮忙打扫。</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-16e002488f2d808694cadaa1a247ca25" style="list-style-type:decimal"><li>在毕业论文的截止日期前疯狂肝论文，中间也和英国多年的老朋友们见面聚餐</li></ol><div class="notion-row notion-block-16e002488f2d805182ccd62761506934"><div class="notion-column notion-block-16e002488f2d80feb1aec11b1c95e1ea" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d80d99b70c5423be3d444"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fa10ccbac-8ef6-4e53-ba07-b7bd32b17500%2F1E0F407B-DD6B-443D-8D4E-84AA40DDB3B9_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-80d9-9b70-c5423be3d444&amp;t=16e00248-8f2d-80d9-9b70-c5423be3d444&amp;width=336&amp;cache=v2" alt="和朋友办了大英图书馆会员卡" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">和朋友办了大英图书馆会员卡</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-16e002488f2d80c99d52e1446bf8288b" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-16e002488f2d802e84b8c67d08707478"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Ff6cb4b6e-e8cc-42b5-8435-c3385c3bab85%2F7E7C0234-F668-479A-B127-89CB835AD6FC_1_105_c.jpeg?table=block&amp;id=16e00248-8f2d-802e-84b8-c67d08707478&amp;t=16e00248-8f2d-802e-84b8-c67d08707478&amp;width=276.4921875&amp;cache=v2" alt="Kings Cross车站上的夕阳" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">Kings Cross车站上的夕阳</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="7" class="notion-list notion-list-numbered notion-block-16e002488f2d802eb4aada0d5e68c9f8" style="list-style-type:decimal"><li>小结：本月的人生规划又推进一步，成果完成了一段很有Reputation的实习并且在科研上也有了突破，并且拿到了澳洲PhD一个导师口头意向的offer。此外，这个月也决定了今年一个最伟大的计划：从英国陆路回国！</li></ol><div class="notion-blank notion-block-16e002488f2d80b8aecce85138d65f85"> </div><h3 class="notion-h notion-h2 notion-block-16e002488f2d8014be19f21e0b7ea503" data-id="16e002488f2d8014be19f21e0b7ea503"><span><div id="16e002488f2d8014be19f21e0b7ea503" class="notion-header-anchor"></div><a class="notion-hash-link" href="#16e002488f2d8014be19f21e0b7ea503" title="九月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">九月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-16d002488f2d81ac9ea0e183006ac419" style="list-style-type:decimal"><li>交完毕业论文后，朋友们也依次毕业回国了。参加了帝国理工朋友的Poster Session，和预科本科硕士认识的每个人告别，并且把他们送到机场。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-16e002488f2d80dda2a2c98a6de30600" style="list-style-type:decimal"><li>花了一天时间用大疆Action4和小白去录制一些伦敦素材，希望以后能制作视频。</li></ol><div class="notion-row notion-block-277002488f2d804b8f84c20c33221699"><div class="notion-column notion-block-277002488f2d80dfaa91d9b9c1752d6b" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.49999999999999994)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80edb25cf1fd32b1062e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:240px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A2d9aaaf5-bdd7-4a4f-bcaf-e7af16967319%3A83CC238B-695E-4CD6-A1FA-D1EA8E45B254_1_102_o.jpeg?table=block&amp;id=27700248-8f2d-80ed-b25c-f1fd32b1062e&amp;t=27700248-8f2d-80ed-b25c-f1fd32b1062e" alt="拍摄London街头ing" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">拍摄London街头ing</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d804c9226dbaccf5c6cee" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.49999999999999994)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80a7aea1de97652cc543"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:240px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A6091e720-711f-4e0f-8b1d-1208795b1bbd%3A0C0B603E-379C-40BC-A1A5-A1B25FC5BFE7_1_102_o.jpeg?table=block&amp;id=27700248-8f2d-80a7-aea1-de97652cc543&amp;t=27700248-8f2d-80a7-aea1-de97652cc543" alt="巴特西电厂下悠哉听歌" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">巴特西电厂下悠哉听歌</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="3" class="notion-list notion-list-numbered notion-block-16e002488f2d80e0a3fcf53a4a539d9d" style="list-style-type:decimal"><li>又一次和好友回到曼彻斯特，观看Man City【曼城】和Inter Milan【国米】的欧冠比赛。比分是无聊的0:0，但是有趣的是和朋友偷偷溜进了曼大的AGLC，在里面找位置睡了一晚上（比赛日的酒店贵的离谱）。</li></ol><div class="notion-row notion-block-277002488f2d808895b8e4accfc98318"><div class="notion-column notion-block-277002488f2d8007aebae54871afcdd6" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.3333333333333333)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80d4b3f3fb7a7cc1d3f5"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:196.6536407470703px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A8e8eac37-93c3-4043-a08c-540e740779c7%3A769D33B0-689C-4ABD-8DAA-BE5E4D022DED_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-80d4-b3f3-fb7a7cc1d3f5&amp;t=27700248-8f2d-80d4-b3f3-fb7a7cc1d3f5" alt="最后一次到伊蒂哈德球场" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">最后一次到伊蒂哈德球场</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d800788fcfbb16ac73746"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A3ae61efb-44a6-43f9-9f7e-d779befd010e%3A119D2B5E-B98C-409B-B1C6-DCA5CDAECB75_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-8007-88fc-fbb16ac73746&amp;t=27700248-8f2d-8007-88fc-fbb16ac73746" alt="可能是最后一次看曼大了" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">可能是最后一次看曼大了</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d805c8d59f1703d68a3da" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.2916666666666667)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8065b418f435fd2f3a11"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:288px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Ac0fcf63e-0302-4f16-ad21-9fba1e7bb4c0%3A44D591E0-ADD3-4748-BEC0-F42E8BF69043_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-8065-b418-f435fd2f3a11&amp;t=27700248-8f2d-8065-b418-f435fd2f3a11" alt="2019vs2024，沧桑了。" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">2019vs2024，沧桑了。</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d804fbb96e48f43223f1a"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:480px"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A95b7d8ec-8073-4e39-8e42-f3610d6c83e7%3A79A3338D-27BF-4AA6-9540-278FE125BBB7_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-804f-bb96-e48f43223f1a&amp;t=27700248-8f2d-804f-bb96-e48f43223f1a" alt="凌晨去赶火车回伦敦" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">凌晨去赶火车回伦敦</figcaption></div></figure><div class="notion-blank notion-block-277002488f2d8003b7b5eb72a39fdef6"> </div></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d8042baccc60dda5debfc" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.375)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8085890dc6359ee3b46c"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:192px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A4dda90e0-d78e-44d7-8fe7-78add609ba82%3ADEDAD771-6845-4FBF-A13A-BB62A62581C2_1_102_a.jpeg?table=block&amp;id=27700248-8f2d-8085-890d-c6359ee3b46c&amp;t=27700248-8f2d-8085-890d-c6359ee3b46c" alt="又是毕业季，曼大经典红爬山虎" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">又是毕业季，曼大经典红爬山虎</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80a282daf071d4722368"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:192px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A750767f2-cef1-4788-abf1-b16ee47ce14e%3AE9BB06BB-AD5E-410E-BF7F-BF0303D5BFA8_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-80a2-82da-f071d4722368&amp;t=27700248-8f2d-80a2-82da-f071d4722368" alt="感谢AGLC收留我们，3年学费没白交，毕业了还用得上" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">感谢AGLC收留我们，3年学费没白交，毕业了还用得上</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d80538feefa88d1eeca4a" style="list-style-type:decimal"><li>9.20日晚，送走最后一个朋友，我也连夜把伦敦的公寓清空了，该寄的行李都寄走了，只留了一个淘宝100多买的盗版耐克背包。9.21凌晨，到家附近的St.Pancras车站乘坐欧洲之星，告别英国，出发回国！</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d8064899ff876a81592a1" style="list-style-type:decimal"><li>第一站荷兰，顺路拜访了在埃因霍温读书的初中关系最好的同学，一起在阿姆斯特丹的船屋过夜，也看了红灯区最劲爆的show。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8067926dc1965730e394" style="list-style-type:decimal"><li>使用长途大巴和火车，陆续经过了捷克🇨🇿布拉格，奥地利🇦🇹维也纳，匈牙利🇭🇺布达佩斯，塞尔维亚🇷🇸贝尔格莱德，于9月最后一天经过7小时大巴到达保加利亚🇧🇬首都索非亚。</li></ol><div class="notion-row notion-block-277002488f2d80ad8cc2de671135007d"><div class="notion-column notion-block-277002488f2d80fca097ca0270cc021c" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.3333333333333333)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d803e843feb07c69a37ac"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Aad132e4b-246e-48de-a651-248100457221%3ACE6E304D-660C-4AE3-98FA-C70FD6EF3EA7_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-803e-843f-eb07c69a37ac&amp;t=27700248-8f2d-803e-843f-eb07c69a37ac" alt="2016年第一次到希思罗机场的Welcome" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">2016年第一次到希思罗机场的Welcome</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d803085dbd399515be0e7"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:205.9765625px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Adecf7cc5-c64b-49be-bf65-bb25eed9c95d%3A2224086B-6455-4762-BCA5-B98CD6370068_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8030-85db-d399515be0e7&amp;t=27700248-8f2d-8030-85db-d399515be0e7" alt="第一次住青旅，来自布拉格" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">第一次住青旅，来自布拉格</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80bb8364d23dc5628a4b"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A05a6080c-4890-47e9-8b76-9be307189ee4%3A33857C69-5A93-4868-BC0F-7B0C58B803AA_1_201_a.heic?table=block&amp;id=27700248-8f2d-80bb-8364-d23dc5628a4b&amp;t=27700248-8f2d-80bb-8364-d23dc5628a4b" alt="经典布达佩斯国会大厦日落版" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">经典布达佩斯国会大厦日落版</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80a0a42ef8b8ee0dd772"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A19a221b5-1d7d-4679-ae21-821eb0343098%3AB3AA9E80-423F-472C-91A8-9E46BD0EA9C3_1_201_a.heic?table=block&amp;id=27700248-8f2d-80a0-a42e-f8b8ee0dd772&amp;t=27700248-8f2d-80a0-a42e-f8b8ee0dd772" alt="冰封纪念碑，从小到大都被这座建筑所震撼，这次专程租车来到这里膜拜，也是本次陆路回国最期待的一项" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">冰封纪念碑，从小到大都被这座建筑所震撼，这次专程租车来到这里膜拜，也是本次陆路回国最期待的一项</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d80ae878fd0ab15b3ccca" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.2916666666666667)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80b8b778ce8bd15f0c97"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A8ace1653-a116-467f-a6d4-b4b0e721ef2e%3A7CA72684-0C1A-46E4-9EA0-45D69734AF8F_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-80b8-b778-ce8bd15f0c97&amp;t=27700248-8f2d-80b8-b778-ce8bd15f0c97" alt="2024年离开英国的Goodbye" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">2024年离开英国的Goodbye</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80a7adc0e988c53214d5"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A57175f13-3685-4e38-86ce-5d13819ce827%3A6CB23EC0-66EF-4C44-85F8-F7BE09E07A23_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-80a7-adc0-e988c53214d5&amp;t=27700248-8f2d-80a7-adc0-e988c53214d5" alt="报了一个人的tour，骑行布拉格" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">报了一个人的tour，骑行布拉格</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d805c93a7d3149323a92d"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:180.25px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Aa3aace54-7208-4c13-a5a6-4b211336ba37%3A62D82F27-80E4-40B8-8893-07C22B50FB25_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-805c-93a7-d3149323a92d&amp;t=27700248-8f2d-805c-93a7-d3149323a92d" alt="贝尔格莱德打枪去了" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">贝尔格莱德打枪去了</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80a2a76ff02975e96e22"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A297b8af5-b7c6-400c-b900-3cf6acc8f64e%3A67180917-BE83-4BAA-B3F6-FE1B5D321E2C_1_201_a.heic?table=block&amp;id=27700248-8f2d-80a2-a76f-f02975e96e22&amp;t=27700248-8f2d-80a2-a76f-f02975e96e22" alt="纪念南斯拉夫被炸中国大使馆遗址" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">纪念南斯拉夫被炸中国大使馆遗址</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d804ab0b4edf463d2fa6e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Aab2646e5-180a-45e0-9e50-7495aa934f1f%3Aimage.png?table=block&amp;id=27700248-8f2d-804a-b0b4-edf463d2fa6e&amp;t=27700248-8f2d-804a-b0b4-edf463d2fa6e" alt="塞尔维亚和保加利亚的边境检查站" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">塞尔维亚和保加利亚的边境检查站</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d80d1afa1ec38c95d0ad7" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.375)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80ecb878ef3014f5f383"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A4f430566-9fb3-405e-84a8-db51908fb9d9%3A6146A469-BFFC-4CD3-B160-2DE90FA4F802_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-80ec-b878-ef3014f5f383&amp;t=27700248-8f2d-80ec-b878-ef3014f5f383" alt="出发前的最后一张" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">出发前的最后一张</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8018935acc3d188eed7e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:231.7317657470703px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A1b67f3b7-ed97-45c4-b38f-438418b2a1e5%3A34C7F70B-B4CE-4963-83B5-A4753CA9E1D5_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8018-935a-cc3d188eed7e&amp;t=27700248-8f2d-8018-935a-cc3d188eed7e" alt="维也纳的金色殿堂听演奏" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">维也纳的金色殿堂听演奏</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d804b816de058a913b22e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A6158b995-92e3-4864-bd5d-fea1d62e3f42%3A4D4E46F1-4B73-4F92-8453-B14F711E4D09_1_201_a.heic?table=block&amp;id=27700248-8f2d-804b-816d-e058a913b22e&amp;t=27700248-8f2d-804b-816d-e058a913b22e" alt="贝尔格莱德友好地兄弟们" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">贝尔格莱德友好地兄弟们</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d803ba478cdcb0fd55d6c"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Af09ea9d2-bb77-40a5-94c6-70d121581aaa%3A931220F0-CE8B-4AA3-BE12-F5372D5229D6_1_201_a.heic?table=block&amp;id=27700248-8f2d-803b-a478-cdcb0fd55d6c&amp;t=27700248-8f2d-803b-a478-cdcb0fd55d6c" alt="买了索非亚-伊斯坦布尔的火车票" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">买了索非亚-伊斯坦布尔的火车票</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="7" class="notion-list notion-list-numbered notion-block-277002488f2d80059926e35202686698" style="list-style-type:decimal"><li>小结：本月正式告别了伦敦和曼城，踏上了陆路回家之旅。第一次尝试全程一个人旅行横跨这么多国家，感觉是一件非常有意义的事情。</li></ol><div class="notion-blank notion-block-277002488f2d80629d5cca756a9990c7"> </div><h3 class="notion-h notion-h2 notion-block-277002488f2d8092b0b4c41a227b7d00" data-id="277002488f2d8092b0b4c41a227b7d00"><span><div id="277002488f2d8092b0b4c41a227b7d00" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d8092b0b4c41a227b7d00" title="十月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">十月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d8078b939d9bab6ed400e" style="list-style-type:decimal"><li>乘坐了本次陆路回国最期待的一次交通：索非亚开往伊斯坦布尔的横跨欧亚大陆的火车专列！同一个卧铺车厢竟还遇到两个曼大校友，三个大叔一路带着我吃喝玩乐</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d803fbe54f146d0209249" style="list-style-type:decimal"><li>在伊斯坦布尔度过三天后，由于计划改变不能再去亚美尼亚和格鲁吉亚，因此选择直接飞往阿塞拜疆🇦🇿巴库，这个看似封闭但却给我惊喜的国家</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d80e9ae74ff991d8a3a14" style="list-style-type:decimal"><li>放弃了买巴库开往哈萨克斯坦🇰🇿阿克套的渡轮票（不固定船次太难抢），直接坐红眼航班飞过去了。阿克套报名了Mangystau地区一日游，风景非常震撼。</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d808082aff9a87e01a39b" style="list-style-type:decimal"><li>又一次借飞机直接飞往哈萨克斯坦🇰🇿阿拉木图，然后坐大巴经霍尔果斯边境回到中国🇨🇳！</li></ol><div class="notion-row notion-block-277002488f2d8044938afe30665092de"><div class="notion-column notion-block-277002488f2d80acbb68e31e95e9d55d" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.3333333333333333)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d803a9c36cfb1de1fdf54"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Ae11c9d37-4314-4619-8b8c-d6d0e3054b31%3A45BF2F01-8CB9-4CB2-8AED-7A26AB6466A9_1_102_a.jpeg?table=block&amp;id=27700248-8f2d-803a-9c36-cfb1de1fdf54&amp;t=27700248-8f2d-803a-9c36-cfb1de1fdf54" alt="传说中的欧亚铁路" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">传说中的欧亚铁路</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80359488eed6bfb65628"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:205.9921875px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Af6cbc18b-b98d-4f25-9c52-5b96f3daa19e%3A9A1A7746-BECE-49EF-9D14-81C715152E91_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-8035-9488-eed6bfb65628&amp;t=27700248-8f2d-8035-9488-eed6bfb65628" alt="博斯普鲁斯上的游船看日落" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">博斯普鲁斯上的游船看日落</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80eea472cce1a546a6d3"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:205.9921875px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A5a1c5c89-298a-43b7-a2cd-d15bff62c2ba%3A9F0C08BF-BA68-4E71-B3B2-D1F4C621EE77_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-80ee-a472-cce1a546a6d3&amp;t=27700248-8f2d-80ee-a472-cce1a546a6d3" alt="成功回家！霍尔果斯口岸前" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">成功回家！霍尔果斯口岸前</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d809fa679e87e4ad469f0" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.2916666666666667)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d806493efd632ea733cc6"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:180.25px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A12b5e789-c062-468c-a35a-08b64ebbeff1%3ABB91ADFB-9EFF-4703-8A3F-7E29F7FF7CD6_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8064-93ef-d632ea733cc6&amp;t=27700248-8f2d-8064-93ef-d632ea733cc6" alt="和同卧铺的大叔畅玩" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">和同卧铺的大叔畅玩</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d803295b9d70fc51f81e2"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:180.25px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A1d3060c4-daf7-4217-bb66-bd07a76e7953%3AA83765AA-F44E-41D9-BC7F-871BB3D6169C_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8032-95b9-d70fc51f81e2&amp;t=27700248-8f2d-8032-95b9-d70fc51f81e2" alt="巴库的标志性火焰建筑" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">巴库的标志性火焰建筑</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8007b4f9d4789be756f9"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:180.25px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Addfb7318-0c05-49e1-910a-11ca00fef5e9%3AAF7CCB0F-2060-4FDD-9880-C96E4A5463D7_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8007-b4f9-d4789be756f9&amp;t=27700248-8f2d-8007-b4f9-d4789be756f9" alt="阿克套里海的日落" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">阿克套里海的日落</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80aaa394ee70b1f00f1c"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:180.25px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Abe645bf5-9e77-4194-bc92-a33109d6998d%3AD606E6F9-A994-4B9B-BFA0-C081C0D8ADE9_1_105_c.jpeg?table=block&amp;id=27700248-8f2d-80aa-a394-ee70b1f00f1c&amp;t=27700248-8f2d-80aa-a394-ee70b1f00f1c" alt="阿拉木图排队买去中国的大巴票" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">阿拉木图排队买去中国的大巴票</figcaption></div></figure></div><div class="notion-spacer"></div><div class="notion-column notion-block-277002488f2d80c3b57fe98836210268" style="width:calc((100% - (2 * min(32px, 4vw))) * 0.375)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80178d2ce0db3955ac90"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:231.7317657470703px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Adbfbca15-e149-4e94-8ba9-7b176898ec40%3A1F76A479-A973-4006-8072-9C5062E48EB6_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8017-8d2c-e0db3955ac90&amp;t=27700248-8f2d-8017-8d2c-e0db3955ac90" alt="伊斯坦布尔蓝色清真寺" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">伊斯坦布尔蓝色清真寺</figcaption></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8081a76aec5ae2ca1eab"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:231.75px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A31b12e36-7816-497b-87aa-6e9c039486ed%3AF3D4C811-80A9-4533-BEBB-B02380F93CFB_4_5005_c.jpeg?table=block&amp;id=27700248-8f2d-8081-a76a-ec5ae2ca1eab&amp;t=27700248-8f2d-8081-a76a-ec5ae2ca1eab" alt="Mangystau地区几亿年前的海底" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">Mangystau地区几亿年前的海底</figcaption></div></figure></div><div class="notion-spacer"></div></div><ol start="5" class="notion-list notion-list-numbered notion-block-277002488f2d805c873df49b0f094e8a" style="list-style-type:decimal"><li>作为主力和老爸一起参加广交会，第一次感觉到辛苦与不易</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d809bac86cbe3da5d1b5b" style="list-style-type:decimal"><li>去香港去身份证，并且成人后第一次去香港迪士尼，极速光轮项目怒刷5次。人少玩的就是爽。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d805aa78bdfb82e717ff1" style="list-style-type:decimal"><li>暂定了澳洲读博的学校和后续安排，但不想在家呆着gap，因此开始找量化相关的工作准备先做着。在一周内快速面试了几家后决定去上海的一家小初创，发现竟然是crypto领域的量化（这极大影响了我后期的发展方向）</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d80238034f7bbedee9657" style="list-style-type:decimal"><li>开始了彭于晏计划！有计划性的系统性的健身了</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-277002488f2d804fab98fbfb40b64e55" style="list-style-type:decimal"><li>小结：本月略微匆忙的结束了回国之旅，但也是为了能作为主力帮助家里去广交会干活。同时拿到了新的香港身份，也快速开始了上海工作。</li></ol><div class="notion-blank notion-block-277002488f2d80078ce0d63b1d558ffc"> </div><h3 class="notion-h notion-h2 notion-block-277002488f2d80e3b54fee89f467c112" data-id="277002488f2d80e3b54fee89f467c112"><span><div id="277002488f2d80e3b54fee89f467c112" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d80e3b54fee89f467c112" title="十一月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">十一月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d80789165d31dc3f0c9d2" style="list-style-type:decimal"><li>经过一周多的实习试用期后，老板很满意，并且很高兴我能继续留下来工作。至此在加密货币领域我开始了自己的新旅程</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d802eb991f008dd22056a" style="list-style-type:decimal"><li>和本科在上海工作的同学们又聚在了一起，吃饭唱歌</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8041acbbc7dea6c9ce12" style="list-style-type:decimal"><li>彭于晏计划有条不紊的进行着</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d80498ec5cd84e8911b3b" style="list-style-type:decimal"><li>小结：本月忙于工作与事业的发展，果然人一旦工作后，生活的多样性就大大减少了hh。但是宏观上看，这段工作对我起到了非常重要的影响。</li></ol><div class="notion-blank notion-block-277002488f2d80d9bfd3c8204abe527f"> </div><h3 class="notion-h notion-h2 notion-block-277002488f2d8060961edecf542c11cd" data-id="277002488f2d8060961edecf542c11cd"><span><div id="277002488f2d8060961edecf542c11cd" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d8060961edecf542c11cd" title="十二月："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">十二月：</span></span></h3><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d8055b747c01671649109" style="list-style-type:decimal"><li>继续工作，也逐渐融入了公司的氛围</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-278002488f2d808a8905c901126990ad" style="list-style-type:decimal"><li>研究生出成绩了！总成绩过了Distinction，并且毕业论文拿了全系最高分</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8012b1e5e38b24f20b2a" style="list-style-type:decimal"><li>公司决定2025年去欧洲过五一节团建，带领老板和同事一起递交了申根签</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d80428dc2e8e52185a2c5" style="list-style-type:decimal"><li>抽空去苏州过了一个周末，没想到最好吃的竟是东北铁锅炖</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-277002488f2d8022b46ad6250b19e4e2" style="list-style-type:decimal"><li>小结：本月继续熟悉工作，也有了一个差不多的CTA策略上线。然而即使刚上线时还有小小盈利，但下半个月的市场暴跌也给策略带来了极大负面影响。这时我对加密货币市场有了更多的理解</li></ol></div></details><div class="notion-blank notion-block-277002488f2d80f59811c58d50cb6d76"> </div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-277002488f2d8089b8f9d3d14a5a013d" data-id="277002488f2d8089b8f9d3d14a5a013d"><span><div id="277002488f2d8089b8f9d3d14a5a013d" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d8089b8f9d3d14a5a013d" title="总结："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">总结：</span></span></h2><div class="notion-text notion-block-277002488f2d80ff885aeab36fd341ee">2024年是终于摆脱了学生身份的一年，也终于在国内职场狠狠体验了一把。但是很幸运的是，现在做的工作都是我2、3年前梦寐以求的工作哈哈。感恩！Peace！</div></main></div>]]></content:encoded>
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            <title><![CDATA[论文精读：《Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models》]]></title>
            <link>https://fantasy-ren.tech//article/DT_Digital_twin_AI</link>
            <guid>https://fantasy-ren.tech//article/DT_Digital_twin_AI</guid>
            <pubDate>Fri, 20 Feb 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[本文从AI视角探讨了目前数字孪生在引入AI技术的一些挑战]]></description>
            <content:encoded><![CDATA[<div id="notion-article" class="mx-auto overflow-hidden "><main class="notion light-mode notion-page notion-block-30d002488f2d80e5aa5cdeef5df7d2e9"><div class="notion-viewport"></div><div class="notion-collection-page-properties"></div><blockquote class="notion-quote notion-block-30d002488f2d807db12dda6f1f047c08"><div>本篇文章属于论文精读系列，从AI研究员角度探讨了目前数字孪生框架在引入AI等技术的挑战，并且提出了数字孪生AI化的四个阶段。文章链接如下：</div></blockquote><div class="notion-row"><a class="notion-bookmark notion-block-30d002488f2d802fba29c40769f6bbd1" href="https://arxiv.org/html/2601.01321v1#S7" target="_blank" rel="noopener noreferrer"><div><div class="notion-bookmark-title">Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models</div><div class="notion-bookmark-description">Digital twins, as precise digital representations of physical systems, have evolved from passive simulation tools into intelligent and autonomous entities through the integration of artificial intelligence technologies. This paper presents a unified four-stage framework that systematically characterizes AI integration across the digital twin lifecycle, spanning modeling, mirroring, intervention, and autonomous management. By synthesizing existing technologies and practices, we distill a unified four-stage framework that systematically characterizes how AI methodologies are embedded across the digital twin lifecycle: (1) modeling the physical twin through physics-based and physics-informed AI approaches, (2) mirroring the physical system into a digital twin with real-time synchronization, (3) intervening in the physical twin through predictive modeling, anomaly detection, and optimization strategies, and (4) achieving autonomous management through large language models, foundation models, and intelligent agents. We provide an in-depth analysis of the synergy between physics-based modeling and data-driven learning, highlighting the transition from traditional numerical solvers to physics-informed and foundation models for physical systems. Furthermore, we examine how generative AI technologies, including large language models and generative world models, transform digital twins into proactive and self-improving cognitive systems capable of reasoning, communication, and creative scenario generation. Through extensive review across eleven application domains such as healthcare, aerospace, smart manufacturing, robotics, and smart cities, we identify both universal challenges including scalability, explainability, and trustworthiness, as well as domain-specific requirements. This paper reveals how AI-driven digital twins are evolving toward more intelligent, interoperable, and ethically responsible ecosystems, highlighting key directions for future interdisciplinary research and development.</div><div class="notion-bookmark-link"><div class="notion-bookmark-link-icon"><img src="https://www.notion.so/image/https%3A%2F%2Farxiv.org%2Ffavicon.ico?table=block&amp;id=30d00248-8f2d-802f-ba29-c40769f6bbd1&amp;t=30d00248-8f2d-802f-ba29-c40769f6bbd1" alt="Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models" loading="lazy" decoding="async"/></div><div class="notion-bookmark-link-text">https://arxiv.org/html/2601.01321v1#S7</div></div></div></a></div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-313002488f2d8060afe8e1ac7e8fba7c" data-id="313002488f2d8060afe8e1ac7e8fba7c"><span><div id="313002488f2d8060afe8e1ac7e8fba7c" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d8060afe8e1ac7e8fba7c" title="从比特到原子：深度解析《Digital Twin AI》——迈向自主世界模型之路"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">从比特到原子：深度解析《Digital Twin AI》——迈向自主世界模型之路</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d80b48626d9d289e09d2c" data-id="313002488f2d80b48626d9d289e09d2c"><span><div id="313002488f2d80b48626d9d289e09d2c" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80b48626d9d289e09d2c" title="引言：当数字孪生遇见大模型"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">引言：当数字孪生遇见大模型</span></span></h3><div class="notion-text notion-block-313002488f2d800c9130e376386e4c39">理查德·费曼曾言：“凡我不能创造的，我都无法理解。”在工业 4.0 的下半场，**数字孪生（Digital Twin, DT）**正经历从“静态映射”到“自主进化”的范式转移。最近，Lehigh University 等机构发表的长篇综述《Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models》系统性地探讨了 AI，尤其是大语言模型（LLM）和世界模型（World Models），如何赋予数字孪生以“灵魂”。</div><hr class="notion-hr notion-block-313002488f2d80c49ee4e0ad1577a11c"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d8018913fdbf4182ec9c5" data-id="313002488f2d8018913fdbf4182ec9c5"><span><div id="313002488f2d8018913fdbf4182ec9c5" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d8018913fdbf4182ec9c5" title="一、 DT AI 的全生命周期：四阶段技术栈深度拆解"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">一、 DT AI 的全生命周期：四阶段技术栈深度拆解</span></span></h3><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-313002488f2d804ea37fe1b431594fd4"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A7e79f14a-1230-4837-9cba-8bd7fe446d7b%3Aimage.png?table=block&amp;id=31300248-8f2d-804e-a37f-e1b431594fd4&amp;t=31300248-8f2d-804e-a37f-e1b431594fd4" alt="人工智能驱动的数字孪生框架及其应用前景" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">人工智能驱动的数字孪生框架及其应用前景</figcaption></div></figure><div class="notion-text notion-block-313002488f2d80b787d9f76ad0d0a14a">论文将数字孪生 AI 的演进分为四个核心阶段，每一阶段都涉及复杂的算法协同：</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-313002488f2d80beb4ecde602ad56fd3" data-id="313002488f2d80beb4ecde602ad56fd3"><span><div id="313002488f2d80beb4ecde602ad56fd3" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80beb4ecde602ad56fd3" title="1. 建模阶段 (Modeling)：物理规律的神经化表达"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">1. 建模阶段 (Modeling)：物理规律的神经化表达</span></span></h4><div class="notion-text notion-block-313002488f2d8013ba70cd9a528de544">传统的数值仿真（如有限元分析）在面对复杂非线性系统时计算极其缓慢。</div><ul class="notion-list notion-list-disc notion-block-313002488f2d80a181e3fd31c69e83e3"><li><b>物理信息人工智能 (Physics-informed AI)</b>：</li><ul class="notion-list notion-list-disc notion-block-313002488f2d80a181e3fd31c69e83e3"><li><b>PINNs (物理信息神经网络)</b>：通过将偏微分方程（PDEs）作为正则化项引入 Loss 函数，使模型在数据稀疏的情况下依然能产出符合物理定律（如能量守恒）的结果。</li><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-313002488f2d80519416eeb4c20d2df6"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Afa20b97a-1db8-4101-96c1-3abec85df505%3Aimage.png?table=block&amp;id=31300248-8f2d-8051-9416-eeb4c20d2df6&amp;t=31300248-8f2d-8051-9416-eeb4c20d2df6" alt="基于物理的方法和人工智能系统" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">基于物理的方法和人工智能系统</figcaption></div></figure><li><b>神经算子 (Neural Operators, 如 FNO)</b>：其核心优势在于“一次训练，处处推理”。相比传统求解器，它能实现跨分辨率的场转换，计算速度提升可达 3-4 个数量级。</li></ul></ul><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-313002488f2d800693f5cde536f05499" data-id="313002488f2d800693f5cde536f05499"><span><div id="313002488f2d800693f5cde536f05499" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d800693f5cde536f05499" title="2. 镜像阶段 (Mirroring)：高保真的实时同步"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2. 镜像阶段 (Mirroring)：高保真的实时同步</span></span></h4><div class="notion-text notion-block-313002488f2d806ca4b4f6675f050080">这是将物理状态实时“克隆”到数字空间的过程。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-313002488f2d803fbfdde555d1b72c60"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A7659b432-4120-47ba-8ad2-8cb03784e9cb%3Aimage.png?table=block&amp;id=31300248-8f2d-803f-bfdd-e555d1b72c60&amp;t=31300248-8f2d-803f-bfdd-e555d1b72c60" alt="生成式人工智能模型" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">生成式人工智能模型</figcaption></div></figure><ul class="notion-list notion-list-disc notion-block-313002488f2d80c9b78bc93aa6df9cff"><li><b>3D 高斯泼溅 (3DGS)</b>：论文强调了 3DGS 在实时渲染中的统治力，它比 NeRF 更适合工业级的大场景，能以 100+ FPS 的速度渲染复杂的工厂细节。</li></ul><ul class="notion-list notion-list-disc notion-block-313002488f2d805e81c3f6ee46b05c30"><li><b>生成式仿真 (Generative Simulation)</b>：利用扩散模型（Diffusion Models）合成极端工况（Edge Cases）数据。例如，模拟飞机引擎在极端沙尘环境下的磨损数据，这在现实中极难获取。</li></ul><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-313002488f2d80fdb14df846739e90a9" data-id="313002488f2d80fdb14df846739e90a9"><span><div id="313002488f2d80fdb14df846739e90a9" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80fdb14df846739e90a9" title="3. 干预阶段 (Intervening)：反事实推理与优化"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3. 干预阶段 (Intervening)：反事实推理与优化</span></span></h4><div class="notion-text notion-block-313002488f2d8031b5e8d71645fd7c2b">数字孪生的核心价值在于“试错成本为零”。</div><ul class="notion-list notion-list-disc notion-block-313002488f2d80a1b083c0f38258c6d4"><li><b>多智能体强化学习 (MARL)</b>：在智慧城市或柔性生产线中，AI 负责协调成百上千个移动实体。论文详细阐述了如何在数字孪生环境中训练 Agent，通过“虚拟试错”找到全局最优的路径或调度方案。</li></ul><ul class="notion-list notion-list-disc notion-block-313002488f2d80dda7f9ff774fb2132e"><li><b>因果推断 (Causal Inference)</b>：AI 不仅预测结果，还通过反事实分析提问：“如果我改变了压力参数 A，是否会导致部件 B 的疲劳加剧？”</li></ul><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-313002488f2d80f6aec9ebf95d79f6e3" data-id="313002488f2d80f6aec9ebf95d79f6e3"><span><div id="313002488f2d80f6aec9ebf95d79f6e3" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80f6aec9ebf95d79f6e3" title="4. 自主管理阶段 (Autonomous Management)：LLM Agent 作为大脑"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4. 自主管理阶段 (Autonomous Management)：LLM Agent 作为大脑</span></span></h4><div class="notion-text notion-block-313002488f2d80738919e68b6e387fed">这是目前最前沿的研究方向，即构建具备推理和决策能力的自主实体。</div><ul class="notion-list notion-list-disc notion-block-313002488f2d8092ac9ee9cd34496829"><li><b>具身智能 (Embodied AI)</b>：LLM 充当高级决策者（Manager），将人类的模糊指令（如“优化本周的能耗”）拆解为底层的控制任务。</li></ul><ul class="notion-list notion-list-disc notion-block-313002488f2d80bdbea0dd4102e9dd29"><li><b>多模态融合</b>：系统整合传感器时间序列、监控视频、维修手册（文本）和 CAD 图纸，构建对物理世界的全面语义理解。</li></ul><hr class="notion-hr notion-block-313002488f2d803b9bd7e36e8997c1c1"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d80e0b952f891cf645c8a" data-id="313002488f2d80e0b952f891cf645c8a"><span><div id="313002488f2d80e0b952f891cf645c8a" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80e0b952f891cf645c8a" title="二、 核心焦点：为什么“世界模型”是 DT 的终极形态？"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">二、 核心焦点：为什么“世界模型”是 DT 的终极形态？</span></span></h3><div class="notion-text notion-block-313002488f2d80929a1ae12fc32064d8">论文提出了一个深刻的观点：<b>数字孪生正在演变为世界模型（World Models）。</b></div><ol start="1" class="notion-list notion-list-numbered notion-block-313002488f2d80299bc2cd25523cb938" style="list-style-type:decimal"><li><b>预测未来状态</b>：世界模型不仅是当前的镜像，它还包含一个内嵌的动力学预测器。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-313002488f2d803b9d3dd1019f092703" style="list-style-type:decimal"><li><b>动作归因</b>：它能理解“动作（Action）”与“环境变化（Observation）”之间的因果链路。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-313002488f2d804fae7ad2bab7c8dbc8" style="list-style-type:decimal"><li><b>想象力驱动的探索</b>：就像 Sora 能够模拟物理互动一样，未来的 DT 将具备在虚拟空间中“想象”出物理上合理的故障或演化过程的能力。</li></ol><hr class="notion-hr notion-block-313002488f2d804db653d4781c585de9"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d806f88e9db25fd04e0ac" data-id="313002488f2d806f88e9db25fd04e0ac"><span><div id="313002488f2d806f88e9db25fd04e0ac" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d806f88e9db25fd04e0ac" title="三、 跨行业应用：从纳米级到城市级"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">三、 跨行业应用：从纳米级到城市级</span></span></h3><table class="notion-simple-table notion-block-313002488f2d80feb6fee15c6e04b8c8"><tbody><tr class="notion-simple-table-row notion-simple-table-header-row notion-block-313002488f2d807eb1e8e32ffdd4596e"><td class="" style="width:120px"><div class="notion-simple-table-cell">行业领域</div></td><td class="" style="width:120px"><div class="notion-simple-table-cell">技术细节与落地路径</div></td></tr><tr class="notion-simple-table-row notion-block-313002488f2d802abb2ddd78d8a88301"><td class="" style="width:120px"><div class="notion-simple-table-cell"><b>个性化医疗</b></div></td><td class="" style="width:120px"><div class="notion-simple-table-cell">利用 <b>人体数字孪生 (Human DT)</b> 结合生成模型，模拟药物分子在特定患者循环系统中的分布。</div></td></tr><tr class="notion-simple-table-row notion-block-313002488f2d80afb580ec05ed87f276"><td class="" style="width:120px"><div class="notion-simple-table-cell"><b>智能制造</b></div></td><td class="" style="width:120px"><div class="notion-simple-table-cell">通过 <b>边云协同 (Edge-Cloud Collaboration)</b> 实现生产线毫秒级的异常检测与自愈。</div></td></tr><tr class="notion-simple-table-row notion-block-313002488f2d80d59a23e35e87060866"><td class="" style="width:120px"><div class="notion-simple-table-cell"><b>智慧能源</b></div></td><td class="" style="width:120px"><div class="notion-simple-table-cell">利用 <b>图神经网络 (GNN)</b> 模拟复杂电网的拓扑演变，应对分布式电源接入带来的波动。</div></td></tr><tr class="notion-simple-table-row notion-block-313002488f2d80268bbbc2acfc698a31"><td class="" style="width:120px"><div class="notion-simple-table-cell"><b>航空航天</b></div></td><td class="" style="width:120px"><div class="notion-simple-table-cell">结合 <b>概率机器学习</b> 进行不确定性量化（UQ），预测卫星或航空发动机的长效寿命。</div></td></tr></tbody></table><hr class="notion-hr notion-block-313002488f2d80eca80fe6d9568947d4"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d809399e4d85915469009" data-id="313002488f2d809399e4d85915469009"><span><div id="313002488f2d809399e4d85915469009" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d809399e4d85915469009" title="四、 个人思考：AI 是否真的“理解”物理？"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">四、 个人思考：AI 是否真的“理解”物理？</span></span></h3><div class="notion-text notion-block-313002488f2d80bd9fe3c2b3c758d494">在深度阅读这篇论文后，我有三点深刻的感悟：</div><ol start="1" class="notion-list notion-list-numbered notion-block-313002488f2d80bc9f5cc396131c7b1e" style="list-style-type:decimal"><li><b>“物理常识”是 AI 走向工业的门票</b>：目前的 LLM 仍然存在严重的物理“幻觉”（比如视频生成中杯子碎了又愈合）。数字孪生 AI 的关键在于<b>硬约束</b>，即如何将数学公式硬编码进神经网络。没有物理约束的 AI 在工业界是危险的“黑盒”。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-313002488f2d803089e1c22cc0ede878" style="list-style-type:decimal"><li><b>数据权属与“合成数据”的悖论</b>：高质量的工业数据极难获取且高度敏感。论文提到的“用 AI 生成数据训练 AI”虽然高效，但如果初始模型存在偏差，是否会导致生成的数字孪生与物理现实产生“生殖隔离”般的误差漂移？</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-313002488f2d80779044f4be61093262" style="list-style-type:decimal"><li><b>人机协作的新形态</b>：未来的工厂可能不再需要操作员盯着屏幕，而是人类与 DT Agent 的“对齐”。人类提供伦理和顶层目标，AI 利用其超越人类的模拟速度在数字空间里进行亿万次演化。</li></ol><hr class="notion-hr notion-block-313002488f2d80e78b04fd1023a0ed77"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-313002488f2d80068dd0d89ac9517a17" data-id="313002488f2d80068dd0d89ac9517a17"><span><div id="313002488f2d80068dd0d89ac9517a17" class="notion-header-anchor"></div><a class="notion-hash-link" href="#313002488f2d80068dd0d89ac9517a17" title="五、 结语"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">五、 结语</span></span></h3><div class="notion-text notion-block-313002488f2d80cea2a4d56e12c08b5b">《Digital Twin AI》这篇综述不仅仅是技术的堆砌，它揭示了一个趋势：<b>AI 正在从纯文本、纯视觉的交互，走向对客观物理规律的深度重构。</b> 数字孪生将不再只是一个监控工具，它将成为 AI 探索物理世界、学习因果关系的“教练场”。</div></main></div>]]></content:encoded>
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            <title><![CDATA[KAN:Komogorov-Arnold Networks简读]]></title>
            <link>https://fantasy-ren.tech//article/kan</link>
            <guid>https://fantasy-ren.tech//article/kan</guid>
            <pubDate>Tue, 28 May 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[一篇对KAN技术理解的追热点的文章，毕竟网上夸它到天上，甚至许多观点认为可以打败MLP，那么我就来看看这到底是什么原理🧐]]></description>
            <content:encoded><![CDATA[<div id="notion-article" class="mx-auto overflow-hidden "><main class="notion light-mode notion-page notion-block-c2620bc88d0d405cbbd5c24229d892cd"><div class="notion-viewport"></div><div class="notion-collection-page-properties"></div><blockquote class="notion-quote notion-block-e71de58772e3479bad9ea788cb739e2f"><div>本篇文章简单记述了对<b>Kolmogorov-Arnold Networks(KAN)</b>技术的理解，文章链接如下：</div></blockquote><div class="notion-row"><a class="notion-bookmark notion-block-472eaf0b5f044ee2b4369d6de9301601" href="https://arxiv.org/abs/2404.19756" target="_blank" rel="noopener noreferrer"><div><div class="notion-bookmark-title">KAN: Kolmogorov-Arnold Networks</div><div class="notion-bookmark-description">Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation...</div><div class="notion-bookmark-link"><div class="notion-bookmark-link-icon"><img src="https://www.notion.so/image/https%3A%2F%2Farxiv.org%2Fstatic%2Fbrowse%2F0.3.4%2Fimages%2Ficons%2Fapple-touch-icon.png?table=block&amp;id=472eaf0b-5f04-4ee2-b436-9d6de9301601&amp;t=472eaf0b-5f04-4ee2-b436-9d6de9301601" alt="KAN: Kolmogorov-Arnold Networks" loading="lazy" decoding="async"/></div><div class="notion-bookmark-link-text">https://arxiv.org/abs/2404.19756</div></div></div><div class="notion-bookmark-image"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Farxiv.org%2Fstatic%2Fbrowse%2F0.3.4%2Fimages%2Farxiv-logo-fb.png?table=block&amp;id=472eaf0b-5f04-4ee2-b436-9d6de9301601&amp;t=472eaf0b-5f04-4ee2-b436-9d6de9301601" alt="KAN: Kolmogorov-Arnold Networks" loading="lazy" decoding="async"/></div></a></div><div class="notion-blank notion-block-55ea6b6ae0f44916a2a75fd8f921db14"> </div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-b386534edd36464faa24fe2c71fb2ab4" data-id="b386534edd36464faa24fe2c71fb2ab4"><span><div id="b386534edd36464faa24fe2c71fb2ab4" class="notion-header-anchor"></div><a class="notion-hash-link" href="#b386534edd36464faa24fe2c71fb2ab4" title="大纲"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">大纲</span></span></h2><div class="notion-text notion-block-468a3e30c85c4e66b461b90ed8fa68f9">依据本文一作Ziming Liu的解读，本文分为大致以下几点进行简读</div><ol start="1" class="notion-list notion-list-numbered notion-block-e33d501c5ce84898a53f747a368737c2" style="list-style-type:decimal"><li>数学背景</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-24d7d9758d8f4049ba4584a863d58e80" style="list-style-type:decimal"><li>KAN架构</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-f4a63f2f8239418591ab80e016a6532c" style="list-style-type:decimal"><li>算法细节</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-bab1a36e0d9949e580dedd010184639d" style="list-style-type:decimal"><li>样例表现</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-ae4b0cee64704838ad59d48cf3cd6cf8" style="list-style-type:decimal"><li>思考</li></ol><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-83e686c2ad524e629a847a39f51efa71" data-id="83e686c2ad524e629a847a39f51efa71"><span><div id="83e686c2ad524e629a847a39f51efa71" class="notion-header-anchor"></div><a class="notion-hash-link" href="#83e686c2ad524e629a847a39f51efa71" title="1. 数学背景"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">1. 数学背景</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-3194d0b248ee4c2fa4c9a3333885bbe4" data-id="3194d0b248ee4c2fa4c9a3333885bbe4"><span><div id="3194d0b248ee4c2fa4c9a3333885bbe4" class="notion-header-anchor"></div><a class="notion-hash-link" href="#3194d0b248ee4c2fa4c9a3333885bbe4" title="1.1 Spline：样条函数"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">1.1 Spline：样条函数</span></span></h3><div class="notion-text notion-block-ddc2c35ae42748bd82f50f38307efe29">根据维基百科，在数学学科数值分析中，样条(Spline)是一种特殊的函数，由多项式分段定义，样条函数是一类分段（片）光滑、并且在各段交界处也有一定光滑性的函数。</div><div class="notion-row notion-block-4e4edb46db9f4caf98ab6f016adfe48f"><div class="notion-column notion-block-b33cf10b85184e2099fb9d04ec4aa7b8" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><div class="notion-text notion-block-a9ec6ccf1adf495ebf9f1cce093a0e4f">（该名称来源于早起工程制图，为了将一些固定点连成一条光滑的曲线，采用具有弹性的木条固定在这些点上，通过样条画出来的曲线不仅经过各固定点，而且连续光滑）</div><div class="notion-blank notion-block-e9b98ca89bbe4283b0a249d59ef6cd90"> </div></div><div class="notion-spacer"></div><div class="notion-column notion-block-208c8dd338184c23aedb8245f7109679" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-532e5369a47741ed95798665dbef4421"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:292px"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F4584f69a-1526-43f3-9413-10d0cfd62ac3%2FUntitled.png?table=block&amp;id=532e5369-a477-41ed-9579-8665dbef4421&amp;t=532e5369-a477-41ed-9579-8665dbef4421&amp;width=384&amp;cache=v2" alt="notion image" loading="lazy" decoding="async"/></div></figure></div><div class="notion-spacer"></div></div><div class="notion-text notion-block-7de3e74c01e342bf80ca3e650d0c0ffa">作为分段多项式函数，样条函数的每两个点之间用一个多项式来表示，这些多项式的阶数相同，但是系数是不一样的。</div><div class="notion-row notion-block-78f910975dd240cab83936af19276945"><div class="notion-column notion-block-eb8441c32be44906b424837f1b7adf85" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><div class="notion-text notion-block-150de957defe48f490303718a3eabcb2"><span class="notion-gray">线性样条</span></div><div class="notion-blank notion-block-311e1dbd72ad4912a6594ffb9b449cbf"> </div><div class="notion-blank notion-block-ea49a44b59964e39a2a331da397cfeab"> </div><div class="notion-blank notion-block-b5734997282843b3819b848d8e1d6862"> </div><div class="notion-blank notion-block-926c7f7a7992424dab636f48b0b6ffcb"> </div><div class="notion-blank notion-block-2901954f1d474b5a806570a5c0334a02"> </div><div class="notion-blank notion-block-a1dfc65950d7472bb3de7a9cfc10a387"> </div><div class="notion-blank notion-block-22e280051cbb48258e082294f7893149"> </div><div class="notion-text notion-block-b44fd0fffb7f42ad8433871935a59e86"><span class="notion-gray">二次样条</span></div><div class="notion-blank notion-block-287dc9d3f10245fcab2dea9c12c733f2"> </div><div class="notion-blank notion-block-b0eb38e74899448da64653e09f1be22b"> </div><div class="notion-blank notion-block-d398f26a3eee44b289299e2ee6516300"> </div><div class="notion-blank notion-block-7a9d712a2c5b431bb269ca9d15523a61"> </div><div class="notion-blank notion-block-802caa4d38774ea59b1ef221b3d191c8"> </div><div class="notion-blank notion-block-faa2d690859249fc931951a5117b54b1"> </div><div class="notion-blank notion-block-118fcc7e27444b3bab45b63dcaf10496"> </div><div class="notion-text notion-block-505de817f0104a849a852cc43d79575b"><span class="notion-gray">三次样条</span></div></div><div class="notion-spacer"></div><div class="notion-column notion-block-3b8ef3e5032249d88e8172dcbbae4215" style="width:calc((100% - (1 * min(32px, 4vw))) * 0.5)"><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-fc11fe42ed9b436eb916d12c919278f2"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:336px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F2ef2102e-3e22-45d3-9ff0-649191f0f94b%2FUntitled.png?table=block&amp;id=fc11fe42-ed9b-436e-b916-d12c919278f2&amp;t=fc11fe42-ed9b-436e-b916-d12c919278f2&amp;width=336&amp;cache=v2" alt="notion image" loading="lazy" decoding="async"/></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-5de7d619006c42889a1a6156d863415f"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:369px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F91d9504a-fc62-4ff6-a723-2915c977ec69%2FUntitled.png?table=block&amp;id=5de7d619-006c-4288-9a1a-6156d863415f&amp;t=5de7d619-006c-4288-9a1a-6156d863415f&amp;width=369&amp;cache=v2" alt="notion image" loading="lazy" decoding="async"/></div></figure><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-a6c2c6c608e744f986658469078685e7"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:399px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F8636f7c2-0b94-4db2-92bb-f60f7dbcfa39%2FUntitled.png?table=block&amp;id=a6c2c6c6-08e7-44f9-8665-8469078685e7&amp;t=a6c2c6c6-08e7-44f9-8665-8469078685e7&amp;width=399&amp;cache=v2" alt="notion image" loading="lazy" decoding="async"/></div></figure></div><div class="notion-spacer"></div></div><div class="notion-text notion-block-8cace05e25c14f80a7a9193b48211423">KAN网络的一个核心就是样条函数，不像MLP，KAN没有保留线性权重，每个权重参数都被参数化为样条的<span class="notion-red">可学习的</span>1维单变量函数所取代。此外，<span class="notion-red">根据作者观点，KAN更像是样条函数和MLP的组合</span>，利用各自的优势并且避免各自的劣势。例如Spline对于低维函数是精确的，易于局部调整，但它无法利用组合结构而存在严重的CoD的诅咒。MLP不受CoD的影响，但由于无法优化单变量函数因此在低维情况下不够精确。为了准确地学习一个函数，一个模型不仅要学习组成结构（外部自由度），还要很好的近似单变量函数（内部自由度）。因此KAN作为两者的结合，外部相似于MLP，内部使用了Spline。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-50cf128171134df7b6dad726cae7f741" data-id="50cf128171134df7b6dad726cae7f741"><span><div id="50cf128171134df7b6dad726cae7f741" class="notion-header-anchor"></div><a class="notion-hash-link" href="#50cf128171134df7b6dad726cae7f741" title="1.2 Kolmogorov-Arnold表示定理"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">1.2 Kolmogorov-Arnold表示定理</span></span></h3><div class="notion-callout notion-gray_background_co notion-block-f7ca40c62cb9474f9906e62383210e3c"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">相比于MLP受启发于通用近似定理(Universal Approximation Theorem)，KAN受启发于Kolmogorov-Arnold Representation Theorem(KART)，若<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>是多元连续函数，则<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>可以被写成一个有限的单元连续函数和二元加法的组合。大致思想即：利用一组简单函数来表示一个多元函数。</div></div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-a18fb36d38db4217b6d844b5bff10762">where <span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span> and <span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>.</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-0f477b63f77d4f7fb401e976a5520e32"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:624px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F897502dd-96f5-425a-aa32-2439e7fe9dad%2FUntitled.png?table=block&amp;id=0f477b63-f77d-4f7f-b401-e976a5520e32&amp;t=0f477b63-f77d-4f7f-b401-e976a5520e32&amp;width=624&amp;cache=v2" alt="两层KAN Layer的shallow KAN" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">两层KAN Layer的shallow KAN</figcaption></div></figure><div class="notion-text notion-block-a62455d8c6594f308a9885107fa72963">该图为浅层KAN(shallow KAN)的网络架构原理，整体还是比较清晰的。利用KART，很多个类似正弦函数的片段加起来就能拟合任意形状的函数，换句话说，用<a class="notion-link" href="https://zh.wikipedia.org/wiki/B%E6%A0%B7%E6%9D%A1" target="_blank" rel="noopener noreferrer">B-Spline</a>这一种激活函数两次求和就够了。<span class="notion-red">其中每个结点</span><span class="notion-red"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></span><span class="notion-red">，即每个函数片段可以对应MLP中的非线性转换作用的激活函数。其中</span><span class="notion-red"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></span><span class="notion-red">代表B-Spline函数，</span><span class="notion-red"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></span><span class="notion-red">则为可学习的参数。</span></div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-f0e9cf7abecb4889bf800bc2db54cf71">在该结构中，使用了两种尺度或分辨率的组合：粗粒度（红圈）和细粒度（蓝圈）网格，在保持计算效率的同时和可以精确捕捉和适应函数变化。上图中<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>值代表网格尺度，<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>越大粒度越细。浅层KAN的结构其实以前已经有人做过研究，但都仅局限于两层变换，本文作者的主要贡献之一便是使网络变深，构建深层KAN(deep KAN)。此外，深层KAN的宽度也不局限于<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>。</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-2a20def949d6405383b0a56d3869631e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:576px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2Fd7c49a11-100b-460c-8a4a-6656092bb41f%2FUntitled.png?table=block&amp;id=2a20def9-49d6-4053-83b0-a56d3869631e&amp;t=2a20def9-49d6-4053-83b0-a56d3869631e&amp;width=576&amp;cache=v2" alt="三层KAN Layer的shallow KAN，其中" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">三层KAN Layer的shallow KAN，其中<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></figcaption></div></figure><details class="notion-toggle notion-block-654acb9d1af541ed8e63bb0270310b2f"><summary>根据KART，两层KAN网络就可以表示所有光滑函数，那为什么要更深？原始的两层构造并没有约束激活函数是否是光滑的，有时需要非光滑或分形的激活函数来表示目标函数（例如<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>）。为避免这种情况，作者因此加深网络。</summary><div></div></details><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-fa0b6b126b134116afe68034a0fec490" data-id="fa0b6b126b134116afe68034a0fec490"><span><div id="fa0b6b126b134116afe68034a0fec490" class="notion-header-anchor"></div><a class="notion-hash-link" href="#fa0b6b126b134116afe68034a0fec490" title="2. KAN架构"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2. KAN架构</span></span></h2><div class="notion-text notion-block-a23acec6fce44e04b51cad3812097343">给定机器学习任务，包含输入输出对<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，目的是想找到一个函数<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>能得到<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>。公式1表明了通过找到合适的单元函数<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>和<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，情况是可行的，这启发了作者去设计一个神经网络，它可以显式的参数化公式1。既然所有的用来学习的函数都是单元函数，因此通过讲所有的1D函数参数化成B-Spline曲线，包含局部B-Spline基函数的的可学习参数，这也就是KAN的原型，即浅层KAN。为了加深加宽KAN，受MLP的启发，定义了KAN Layer。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-7f1d2771bcd94e0ab914938ea6428c27" data-id="7f1d2771bcd94e0ab914938ea6428c27"><span><div id="7f1d2771bcd94e0ab914938ea6428c27" class="notion-header-anchor"></div><a class="notion-hash-link" href="#7f1d2771bcd94e0ab914938ea6428c27" title="2.1 KAN Layer"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2.1 KAN Layer</span></span></h3><div class="notion-text notion-block-e2de1a82f842424cb7228c30648be411">一个拥有<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>-D输入和<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>-D输出的KAN层可以被定义为1D函数矩阵</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-49b019ac67b94e03ac363411eec84cdc">其中<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>包含可训练的参数。</div><div class="notion-text notion-gray_background notion-block-b7e9cde50ca1447f8473edb7d6725f35">KAN的形状可以被定义为整数数组<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，其中<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>是在第<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>层上的节点数量。</div><ul class="notion-list notion-list-disc notion-block-5a64fe2880c947be81cee3a149686f1a"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>: 第<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>层上的第<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>个节点</li></ul><ul class="notion-list notion-list-disc notion-block-ff0eda592684464dbbbed73b113f26b9"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>: <span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的激活值</li></ul><ul class="notion-list notion-list-disc notion-block-6c6d4156e6bd41198b8026dc9fc663e9"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>: 连接<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>和<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的激活函数（因此在第<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>层和第<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>层之间，有<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>个激活函数）</li></ul><div class="notion-text notion-gray_background notion-block-5b1189b6295f4c17a8ac66f9b5e814f6"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的前激活值为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，后激活值为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></div><div class="notion-text notion-block-0fb29906fadc4a769ffcd53f1a968e2a">以此类推，神经元<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的激活值就是所有他的前激活函数的后激活值之和，表示为</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-85c3b0427d564ca6bbb277e47920f9e5">用矩阵的表示方法为</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><ul class="notion-list notion-list-disc notion-block-a7b9665d9fbf4239b74869d44015f001"><li><span class="notion-red_background"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></span><span class="notion-red_background">: KAN第</span><span class="notion-red_background"><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></span><span class="notion-red_background">层的函数矩阵，也就是所称的KAN层</span></li></ul><hr class="notion-hr notion-block-8c224527a0724a35888a850933f400c4"/><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-ea37ae4772f44872bb5720ecd6c3ce14" data-id="ea37ae4772f44872bb5720ecd6c3ce14"><span><div id="ea37ae4772f44872bb5720ecd6c3ce14" class="notion-header-anchor"></div><a class="notion-hash-link" href="#ea37ae4772f44872bb5720ecd6c3ce14" title="2.2 KAN网络"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2.2 KAN网络</span></span></h3><div class="notion-text notion-block-c398eb37dc514a3ea9cdf25592a3f780">一个KAN网络因此通常是<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>个层的组合：输入为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，输出为</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-5235052d5fc44c46af9dbfc648064124">为了直观比较，<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>。MLPs分开使用<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>和<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>进行非线性化操作，而KANs仅使用<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>来全部操作。</div><div class="notion-callout notion-gray_background_co notion-block-8681559336fb4cf5bbbf5c90934e36b7"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">相比于原始的浅层KAN的形状是<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，深层的KAN变成了多层级联，进一步放开了结构限制使隐层节点数可以自由发挥。</div></div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-e4f7e22f809b492494a880f56a3b941f" data-id="e4f7e22f809b492494a880f56a3b941f"><span><div id="e4f7e22f809b492494a880f56a3b941f" class="notion-header-anchor"></div><a class="notion-hash-link" href="#e4f7e22f809b492494a880f56a3b941f" title="3. 算法细节"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3. 算法细节</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-c9728df8a70749ef8a0b0549405e4623" data-id="c9728df8a70749ef8a0b0549405e4623"><span><div id="c9728df8a70749ef8a0b0549405e4623" class="notion-header-anchor"></div><a class="notion-hash-link" href="#c9728df8a70749ef8a0b0549405e4623" title="3.1 B-Spline函数"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.1 B-Spline函数</span></span></h3><div class="notion-text notion-block-ea89cc132a214be49eca1fba7c9cb162">常见的B-Spline函数是由Cox-de Boor递归函数组成，这也是KAN作者实际工程中所采用的。</div><div class="notion-text notion-block-0d5f677c63e748fd9fcff4cad4c15e8a">当B-Spline的度数为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>时，就像常数片段多项式</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-5e5e0457a8bc4c19a22a83a8fe9676e3">对于更高阶的<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，B-Spline函数就被递归的定义</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-callout notion-gray_background_co notion-block-a29095f90828496e97c13aea2b61c385"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">一个优美的公式，但是由于其非线性的问题，计算过程很多都是递归的形式，也造成了对算力的极大消耗。后期许多跟进的研究比如Efficient-KAN都在此基础上有进行优化。</div></div><div class="notion-blank notion-block-6827259ce8724efda766b1d72ec3464f"> </div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-9a319ae818e34938b3a3c07ad323097a" data-id="9a319ae818e34938b3a3c07ad323097a"><span><div id="9a319ae818e34938b3a3c07ad323097a" class="notion-header-anchor"></div><a class="notion-hash-link" href="#9a319ae818e34938b3a3c07ad323097a" title="3.2 残差激活函数"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.2 残差激活函数</span></span></h3><div class="notion-text notion-block-f5965f36c1c34e93a1245560a04f5565">定义了<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，其中包含了基础函数<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>和Spline样条函数</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-callout notion-gray_background_co notion-block-4fbc7fa661f9414fae5ef6164454f2c8"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">由于单纯的使用spline函数作为激活函数会导致函数不光滑，当网格节点增多时spline近似于震荡。因此作者在这里加入光滑函数<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>作为基底，以此为基础加入spline的扰动进行初始化。</div></div><div class="notion-text notion-block-929eed4dfc254adf989022508bf56727">其中设置</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-a8ac6e04db144c2896c47a1845dd3778">并且样条函数通常参数化为B-Spline样条的线性组合</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-42a1482aa0144aafaa4c7808818e6e43">其中<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>是可训练参数。</div><div class="notion-callout notion-gray_background_co notion-block-039b425b8e2542fc9077f9dea94e2efa"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">- 原则上<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>是多余的，因为它可以成为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>和<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的一部分，但这个<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>仍被包含用来更好地控制激活函数的整体大小</div></div><div class="notion-callout notion-gray_background_co notion-block-19898924919f42b493dbf6f6ff3f8de1"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">- <span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>由Google Brain的论文首次提出，可以被看作是Sigmoid函数的变体</div></div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-b24f331c1b024c3e81c5dcd735578e6b" data-id="b24f331c1b024c3e81c5dcd735578e6b"><span><div id="b24f331c1b024c3e81c5dcd735578e6b" class="notion-header-anchor"></div><a class="notion-hash-link" href="#b24f331c1b024c3e81c5dcd735578e6b" title="3.3 尺度初始化"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.3 尺度初始化</span></span></h3><div class="notion-text notion-block-2d3d7b41eaa24d68a9dc5da9ca899b28">每个激活函数都被初始化为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，并使用Xavier初始法初始化<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>。</div><div class="notion-callout notion-gray_background_co notion-block-84698efd61cf433daa7b28c5b8ba3588"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">这里也有作者的一些trick，spline函数的初始化并不完全是0，而是几乎为0，否则节点就会出现简并的问题。这一点类似于MLP中初始化也并不完全都是0。</div></div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-f9b1318b51e0492fb3c8d827ffdc78f2" data-id="f9b1318b51e0492fb3c8d827ffdc78f2"><span><div id="f9b1318b51e0492fb3c8d827ffdc78f2" class="notion-header-anchor"></div><a class="notion-hash-link" href="#f9b1318b51e0492fb3c8d827ffdc78f2" title="3.4 更新Spline网格"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.4 更新Spline网格</span></span></h3><div class="notion-text notion-block-f4a9da4e474b4c2aa697ed6bcb405837">根据输入激活动态更新每个网格，以解决Spline样条在有界区域上的定义。但在训练过程中，激活值可以从固定区域里进化。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-771e065f9f8f4f42a73536f07b4b7889" data-id="771e065f9f8f4f42a73536f07b4b7889"><span><div id="771e065f9f8f4f42a73536f07b4b7889" class="notion-header-anchor"></div><a class="notion-hash-link" href="#771e065f9f8f4f42a73536f07b4b7889" title="3.5 参数计数"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.5 参数计数</span></span></h3><div class="notion-text notion-block-630ac6638e074588aae7fe07427280de">为了简化这一部分，作出如下假设：</div><ol start="1" class="notion-list notion-list-numbered notion-block-639a788050524308aefc8b2fd3f4e86b" style="list-style-type:decimal"><li>KAN网络的深度为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，每层网络的节点数都相等且为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-2d90c39eae064a10a4dea6ee7ae32286" style="list-style-type:decimal"><li>Spline函数的阶数为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>（通常<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>），区间为<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>（对应<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>的网格点）</li></ol><div class="notion-text notion-block-9ed5492495874702a39000cf78a95d1f">根据作者所述，这样架构的KAN总共有大约<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>或<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>个参数，相反的是在MLP中这样的架构只有<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>个参数，这看起来比KAN更有效。但幸运的事KAN往往只需要更小的架构，更少的节点数就能得到更好的泛化能力和可解释性。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-441c57a276694b3aa295c63cef58ad47" data-id="441c57a276694b3aa295c63cef58ad47"><span><div id="441c57a276694b3aa295c63cef58ad47" class="notion-header-anchor"></div><a class="notion-hash-link" href="#441c57a276694b3aa295c63cef58ad47" title="3.6 准确性提升-Grid Extension"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3.6 准确性提升-Grid Extension</span></span></h3><div class="notion-text notion-block-46f3b3c8a1bf427b88d0c400c70d1e1d">通过改变网格大小，Spline函数可以被任意调整其精确度，由此作为继承者，KAN也有同样的特性，并且不需要从头重新训练。基本逻辑是开始时使用较少参数训练，然后通过简单的细化样条网格来增加参数，并继续训练该模型。</div><div class="notion-callout notion-gray_background_co notion-block-50cc3a5592084e94950bcbb50a4b45b7"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">这是KAN利用了Spline特性的又一大优势。相比于MLP的为了提高精度，需要昂贵的增加宽度和深度并且重新训练，KAN仅需利用Grid Extension就可以继续优化。</div></div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-641f6c59c9544d519759471112f1d7ad" data-id="641f6c59c9544d519759471112f1d7ad"><span><div id="641f6c59c9544d519759471112f1d7ad" class="notion-header-anchor"></div><a class="notion-hash-link" href="#641f6c59c9544d519759471112f1d7ad" title="4. 样例表现"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4. 样例表现</span></span></h2><div class="notion-text notion-block-437cc887b45045f69a8a783db21ce136">在原作中，两种任务被用来测试并验证相对于MLP而言KAN的有效性-回归和解PDE。此外，作者也在精确性（RMSE Loss）和模型复杂度（参数数量）两个维度上对KAN和MLP进行了比较。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-2ab0548d67d048a396a70349f9c0053f" data-id="2ab0548d67d048a396a70349f9c0053f"><span><div id="2ab0548d67d048a396a70349f9c0053f" class="notion-header-anchor"></div><a class="notion-hash-link" href="#2ab0548d67d048a396a70349f9c0053f" title="4.1 Symbolic Formula"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.1 Symbolic Formula</span></span></h3><div class="notion-text notion-block-1d3e0b9f3534487e86af988838ddeae9">作者首先用了5个Symbolic Formula的例子实验，这5个函数都可以被KART表示，因此已经在理论上证明了KAN的优越性。</div><ol start="1" class="notion-list notion-list-numbered notion-block-548ca3338fed422abdb6b0891bfb2a64" style="list-style-type:decimal"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>，Bessel函数；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-192845de0bf64f7e9310d3a34808dfd4" style="list-style-type:decimal"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>;</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-6d9c951b164241c1bbf4a07f47596a2f" style="list-style-type:decimal"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>;</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-f2ef56e2c36a432580fadf2b06da8c07" style="list-style-type:decimal"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>;</li></ol><ol start="5" class="notion-list notion-list-numbered notion-block-6fdc1312d5864e0e814b4eec5e182d08" style="list-style-type:decimal"><li><span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>。</li></ol><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-4aa6a7fbcb18440caedfef6bafc9bc69"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F5e560a0b-f824-4843-b6cb-32fbc1af9ef2%2FUntitled.png?table=block&amp;id=4aa6a7fb-cb18-440c-aedf-ef6bafc9bc69&amp;t=4aa6a7fb-cb18-440c-aedf-ef6bafc9bc69&amp;width=635.9944458007812&amp;cache=v2" alt="在5个简单例子上的对KAN和MLP的比较结果。" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">在5个简单例子上的对KAN和MLP的比较结果。</figcaption></div></figure><div class="notion-callout notion-gray_background_co notion-block-e2f292eefdbf493a9db97b5f246496fa"><div class="notion-page-icon-inline notion-page-icon-span"><span class="notion-page-icon" role="img" aria-label="👉">👉</span></div><div class="notion-callout-text">上述的实验例子都是已经证实过的可知用某确切Spline函数设置可解的，换句话说就是可知对每个Symbolic最优的KAN架构。但这种理想情况并不常见。</div></div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-e7362744fe844aa1a317f1836f8f0a24" data-id="e7362744fe844aa1a317f1836f8f0a24"><span><div id="e7362744fe844aa1a317f1836f8f0a24" class="notion-header-anchor"></div><a class="notion-hash-link" href="#e7362744fe844aa1a317f1836f8f0a24" title="4.2 Special Functions"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.2 Special Functions</span></span></h3><div class="notion-text notion-block-33fdfc97615f4de486d091899cbcde21">在实践中，最优的KAN被承诺存在，但并不知其先验形状。因此实验被拓展到更多的特殊函数以验证其有效性。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-6b7b2d06b9694e7dad48402e7c41d1e7"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F33df4eca-15e2-4c78-935a-762d76f7d8cc%2FUntitled.png?table=block&amp;id=6b7b2d06-b969-4e7d-ad48-402e7c41d1e7&amp;t=6b7b2d06-b969-4e7d-ad48-402e7c41d1e7&amp;width=708&amp;cache=v2" alt="KAN和MLP用于拟合特殊函数的比较。" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">KAN和MLP用于拟合特殊函数的比较。</figcaption></div></figure><div class="notion-text notion-block-5fc2030ae26841ecb3e2aa729046c6ef">实验又一次的证明了KAN相对于MLP的优越性</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-bc6e6710f0ee4456b79d4616b5f54d16" data-id="bc6e6710f0ee4456b79d4616b5f54d16"><span><div id="bc6e6710f0ee4456b79d4616b5f54d16" class="notion-header-anchor"></div><a class="notion-hash-link" href="#bc6e6710f0ee4456b79d4616b5f54d16" title="4.3 解PDE"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.3 解PDE</span></span></h3><div class="notion-text notion-block-55ee498aa8ba473eb58807bae5497e53">本论文作者的方向是AI4S，解PDE也正是他提出KAN的最初目的，挑战MLP的地位其实并非本意。实验中作者首先在经典的零狄利克雷边界的Poisson方程上进行比较，其中定义空间域<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span></div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-b0c2febe71954c279195838df5afbd07">令<span role="button" tabindex="0" class="notion-equation notion-equation-inline"><span></span></span>.该函数的标准解为</div><span role="button" tabindex="0" class="notion-equation notion-equation-block"><span></span></span><div class="notion-text notion-block-67d4910172fa4c1e9d1de59bcfc70015">实验利用了物理嵌入神经网络PINN<span class="notion-pink">（有幸这是我本科研究的一部分）</span>的思想，最小化网络在PDE上的残差来求解。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-123ede7067a14297b5168aea516f0009"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F932afe1d-0b60-4920-96cd-35919347d534%2FUntitled.png?table=block&amp;id=123ede70-67a1-4297-b516-8aea516f0009&amp;t=123ede70-67a1-4297-b516-8aea516f0009&amp;width=635.977783203125&amp;cache=v2" alt="PDE上的比较。KAN有更快的收敛速度，更低的loss以及更陡峭的缩放定律。" loading="lazy" decoding="async"/><figcaption class="notion-asset-caption">PDE上的比较。KAN有更快的收敛速度，更低的loss以及更陡峭的缩放定律。</figcaption></div></figure><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-fd3a7113c6b444fda0cce7520a9ccac6" data-id="fd3a7113c6b444fda0cce7520a9ccac6"><span><div id="fd3a7113c6b444fda0cce7520a9ccac6" class="notion-header-anchor"></div><a class="notion-hash-link" href="#fd3a7113c6b444fda0cce7520a9ccac6" title="4.4 持续学习的比较"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.4 持续学习的比较</span></span></h3><div class="notion-text notion-block-ac968f1aaaa04a74be1ce82c70df4aba">通过在拥有5个高斯峰的一维回归任务上持续学习，展示了KAN可以完全避免灾难性遗忘，而MLP不具备这样的能力。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-02c0980d67af4a698e027b7f8d449c29"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/https%3A%2F%2Fprod-files-secure.s3.us-west-2.amazonaws.com%2F0ab98ef0-07c9-49df-acf5-64da2f93335e%2F3d3d7313-3c02-44a9-a7a3-57a599afe23f%2FUntitled.png?table=block&amp;id=02c0980d-67af-4a69-8e02-7b7f8d449c29&amp;t=02c0980d-67af-4a69-8e02-7b7f8d449c29&amp;width=708&amp;cache=v2" alt="notion image" loading="lazy" decoding="async"/></div></figure><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-b07d145df0b64ee9a81222201f7041dc" data-id="b07d145df0b64ee9a81222201f7041dc"><span><div id="b07d145df0b64ee9a81222201f7041dc" class="notion-header-anchor"></div><a class="notion-hash-link" href="#b07d145df0b64ee9a81222201f7041dc" title="思考"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">思考</span></span></h2><div class="notion-text notion-block-cc7e2a1a6a9a4491b419880e29b7c827">尽管DL界对于深度网络的架构有各种变形，但都是基于MLP的逻辑，KAN的出现无疑是对DL的一种更底层上的启发。尽管KAN的原始思想并不新颖，过往的关于浅层KAN的实验也受到了硬件发展的约束，但学术界再一次有工作聚焦到了KART上，并通过结合更先进的硬件技术和深层KAN的架构证明了这种思想的有效性。相比于MLP，实验证明了即使拥有更少的参数和更简单的架构，KAN都具有更好的表现，尽管当参数数量相同时，KAN由于其内部的递归运算导致计算时间又远大于MLP，但这一劣势也会在未来被算力的发展所缓解。此外，通过将非线性的复杂问题通过内部函数化，提高内部自由度，降低外部自由度，这一工作预示了AI学术界即将开始一小波从MLP的整体论走向了KAN的还原论的趋势，符号主义相关的研究也会有新的活力迸发。</div><div class="notion-blank notion-block-de207b348dcd43ee84ae5b38059e8474"> </div><div class="notion-text notion-block-e432dd604bf94c11a1fcbbfaee7fe7a9">当然，关于KAN的争议也是存在的。在KAN出来的几周内，有许多关注的研究员已经尝试了将KAN应用于常规的AI应用场景中，例如结合CNN做图像识别，其结果并不完全优于MLP，实际的二者选择更应看数据和任务本身，是更贴近还原论还是整体论。正如作者所说，KAN的出现本身是为了AI4S中的一些问题，作者更倾向于将其描述成AI+Science的“语言模型”，这也符合KAN的核心思想，即利用抽象连接的曲线的数学模型来拟合Science中的各种更抽象的函数，KAN没有完全向符号主义靠拢，也吸收了连接主义思想。</div><div class="notion-blank notion-block-81af01ab20bd47a39458624a2e11dcba"> </div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-98cda9ae7cb24de3a866bfb12ae2eee7" data-id="98cda9ae7cb24de3a866bfb12ae2eee7"><span><div id="98cda9ae7cb24de3a866bfb12ae2eee7" class="notion-header-anchor"></div><a class="notion-hash-link" href="#98cda9ae7cb24de3a866bfb12ae2eee7" title="参考资料"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">参考资料</span></span></h2><div class="notion-text notion-block-c30924ce1e36445ea8e6890a78d8a30f"><a class="notion-link" href="https://arxiv.org/abs/2404.19756" target="_blank" rel="noopener noreferrer">https://arxiv.org/abs/2404.19756</a></div><div class="notion-text notion-block-9a3cff77a4bb4904be366ffc63985a74"><a class="notion-link" href="https://www.bilibili.com/video/BV1bz421m7dd/" target="_blank" rel="noopener noreferrer">https://www.bilibili.com/video/BV1bz421m7dd/</a></div><div class="notion-text notion-block-0f0340a965b644a6b057960220980498"><a class="notion-link" href="https://www.bilibili.com/video/BV1Hb421b72f" target="_blank" rel="noopener noreferrer">https://www.bilibili.com/video/BV1Hb421b72f</a>/</div><div class="notion-blank notion-block-83c1d575ff3449c3afb61594ae1c9ba9"> </div><div class="notion-blank notion-block-a2d3736af5c14ce19db0beed570825f6"> </div></main></div>]]></content:encoded>
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            <title><![CDATA[论文精读：《Digital twin for intelligent tunnel construction》]]></title>
            <link>https://fantasy-ren.tech//article/DT_Digital_twin_for_intelligent_tunnel_construction</link>
            <guid>https://fantasy-ren.tech//article/DT_Digital_twin_for_intelligent_tunnel_construction</guid>
            <pubDate>Mon, 22 Sep 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[本文作为一篇综述论文，深入探讨了隧道施工中Digital Twin数字孪生技术的解决方案潜力。通过系统性的分析，本文从入传感器网络等多个角度提出了为隧道工程量身定制的改进型概念框架。]]></description>
            <content:encoded><![CDATA[<div id="notion-article" class="mx-auto overflow-hidden "><main class="notion light-mode notion-page notion-block-276002488f2d80d5a05ee028c3821aba"><div class="notion-viewport"></div><div class="notion-collection-page-properties"></div><blockquote class="notion-quote notion-block-276002488f2d807c9445f5f62b854a5b"><div>本篇文章属于论文精读系列，对数字孪生技术在智能隧道领域的研究进行了大概的梳理和总结，并创新性的提出了新的数字孪生框架，文章链接如下：</div></blockquote><div class="notion-row"><a class="notion-bookmark notion-block-277002488f2d803b81aefa3ef4433be5" href="https://www.sciencedirect.com/science/article/abs/pii/S0926580523004703" target="_blank" rel="noopener noreferrer"><div><div class="notion-bookmark-title">www.sciencedirect.com</div><div class="notion-bookmark-link"><div class="notion-bookmark-link-text">https://www.sciencedirect.com/science/article/abs/pii/S0926580523004703</div></div></div></a></div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-276002488f2d802c9723cb92409a2a00" data-id="276002488f2d802c9723cb92409a2a00"><span><div id="276002488f2d802c9723cb92409a2a00" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d802c9723cb92409a2a00" title="1. 引言"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">1. 引言</span></span></h2><div class="notion-text notion-block-277002488f2d80fd9222e4741b59f6d2">本篇发表于《Automation in Construction》的综述论文，由同济大学团队撰写，系统性地探讨了数字孪生（Digital Twin, DT）技术在智能隧道施工中的应用。论文从隧道工程的<b>复杂性</b>和<b>不确定性</b>切入，指出传统方法在实时性、精确性和决策效率方面的不足，提出DT作为新一代智能化解决方案的巨大潜力。</div><div class="notion-text notion-block-277002488f2d80d1a86fd026927df022">作为一篇综述类论文，本文引出了一些重要观点：</div><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d8018bcdbfa648e474358" style="list-style-type:decimal"><li>提出了<b>四个核心研究问题(RQs)</b>，聚焦于数字孪生(DT)的定义、技术现状、框架构建及价值实现</li><ol class="notion-list notion-list-numbered notion-block-277002488f2d8018bcdbfa648e474358" style="list-style-type:lower-alpha"><li>如何定义隧道施工的Digital Twin？它与其他概念有何不同？</li><li>目前隧道领域数据采集、连接和建模部分的Digital Twin的研究现状和局限是什么？</li><li>如何建立一个专门针对智能隧道施工，重点关注于关闭信息和控制回路的Digital Twin概念框架？</li><li>如何实现隧道工程中的Digital Twin的价值？Digital Twin的发展前景如何？</li></ol></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d807f95e2ff9a21ef4626" style="list-style-type:decimal"><li>指出隧道施工存在数据稀缺性、地质不确定性和决策延迟等核心挑战</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d80108fb0e94ec3de83d6" style="list-style-type:decimal"><li>强调Digital Twin相比BIM等技术的优势在于<span class="notion-default"><span class="notion-red_background"><b>实时映射</b></span></span>和<span class="notion-red_background"><b>双向交互</b></span>能力</li></ol><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-276002488f2d80bf8a3ed280f82ffb11" data-id="276002488f2d80bf8a3ed280f82ffb11"><span><div id="276002488f2d80bf8a3ed280f82ffb11" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80bf8a3ed280f82ffb11" title="2. 背景研究：为什么隧道需要数字孪生？"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2. 背景研究：为什么隧道需要数字孪生？</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d8091acfcde2fa7e6d6ad" data-id="276002488f2d8091acfcde2fa7e6d6ad"><span><div id="276002488f2d8091acfcde2fa7e6d6ad" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8091acfcde2fa7e6d6ad" title="2.1 隧道施工的独特挑战"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2.1 隧道施工的独特挑战</span></span></h3><div class="notion-text notion-block-277002488f2d80708c79eb7abc1c5df0">隧道施工是一个<b>动态复杂系统</b>，具有三个显著特征：<b>地质条件的不确定性</b>（随开挖逐步揭露）、<b>多物理场耦合</b>（力学、热力学、渗流）以及<b>短暂决策窗口</b>（新奥法施工中围岩稳定时间有限）。当前依赖人工勘察、经验判断和断面分析的传统方法难以应对这些挑战。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d80a380dbf39fc6bae1df" data-id="276002488f2d80a380dbf39fc6bae1df"><span><div id="276002488f2d80a380dbf39fc6bae1df" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80a380dbf39fc6bae1df" title="2.2 数字孪生的概念界定"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2.2 <b>数字孪生的概念界定</b></span></span></h3><div class="notion-text notion-block-277002488f2d80c79d85f03bc506703d">论文通过对比制造业、航空航天等领域的DT定义，提出了针对隧道工程的DT概念：</div><blockquote class="notion-quote notion-block-277002488f2d80b3a335f93d2106cb37"><div>&quot;网络空间中隧道实体的多物理场动态副本，通过双向连接实现高保真描述、模拟、预测和控制，并通过自学习实现物理实体的持续逼近&quot;</div></blockquote><div class="notion-text notion-block-277002488f2d80b0a7c3d2b8e8e2c03d">这一概念强调四大核心特征：<b>多源信息融合</b>、<b>实时交互更新</b>、<b>虚拟空间呈现</b>和<b>仿真分析能力</b>。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-277002488f2d8048bf3beb05ab256b23" data-id="277002488f2d8048bf3beb05ab256b23"><span><div id="277002488f2d8048bf3beb05ab256b23" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d8048bf3beb05ab256b23" title="2.3 数字孪生和相关技术的辨析"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">2.3 数字孪生和相关技术的辨析</span></span></h3><div class="notion-text notion-block-277002488f2d80f5920fdab26965ada8">本文通过表格清晰区分了相关概念：</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8024aa03d25f2a21f585"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A69ad173f-e0b3-4826-b3c4-5dd907b113a6%3A306c2b94-9b59-4c23-b91b-fa93ffa3b6be.png?table=block&amp;id=27700248-8f2d-8024-aa03-d25f2a21f585&amp;t=27700248-8f2d-8024-aa03-d25f2a21f585" alt="notion image" loading="lazy" decoding="async"/></div></figure><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-276002488f2d80279adbcf9e65abaf75" data-id="276002488f2d80279adbcf9e65abaf75"><span><div id="276002488f2d80279adbcf9e65abaf75" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80279adbcf9e65abaf75" title="3. 文献分析"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">3. 文献分析</span></span></h2><div class="notion-text notion-block-277002488f2d8069a7ecfcfda2e16060">通过对314篇文献的系统分析，论文揭示了DT研究的<b>时间趋势</b>和<b>主题分布</b>。研究发现：DT在隧道领域的研究从2019年才开始显著增长，目前主要集中运维阶段，理论研究多于实践应用。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80c4ab78fe34db807fd1"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A8603ebcf-7750-45ae-a269-dce309967f10%3Aimage.png?table=block&amp;id=27700248-8f2d-80c4-ab78-fe34db807fd1&amp;t=27700248-8f2d-80c4-ab78-fe34db807fd1" alt="notion image" loading="lazy" decoding="async"/></div></figure><div class="notion-text notion-block-277002488f2d8084957dee21788b822a">关键词共现网络分析显示，DT与BIM、物联网、人工智能、决策支持等技术紧密关联，形成六个主要聚类，反映了该领域多学科交叉的特点。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80849867cd60cca7a49c"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Ab044882e-0374-48fc-805e-4ff6a1b45e09%3Aimage.png?table=block&amp;id=27700248-8f2d-8084-9867-cd60cca7a49c&amp;t=27700248-8f2d-8084-9867-cd60cca7a49c" alt="notion image" loading="lazy" decoding="async"/></div></figure><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-276002488f2d807dad7cd736ddc60028" data-id="276002488f2d807dad7cd736ddc60028"><span><div id="276002488f2d807dad7cd736ddc60028" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d807dad7cd736ddc60028" title="4. 智能隧道施工中的数字孪生技术研究进展"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4. 智能隧道施工中的数字孪生技术研究进展</span></span></h2><div class="notion-text notion-block-277002488f2d80ad9831e0bc6ce7d35a">本章进行了技术深度解析：Digital Twin<b>三大核心组件</b></div><ul class="notion-list notion-list-disc notion-block-277002488f2d8056a3b5c7e968c79b0d"><li>实时孪生数据获取技术</li></ul><ul class="notion-list notion-list-disc notion-block-277002488f2d807e80bef8090e95e507"><li>物理-虚拟连接技术</li></ul><ul class="notion-list notion-list-disc notion-block-277002488f2d807d901feb444666dac5"><li>数字孪生建模技术体系</li></ul><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d8016b336d46e9585e108" data-id="276002488f2d8016b336d46e9585e108"><span><div id="276002488f2d8016b336d46e9585e108" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8016b336d46e9585e108" title="4.1 双数据采集"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.1 双数据采集</span></span></h3><div class="notion-text notion-block-277002488f2d80faac74f7e2d4a8de8c">论文将数据获取技术分为两类</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d8090b4d0f2690fb16fc3" data-id="276002488f2d8090b4d0f2690fb16fc3"><span><div id="276002488f2d8090b4d0f2690fb16fc3" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8090b4d0f2690fb16fc3" title="4.1.1 常规传感器"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.1.1 常规传感器</span></span></h4><ol start="1" class="notion-list notion-list-numbered notion-block-276002488f2d808c81b1d9baa876e495" style="list-style-type:decimal"><li>传感器网络</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-276002488f2d8086848ffbaeac41e2d3" style="list-style-type:decimal"><li>物联网</li></ol><div class="notion-text notion-block-277002488f2d80ed8e0ddad8265cb62f">包括摄影测量、LiDAR、DIC等技术，具有非接触、大范围优势。计算机视觉（CV）在目标检测、图像分割、运动识别方面取得显著进展，如FCN网络在TBM隧道渗水识别中达到高精度，U-Net在岩渣分类中误差仅4%。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d8061b20adafa08000af4"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:541.9791259765625px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A0a6ad3ce-b5bd-40fc-87f4-cb8a9f55a18e%3Aimage.png?table=block&amp;id=27700248-8f2d-8061-b20a-dafa08000af4&amp;t=27700248-8f2d-8061-b20a-dafa08000af4" alt="notion image" loading="lazy" decoding="async"/></div></figure><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d80059b74c6bd54f9c0f5" data-id="276002488f2d80059b74c6bd54f9c0f5"><span><div id="276002488f2d80059b74c6bd54f9c0f5" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80059b74c6bd54f9c0f5" title="4.1.2 基于视觉的传感方法"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.1.2 基于视觉的传感方法</span></span></h4><ol start="1" class="notion-list notion-list-numbered notion-block-276002488f2d80509156c22a2da81c36" style="list-style-type:decimal"><li>基于视觉的传感器</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-276002488f2d80459e72deb88f8507e2" style="list-style-type:decimal"><li>基于计算机视觉的语义数据采集</li></ol><div class="notion-text notion-block-277002488f2d80e784c2c979eb0becbc">包括摄影测量、LiDAR、DIC等技术，具有非接触、大范围优势。计算机视觉（CV）在目标检测、图像分割、运动识别方面取得显著进展，如FCN网络在TBM隧道渗水识别中达到高精度，U-Net在岩渣分类中误差仅4%。</div><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80e6becffee57b72908f"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:565.9765625px;max-width:100%;flex-direction:column"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3Ac5d56371-d488-466d-8e82-862b50384442%3Aimage.png?table=block&amp;id=27700248-8f2d-80e6-becf-fee57b72908f&amp;t=27700248-8f2d-80e6-becf-fee57b72908f" alt="notion image" loading="lazy" decoding="async"/></div></figure><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d80b183a4cfe89406a02d" data-id="276002488f2d80b183a4cfe89406a02d"><span><div id="276002488f2d80b183a4cfe89406a02d" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80b183a4cfe89406a02d" title="4.2 物理连接和虚拟连接"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.2 物理连接和虚拟连接</span></span></h3><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d806e8f6bf3ccda3893a4" data-id="276002488f2d806e8f6bf3ccda3893a4"><span><div id="276002488f2d806e8f6bf3ccda3893a4" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d806e8f6bf3ccda3893a4" title="4.2.1 通信和数据传输"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.2.1 通信和数据传输</span></span></h4><div class="notion-text notion-block-277002488f2d80c9a1d5c0877cee0021">包含有线、无线（蓝牙、Wi-Fi、ZigBee）和蜂窝通信（5G、NB-IoT）三类方式，各适应不同场景需求。</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d808b9f59e77eb17f4883" data-id="276002488f2d808b9f59e77eb17f4883"><span><div id="276002488f2d808b9f59e77eb17f4883" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d808b9f59e77eb17f4883" title="4.2.2 数据处理"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.2.2 数据处理</span></span></h4><div class="notion-text notion-block-277002488f2d80faa0d5c61aadfcfaa9">ETL传统方法处理结构化数据，自然语言处理（NLP）技术挖掘文本数据价值，如从事故报告中提取&quot;安全冲突&quot;模式。</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-277002488f2d808e9997f3d5d83fb1e6" data-id="277002488f2d808e9997f3d5d83fb1e6"><span><div id="277002488f2d808e9997f3d5d83fb1e6" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d808e9997f3d5d83fb1e6" title="4.2.3 远程控制"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.2.3 远程控制</span></span></h4><div class="notion-text notion-block-277002488f2d807dac68e534c84ee794">实现决策反馈执行，如TBM掘进远程控制、除尘系统自动调节等创新应用。</div><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d8019b6b4f03710224a9f" data-id="276002488f2d8019b6b4f03710224a9f"><span><div id="276002488f2d8019b6b4f03710224a9f" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8019b6b4f03710224a9f" title="4.3 数字孪生建模"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.3 数字孪生建模</span></span></h3><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d80478e80df77497c6792" data-id="276002488f2d80478e80df77497c6792"><span><div id="276002488f2d80478e80df77497c6792" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80478e80df77497c6792" title="4.3.1 几何模型"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.3.1 几何模型</span></span></h4><ol start="1" class="notion-list notion-list-numbered notion-block-276002488f2d80958beee17d420226ca" style="list-style-type:decimal"><li>基于点云的高精度模型：提供高精度几何重建，但处理效率低下且易受环境遮挡；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-276002488f2d8001ae2df2270bbbeffe" style="list-style-type:decimal"><li>基于真实数据的参数建模：支持灵活修改和轻量化表达，如基于IFC的隧道结构模型；</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-276002488f2d803ba5dcca55be4485b9" style="list-style-type:decimal"><li>多尺度模型：融合BIM与GIS，实现LOD分级管理，平衡精度与效率。</li></ol><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d808d8552f530066cdb0e"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A2a8d5731-1c2c-4037-97ff-0a74314b8974%3Aimage.png?table=block&amp;id=27700248-8f2d-808d-8552-f530066cdb0e&amp;t=27700248-8f2d-808d-8552-f530066cdb0e" alt="notion image" loading="lazy" decoding="async"/></div></figure><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d801ba65fd12f4b54105b" data-id="276002488f2d801ba65fd12f4b54105b"><span><div id="276002488f2d801ba65fd12f4b54105b" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d801ba65fd12f4b54105b" title="4.3.2 语义和知识模型"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.3.2 语义和知识模型</span></span></h4><ol start="1" class="notion-list notion-list-numbered notion-block-276002488f2d807e8b8be353b1337912" style="list-style-type:decimal"><li>语义模型：基于RDF/OWL构建语义模型，增强跨学科信息互操作；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-276002488f2d806697c7d44a38d770d8" style="list-style-type:decimal"><li>知识模型：知识图谱技术实现经验知识的形式化表达和推理应用。</li></ol><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d8019bab4d413c024b8e5" data-id="276002488f2d8019bab4d413c024b8e5"><span><div id="276002488f2d8019bab4d413c024b8e5" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8019bab4d413c024b8e5" title="4.3.3 分析模型"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">4.3.3 分析模型</span></span></h4><ol start="1" class="notion-list notion-list-numbered notion-block-276002488f2d80b6bb1ffa7578175aba" style="list-style-type:decimal"><li>基于实际数据的分析模型：基于监测数据的模型更新与校正；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-276002488f2d80f889d9c15681d67ac9" style="list-style-type:decimal"><li>数字数值积分法：BIM-to-FEM转换实现分析自动化；</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-276002488f2d806ba1f7ced03439732a" style="list-style-type:decimal"><li>基于人工智能的分析模型：机器学习替代复杂数值模拟，提升计算效率。</li></ol><figure class="notion-asset-wrapper notion-asset-wrapper-image notion-block-277002488f2d80be8306e46fcab10b73"><div style="position:relative;display:flex;justify-content:center;align-self:center;width:100%;max-width:100%;flex-direction:column;height:100%"><img style="object-fit:cover" src="https://www.notion.so/image/attachment%3A0bdd7122-3ae3-4b01-8542-f2a2b92a914f%3Aimage.png?table=block&amp;id=27700248-8f2d-80be-8306-e46fcab10b73&amp;t=27700248-8f2d-80be-8306-e46fcab10b73" alt="notion image" loading="lazy" decoding="async"/></div></figure><blockquote class="notion-quote notion-block-277002488f2d80138eafd63932371bff"><div>技术综述全面且深入，覆盖了从数据采集到应用的完整链条。特别是对视觉感知和AI分析的介绍反映了最新研究进展。然而，技术介绍偏重独立应用，对技术间集成融合讨论不足。部分性能数据（如精度、效率指标）缺乏对比分析，难以评估技术方案的优劣。</div></blockquote><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-276002488f2d809eb66de305737569c7" data-id="276002488f2d809eb66de305737569c7"><span><div id="276002488f2d809eb66de305737569c7" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d809eb66de305737569c7" title="5. 讨论和未来方向"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5. 讨论和未来方向</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d80b08dd9cc8993592d46" data-id="276002488f2d80b08dd9cc8993592d46"><span><div id="276002488f2d80b08dd9cc8993592d46" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80b08dd9cc8993592d46" title="5.1 数字孪生的挑战"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5.1 数字孪生的挑战</span></span></h3><div class="notion-text notion-block-277002488f2d801490a7cba0afcefdf6">论文从四个维度展望数字孪生的价值：</div><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d801fb765d186a3e0910e" style="list-style-type:decimal"><li><b>实时感知增强洞察</b>：解决NATM隧道短暂决策窗口问题</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d8036b8c5c1f7899798d3" style="list-style-type:decimal"><li><b>增强可视化辅助诊断</b>：VR/AR技术提升交互体验</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8042bb08db1a52c4e7f5" style="list-style-type:decimal"><li><b>增强分析支持决策</b>：多方法耦合解耦复杂问题</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d806fb747fc8ca01a8d49" style="list-style-type:decimal"><li><b>自动化改变施工模式</b>：远程无人化施工成为可能</li></ol><div class="notion-blank notion-block-277002488f2d80409963f57f837664af"> </div><div class="notion-text notion-block-277002488f2d800e9f36e922aaf11f36">同时该领域也存在挑战与研究空白：</div><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d802a9232c4a6c94a2ff1" style="list-style-type:decimal"><li><b>技术层面</b>：模型保真度与计算效率的矛盾、多源异构数据融合、跨平台互操作等挑战亟待解决。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d804cb642d0725b46fb44" style="list-style-type:decimal"><li><b>理论层面</b>：大变形、岩爆、岩溶等特殊问题的分析算法需要进一步发展和适配。</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8038af4cce1e08cea7d2" style="list-style-type:decimal"><li><b>非技术层面</b>：数据安全、标准体系、经济性、组织变革等影响因素尚未充分探讨。</li></ol><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-276002488f2d807ea94dc9d00d9afd3a" data-id="276002488f2d807ea94dc9d00d9afd3a"><span><div id="276002488f2d807ea94dc9d00d9afd3a" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d807ea94dc9d00d9afd3a" title="5.2 智能施工的新概念数字孪生"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5.2 智能施工的新概念数字孪生</span></span></h3><div class="notion-text notion-block-277002488f2d80c5bf86f111299d47f4">论文提出一个针对隧道工程的特制数字孪生框架，包含三大组成部分。</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d8027af5ecedf308ed852" data-id="276002488f2d8027af5ecedf308ed852"><span><div id="276002488f2d8027af5ecedf308ed852" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d8027af5ecedf308ed852" title="5.2.1 物理实体"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5.2.1 物理实体</span></span></h4><div class="notion-text notion-block-277002488f2d80728546da359d4ba33b">包含地质、结构、机械、人员等多类对象，不仅是感知对象，也是执行主体（如TBM既是感知对象也是控制器）。</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d80fc9f35de1181704808" data-id="276002488f2d80fc9f35de1181704808"><span><div id="276002488f2d80fc9f35de1181704808" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80fc9f35de1181704808" title="5.2.2 连接层"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5.2.2 连接层</span></span></h4><div class="notion-text notion-block-277002488f2d802bb028dffa77f0586f">实现虚实映射的数据处理、传输和控制功能，强调跨协议互操作能力。</div><h4 class="notion-h notion-h3 notion-h-indent-2 notion-block-276002488f2d80be9cbdcbe3266ef13c" data-id="276002488f2d80be9cbdcbe3266ef13c"><span><div id="276002488f2d80be9cbdcbe3266ef13c" class="notion-header-anchor"></div><a class="notion-hash-link" href="#276002488f2d80be9cbdcbe3266ef13c" title="5.2.3 虚拟模型"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">5.2.3 虚拟模型</span></span></h4><div class="notion-text notion-block-277002488f2d801da5fdf1312142039c">核心部分，包含几何、语义和分析三大模型，支持多层次、多粒度表达。</div><blockquote class="notion-quote notion-block-277002488f2d808eb2aeec6c98c17bf7"><div>论文还提出了四维需求框架：信息，时间，物理，技术。从多维度定义数字孪生系统需求，特别是强调了不确定性表征和处理的重要性。</div></blockquote><hr class="notion-hr notion-block-277002488f2d80f786adc2acbfcb701e"/><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-277002488f2d80b69860c5e4a63b5151" data-id="277002488f2d80b69860c5e4a63b5151"><span><div id="277002488f2d80b69860c5e4a63b5151" class="notion-header-anchor"></div><a class="notion-hash-link" href="#277002488f2d80b69860c5e4a63b5151" title="小结："><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">小结：</span></span></h2><div class="notion-text notion-block-277002488f2d80b78155c799a1ef567d">论文系统性的总结了数字孪生在智能隧道施工中的技术体系、框架设计和应用前景，主要贡献包括：</div><ol start="1" class="notion-list notion-list-numbered notion-block-277002488f2d807f8e1eed01899d5b06" style="list-style-type:decimal"><li>明确了隧道DT的清晰定义和特征；</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-277002488f2d80948cc5e5c66c9c0e79" style="list-style-type:decimal"><li>全面综述了关键技术的发展现状；</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-277002488f2d8014adbde9f99ca54acc" style="list-style-type:decimal"><li>提出了专用概念框架和四维需求模型；</li></ol><ol start="4" class="notion-list notion-list-numbered notion-block-277002488f2d805bb83fd8ae78970236" style="list-style-type:decimal"><li>基于Gemini原则展望了应用价值。</li></ol><div class="notion-text notion-block-277002488f2d80578f46c6f1d1b10a65">本论文是数字孪生在隧道工程领域较为全面和系统的综述，具有重要的理论参考价值和实践指导意义。技术综述内容丰富，框架设计具有创新性，对未来研究方向的判断具有前瞻性。但是，值得注意的是，该论文也存在一定局限性，比如偏重技术综述而缺乏实际案例的验证和经济效益分析、对标准体系等非技术因素关注不足等。</div></main></div>]]></content:encoded>
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            <title><![CDATA[监控Binance的公告板]]></title>
            <link>https://fantasy-ren.tech//article/binance-monitor</link>
            <guid>https://fantasy-ren.tech//article/binance-monitor</guid>
            <pubDate>Sun, 13 Apr 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[本文介绍了如何利用python监控binance的公告板，以期对短线交易做出一些消息判断。]]></description>
            <content:encoded><![CDATA[<div id="notion-article" class="mx-auto overflow-hidden "><main class="notion light-mode notion-page notion-block-1d4002488f2d8005a14ad7914d3306f8"><div class="notion-viewport"></div><div class="notion-collection-page-properties"></div><blockquote class="notion-quote notion-block-1d4002488f2d8034af7cd3def260c3f5"><div>最近通过各种方式研究了Binance公告板的作用，对于做crypto的短线交易具有一定的启发作用，各种利多或利空消息都会对对应的币种造成持续又短暂的上升或下降趋势。因此笔者决定利用python采取对Binance公告板的实时抓取监控，并且通过飞书群机器人发出通告及时作出手动交易。</div></blockquote><div class="notion-text notion-block-1d4002488f2d800aaccdfca823369fbb"><b>本博客的技术点：</b></div><ol start="1" class="notion-list notion-list-numbered notion-block-1d4002488f2d8009971affbd440c439c" style="list-style-type:decimal"><li>利用Selenium自动化实时爬取Binance Announcement页面</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-1d4002488f2d802d842fdd16c85b67a4" style="list-style-type:decimal"><li>每当有新的公告发出时，飞书群机器人会作出反应通知</li></ol><ol start="3" class="notion-list notion-list-numbered notion-block-1d4002488f2d80e98591d518046be833" style="list-style-type:decimal"><li>当驱动器失效时，会自动重启Selenium驱动</li></ol><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-1d4002488f2d80d6b910c1563e23fe43" data-id="1d4002488f2d80d6b910c1563e23fe43"><span><div id="1d4002488f2d80d6b910c1563e23fe43" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d80d6b910c1563e23fe43" title="技术调查"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">技术调查</span></span></h2><div class="notion-text notion-block-1d4002488f2d80cdb4e5f79f16fbdc1a">Binance的网站（<a class="notion-link" href="https://www.binance.com/zh-CN/support/announcement" target="_blank" rel="noopener noreferrer">https://www.binance.com/zh-CN/support/announcement</a>）存在一定的反爬机制，单纯的使用requests库抓是无法成功得到响应。</div><div class="notion-blank notion-block-1d4002488f2d80e5a0aac1ea69edb51b"> </div><div class="notion-text notion-block-1d4002488f2d8049a384cf6648df5932">考虑到Selenium可以模拟Chrome驱动的打开方式获得网页内容，因此即使Selenium速度较慢，但公告发出对crypto标的的趋势影响有一定持续时间，因此直接采用Selenium也是acceptable。</div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-1d4002488f2d8027ba2ffc0c741a16e3" data-id="1d4002488f2d8027ba2ffc0c741a16e3"><span><div id="1d4002488f2d8027ba2ffc0c741a16e3" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d8027ba2ffc0c741a16e3" title="技术实现"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">技术实现</span></span></h2><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d80f596c1eb45a5740395" data-id="1d4002488f2d80f596c1eb45a5740395"><span><div id="1d4002488f2d80f596c1eb45a5740395" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d80f596c1eb45a5740395" title="导入必要库"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">导入必要库</span></span></h3><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d80d8a965d9790cf91847" data-id="1d4002488f2d80d8a965d9790cf91847"><span><div id="1d4002488f2d80d8a965d9790cf91847" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d80d8a965d9790cf91847" title="定义驱动设置"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">定义驱动设置</span></span></h3><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d807d9cf9c526ffaf62d1" data-id="1d4002488f2d807d9cf9c526ffaf62d1"><span><div id="1d4002488f2d807d9cf9c526ffaf62d1" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d807d9cf9c526ffaf62d1" title="自定义爬取"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">自定义爬取</span></span></h3><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d8084b939c7374d9e1bba" data-id="1d4002488f2d8084b939c7374d9e1bba"><span><div id="1d4002488f2d8084b939c7374d9e1bba" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d8084b939c7374d9e1bba" title="添加飞书机器人"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">添加飞书机器人</span></span></h3><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d80fcba32ede07a4b4102" data-id="1d4002488f2d80fcba32ede07a4b4102"><span><div id="1d4002488f2d80fcba32ede07a4b4102" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d80fcba32ede07a4b4102" title="定时执行脚本"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">定时执行脚本</span></span></h3><h3 class="notion-h notion-h2 notion-h-indent-1 notion-block-1d4002488f2d808ba461f25d1f27fb63" data-id="1d4002488f2d808ba461f25d1f27fb63"><span><div id="1d4002488f2d808ba461f25d1f27fb63" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d808ba461f25d1f27fb63" title="运行指令"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">运行指令</span></span></h3><div class="notion-text notion-block-1d4002488f2d80c9b5e0c51367136b50">通过nohup指令可以将脚本持续化运行在本地，防止因电脑长时间待机造成任务中止。</div><div class="notion-text notion-block-1d4002488f2d8004bb70dd52fc4ab58a">脚本产生的log日志将被记录在<code class="notion-inline-code">bn_announcement.output</code> 中。</div><div class="notion-text notion-block-1d4002488f2d8005b332eae9debb2a9d">若想停止运行脚本，直接kill任务的pid即可。</div><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-1d4002488f2d80d38208cd1b5c0ba279" data-id="1d4002488f2d80d38208cd1b5c0ba279"><span><div id="1d4002488f2d80d38208cd1b5c0ba279" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d80d38208cd1b5c0ba279" title="风险提示"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">风险提示</span></span></h2><ol start="1" class="notion-list notion-list-numbered notion-block-1d4002488f2d80b4810cd280a176a401" style="list-style-type:decimal"><li>Selenium的Chrome Driver在长时间运行过程中可能会突然中止session断开连接，因此一定要添加异常判断，然后重启Driver。</li></ol><ol start="2" class="notion-list notion-list-numbered notion-block-1d4002488f2d800cbb51d76b06e6d01e" style="list-style-type:decimal"><li><span class="notion-red"><b>目前尚不明确Binance对此类爬取是否有次数限制，因此存在一定的被封锁ip的风险。</b></span></li></ol><h2 class="notion-h notion-h1 notion-h-indent-0 notion-block-1d4002488f2d802aa9e7d2464bfb59c0" data-id="1d4002488f2d802aa9e7d2464bfb59c0"><span><div id="1d4002488f2d802aa9e7d2464bfb59c0" class="notion-header-anchor"></div><a class="notion-hash-link" href="#1d4002488f2d802aa9e7d2464bfb59c0" title="可改进空间"><svg viewBox="0 0 16 16" width="16" height="16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z"></path></svg></a><span class="notion-h-title">可改进空间</span></span></h2><ul class="notion-list notion-list-disc notion-block-1d4002488f2d80f8bfa9e8354ce10c71"><li>爬取时间</li><ul class="notion-list notion-list-disc notion-block-1d4002488f2d80f8bfa9e8354ce10c71"><li>首次启动时因为包含了Driver的启动，因此抓取时间会较长，延迟达到8s左右。但在后续的爬取时，延迟会降到0.6-1.2s。<b>因此首要的改进方向在于降低其延迟，以达到更快的公告提醒。</b></li><li>在脚本抓到新公告并推送飞书的过程中，由于使用了<code class="notion-inline-code">requests.Post</code> ,也存在1s多的延迟。<b>改进点可能在多方面的考虑不同的消息推送机制，例如telegrame等。</b></li></ul></ul><ul class="notion-list notion-list-disc notion-block-1d4002488f2d80cd9a6ace6ae457c149"><li>多平台的公告</li><ul class="notion-list notion-list-disc notion-block-1d4002488f2d80cd9a6ace6ae457c149"><li>目前只进行了Binance的公告板监控，但其他交易所也同样会产生类似的作用。<b>后期可能会对多个交易所例如okx同样进行监控以达到信息来源丰富化。</b></li></ul></ul><div class="notion-blank notion-block-1d4002488f2d80589f32c329d338cad9"> </div><div class="notion-blank notion-block-1d4002488f2d8040a06ae03b03a43207"> </div></main></div>]]></content:encoded>
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            <title><![CDATA[AutoGen：构建股票分析的多代理智能体]]></title>
            <link>https://fantasy-ren.tech//article/autogen</link>
            <guid>https://fantasy-ren.tech//article/autogen</guid>
            <pubDate>Fri, 02 Jul 2021 00:00:00 GMT</pubDate>
            <description><![CDATA[AutoGen 是由微软开发的一个新的 Agents 项目，刚一上线就登上 GitHub 热榜，狂揽 11k 星。它允许你根据需要创建任意数量的 Agents，并让它们协同工作以执行任务。本文对如何使用AutoGen分析股票作出了一个简单尝试]]></description>
            <content:encoded><![CDATA[AutoGen 是由微软开发的一个新的 Agents 项目，刚一上线就登上 GitHub 热榜，狂揽 11k 星。它允许你根据需要创建任意数量的 Agents，并让它们协同工作以执行任务。本文对如何使用AutoGen分析股票作出了一个简单尝试]]></content:encoded>
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