Blogpost | Yi Zhuang

2025AOGS会议报告列表

Mon, 21 Jul 2025 00:00:00 +0000

为了方便找相关的报告听，爬了一下日程网站上的会议列表。格式原因地点没法很好的处理记录下来。另外不包括不以表格形式呈现特邀报告。

分享一篇国家地理关于蝴蝶效应的科普介绍

Mon, 30 Jun 2025 00:00:00 +0000

D老师翻译，我自己简单校对。但是这篇介绍很多地方都没有深入展开，逻辑也不甚明确，大概看看就好。以下是原文和译文。

The butterfly effect is a real phenomenon—but not how you think

The popular concept has been depicted in everything from film to social media testimonials, but the real science behind the butterfly effect can help scientists predict the future.

By Olivia Campbell June 7, 2025

文章链接：https://www.nationalgeographic.com/science/article/real-butterfly-effect-chaos-theory

蝴蝶效应确实存在——但可能与你所想象的不同

从电影到社交媒体，蝴蝶效应这一流行概念已被广泛描绘，但其背后的科学原理能够帮助科学家预测未来。

作者：Olivia Campbell 2025年6月7日

In 1961, MIT meteorologist Edward Lorenz was inputting numbers into a weather prediction program. His model was based on a dozen variables, the value of one being .506127. When he ran the model again, he rounded that number to .506, then left the room to grab a coffee. When he came back, he discovered this tiny change had resulted in a dramatically different weather prediction.

1961年，麻省理工学院气象学家Edward Lorenz正在向他的天气预测程序输入数据。他的模型基于十二个变量，其中某个变量的值为0.506127。当他再次重复试验时，无心之下将该数值约化为0.506后启动程序，随后离开房间去喝咖啡。回来后他惊奇地发现，这个微小改动竟导致天气预报与之前的结果天差地别。

When presenting his resultant groundbreaking model of chaos and the potential of extreme chaotic unpredictability at the 1972 meeting of the American Association for the Advancement of Science (AAAS), Lorenz posed the question: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?"

在1972年美国科学促进会（AAAS）会议上，Lorenz展示这项开创性的关于混沌理论模型与极端无序系统不可预测性的研究时，提出了一个著名问题：“巴西的一只蝴蝶扇动翅膀，是否会在德克萨斯州引发一场龙卷风？”

Richard A. Anthes, former president of the University Corporation for Atmospheric Research in Boulder, Colorado (now president emeritus), says Lorenz was illustrating how, “in a system of apparently simple mathematical equations, an infinitesimal change in the initial position of the particle can cause huge changes in its future position—a tiny change now may lead to gigantic and unpredictable change in the future.”

科罗拉多大学大气研究联合会前主席（现荣誉主席）Richard A. Anthes解释道，Lorenz阐明了如下的道理：“在看似简单的数学方程系统中，粒子初始位置的极小变化会导致其未来位置的巨大改变——即此刻微小的扰动可能引发未来不可预知的剧变。”

This analogy—that small, seemingly insignificant acts by individuals can lead to disruption or chaos in the future—so simply and beautifully rendered with Lorenz’s captivating metaphor, captured the imaginations of scientists and the public alike.

这个用诗意比喻与精妙诠释的类比——个体看似微不足道的行为可能在未来引发巨大的破坏或混乱——同时俘获了科学家与公众的想象力。

The butterfly effect “disrupted science at a philosophical level, showing that modeling the future is only predictable to an extent, and that ‘chaos,’ as Lorenz put it, is always present but difficult to discern,” explains Bo-Wen Shen, an associate professor of mathematics and statistics at San Diego State University who’s written extensively about the butterfly effect. Shen thinks this is because the idea that even the slightest perturbations may have significant impacts “offers hope to individuals, encouraging them to take small actions that could have a profound and positive effect.”

“蝴蝶效应在哲学层面颠覆了科学认知，表明对未来的模拟预测存在根本局限性。Lorenz所说的’混沌’始终存在，同时也难以察觉，“圣迭戈州立大学数学与统计学副教授Bo-Wen Shen解释道。他撰写了大量关于蝴蝶效应的研究论文，认为这一理论之所以广受欢迎，是因为"最微小的扰动也可能产生重大影响"的理念"赋予个体希望，鼓励他们采取可能带来深远积极影响的微小行动”。

The concept has been the subject of films and was more recently a social media trend in which people shared their butterfly effect stories: seemingly random events—a car breaking down, a missed train, a broken shoe—that lead to significant moments in their life, such as meeting a future spouse or avoiding a bigger catastrophe.

These stories often misunderstand Lorenz’s original concept and more accurately describe a coincidence.

While the butterfly effect may be prone to oversimplification in pop culture, scientists are still using the concept to predict how what we do in the present will change future.

蝴蝶效应这一概念已成为多部电影的主题，近期更成为社交媒体热潮，人们分享着他们的"蝴蝶效应"故事：汽车抛锚、错过火车、鞋子破损等看似随机的事件，最终导向遇见终身伴侣或避免重大灾难等人生转折点。这些故事往往误解了Lorenz的原意，更准确地说应属于一种巧合。尽管流行文化可能过度简化了蝴蝶效应，科学家仍在运用这一原理预测当下行为如何改变未来。

Why the butterfly effect is the subject of scientific debate

为何蝴蝶效应引发科学争议

The main disconnect around popular interpretations of the butterfly effect lies in the belief that the ability of a tiny perturbation to create an organized disturbance at large distances is a real phenomenon.

公众认知与科学本质的核心分歧在于：人们相信微小扰动能在很远的地方引发结构性异常是真实存在的物理现象。

“[It] is a metaphor,” Shen insists, noting that leading experts on the subject recently agreed that it is a Schrödinger’s cat of an idea: never scientifically proven or disproven.

“The metaphorical definition of the butterfly effect is widely accepted as literally true. It is not,” asserts Roger Pielke Sr, professor emeritus of the department of atmospheric science at Colorado State University. “The bottom line, with respect to whether a butterfly flap can result in the development of a tornado thousands of kilometers away (or even locally), is that it cannot under any circumstances. The answer is a categorical NO.”

“这只是比喻，“Bo-Wen Shen强调，并指出该领域权威专家近期达成共识：这如同薛定谔的猫，从未被科学证实或证伪。科罗拉多州立大学大气科学系荣誉教授Roger Pielke Sr断言：“蝴蝶效应的隐喻定义被广泛误认为物理事实。关于蝴蝶振翅能否引发数千公里外（甚至本地）龙卷风的问题，答案在任何情况下都是绝对否定的。”

If you’re confused, don’t worry. Even experts don’t agree on what the concept truly means. Physics Today was home to a spirited back-and-forth of papers on the topic in 2024, between Shen’s team and Oxford University climate physics professor Tim Palmer, debating the nature of the butterfly effect and its implications.

若你感到困惑，无需担忧——即便专家们也意见不一。2024年《今日物理》期刊上，Bo-Wen Shen团队与牛津大学气候物理学教授Tim Palmer就该理论本质展开激烈论战。

Palmer believes that when detailing the butterfly effect, Lorenz was describing how weather is the culmination of seemingly independent atmospheric patterns collectively and momentarily changing the environment. In a 2017 Oxford podcast, he says to imagine weather like a set of Russian dolls: Within a 1,000-kilometer wide low pressure system are 100-kilometer thunderstorm clouds, and within those, sub clouds with turbulent eddies, and within those sub clouds, yet smaller turbulence eddies.

Palmer认为，Lorenz实则在描述天气如何由看似独立的大气模态共同瞬时变化而形成。他在2017年牛津播客中建议将天气想象成俄罗斯套娃：1000公里宽的低压系统内含着100公里尺度的雷暴云，其中又嵌套着湍流涡旋形成的子云团，子云团内还有更微小的湍流。

Palmer has his own ideas about how the butterfly effect should be defined and how it’s misunderstood, saying in 2014 scientific article that “there are finite predictability horizons which cannot be extended by reducing uncertainty in initial conditions.”

Palmer在他2014年的论文中提出了对蝴蝶效应的独特解读：“存在无法通过降低初始状态不确定性来延长的，有限的可预测时限”。

Shen says the butterfly effect is best illustrated using this proverb-like folktale (first recorded by poet George Herbert in 1640):

“For want of a nail, the shoe was lost.

For want of a shoe, the horse was lost.

For want of a horse, the rider was lost.

For want of a rider, the battle was lost.

For want of a battle, the kingdom was lost.

And all for the want of a horseshoe nail.”

Bo-Wen Shen则认为，1640年诗人George Herbert记载的寓言最能诠释该现象： “缺蹄钉，失一只蹄铁；失蹄铁，折一匹战马；折战马，损一位骑士；损骑士，输一场战役；输战役，亡一个帝国—— 皆因少一枚马蹄钉。”

“The verse suggests that any slight perturbation can eventually yield a substantial effect on numerical integrations,” Shen notes. “Lorenz believed that the folklore better illustrated the simpler phenomenon of instability.” The verse also reminds us that subsequent small events will not reverse the outcome.

“这诗句表明任何微小扰动，通过数值积分过程，最终都可能产生可观的影响，“Bo-Wen Shen指出，“Lorenz认为民谚更简明地阐释了不稳定性现象。“诗句同时也暗示了后续小事件无法逆转既定结果。

Making sense of chaos

解读混沌之谜

The butterfly effect has been instrumental in scientifically defining chaos.

蝴蝶效应推动了针对混沌现象的科学研究。

“One extraordinary contribution by Prof. Lorenz is that his models and methods have provided foundations that have inspired numerous studies and further advanced our understanding of chaotic nature and limited predictability,” says Shen.

Scientists have since discovered that chaotic systems—such as weather, the population growth of a single species, or even the flow of traffic—either produce single chaotic solutions that are seemingly random but actuality just hypersensitive to their initial conditions, or coexisting chaotic and regular solutions. Minor changes may not always cause significant impacts, or their effects may be limited in the real world.

“Lorenz教授的卓越贡献在于，其提出的模型与方法为无数研究奠定了基础，深化了我们对混沌现象本质及预测局限的理解，“Bo-Wen Shen表示。科学家已发现，天气、单一物种种群增长甚至交通流量等混沌系统，要么产生对初始条件极度敏感、看似随机实则确定的单一混沌解，要么同时存在混沌解与规则解。现实中，微小变化产生的效应可能有限，未必总能引发重大影响。

“Imagine a vast river flowing towards the ocean. The overall current of the river influences the movements of smaller eddies and swirls. Even though these smaller features might appear chaotic and unpredictable on their own, the larger-scale context provides a framework for understanding their behavior,” explains Shen. “By observing these larger-scale weather patterns, we can gain more insight into how these smaller, more chaotic events might unfold.”

Or as Anthes puts it, “not all butterflies make a difference.”

“想象一条奔流向海的大河。主流决定着较小的涡旋的运动轨迹，尽管这些小涡流本身看似混沌难测，但宏观背景为其行为提供了理解框架，“Bo-Wen Shen解释道，“通过观察大尺度天气模式，我们能更深入把握小尺度混沌事件的演变规律。“或如Anthes所言：“并非所有蝴蝶都能掀起风暴。”

According to Lorenz’ theory, you can’t measure the weather today meticulously enough to accurately predict the weather in the far future; the practical limit to weather prediction caps at a couple of weeks.

Shen wants to test those limits. He and his team have published papers using Lorenz’ models and offered a new perspective on the dual nature of chaos and order in weather and climate.

根据Lorenz理论，人类永远无法精确测量当前天气来准确预测遥远未来的天气，实际预测极限仅为数周。Bo-Wen Shen团队正运用Lorenz模型探索这一极限，为天气与气候中混沌与有序的双重性质提供新见解。

How the butterfly theory applies to a changing climate

蝴蝶理论在气候变化中的应用

While the main usefulness of the butterfly effect lies in weather prediction, it can also help scientists model climate change. Recently, researchers were hoping to use AI to help simulate the butterfly effect to improve weather predictions. Sadly, AI failed to simulate the butterfly effect. This doesn’t negate the butterfly effect, it just tells us that AI cannot conceive of it.

虽然蝴蝶效应主要应用于天气预报，它也能助力科学家模拟气候变化。近期研究者尝试用AI模拟蝴蝶效应以提升天气预测精度，但AI未能成功模拟——这并未否定蝴蝶效应本身，仅说明现有AI尚无法理解该现象。

The impact of Lorenz and his butterfly effect continues to unfold. Chaos theory has revolutionized various branches of physics, biology, engineering, economics, even social science. Anthes says Lorenz’ model has had an enormous effect on all fields in which the future depends on the present.

Lorenz和他所提出的蝴蝶效应产生的影响仍在持续。混沌理论已革新物理学、生物学、工程学、经济学乃至社会科学多个领域。Anthes指出，Lorenz模型对所有"未来取决于当下"的学科都产生深远影响。

“The concept of the butterfly effect applies to almost any complex system in which the future state depends on the present state … the atmosphere and oceans, climate, physics, biological systems including human health, and society in general including economics and political systems,” says Anthes. “Seemingly small changes can have enormous and unpredictable, as well as unintended, consequences in the future.”

Anthes进一步阐释道：“蝴蝶效应的概念适用于几乎所有未来状态取决于当前状态的复杂系统——大气与海洋、气候系统、物理现象、包括人类健康在内的生物系统，以及涵盖经济政治结构的整体社会。表面微小的改变，都可能在未来引发难以预料且偏离本意的巨大连锁反应。”

In 2011, MIT opened a climate research institute named after Lorenz that funds scientific research without an obvious real-world application. This type of “pure research,” as it’s called, will help us learn about all the small actions that may be as consequential as the flap of a butterfly’s wings.

2011年，麻省理工学院创立了以Lorenz命名的气候研究中心，资助那些当下暂无明确应用价值的科学研究。这类"纯理论研究"将帮助我们认识那些可能如蝴蝶振翅般影响深远的所有微小变化或微小行动。

作业脚本中频繁执行mpirun导致slurm请求过于频繁的问题

Tue, 15 Apr 2025 00:00:00 +0000

记录近日碰到的一个问题。

问题表现

一模一样的程序，一个月前还好好的，最近重新提交作业跑起来就不太对劲，具体两个表现：

运行速度特别慢，有时候甚至直接空转无输出。
使用squeue等指令时经常出现request too frequently的提示。

一些测试

最开始还不知道这两个表现其实是同一个问题。想先解决1，给作业加了一堆计时代码，换节点换编译器测试都没搞明白，一会儿跑的时间正常一会儿又不正常。
想解决2，客服反馈说账户作业存在高频slurm请求。在管理员那边的后台Log里会显示为很多的“REQUEST HET JOB ALLOC INFO”和“REQUEST JOB STEP CREATE”日志。但问题是我的程序里面完全没写过任何sbatch，squeue等指令，客服也不懂，害我只能分割demo一遍遍测试，测了半天又说同节点有其他作业运行干扰结果。
最后偶然在一次小demo的测试中发现只运行mpirun也会在日志中出现srun: request too frequently，才让我把一切都想明白。

问题根源

提交的作业脚本中会循环执行mpirun指令，频率太高（大约7秒1次，并且四十多个作业同时跑，会叠加频率），而每次执行mpirun时，均自动会引发srun指令（原因未知，可能是需要和slurm系统申请进程资源）。

srun指令属于slurm指令，高频调用时会触发频率限制，不仅手动执行squeue等会提示request too frequently，作业中运行的程序也会同样受到限制而需要等待重试。因此，运行速度就在这里卡住了，如果一直在等待重试，就会表现出空转的情况。

解决方案

最简单：降频，我在作业脚本中每次运行mpirun前添加等待两三秒的指令就改善了不少。形象来说就是一大堆车都想快速通过十字路口时就一团混乱谁也过不去，但是加上一些等待时间后就全都可以顺利通过了，虽然对于每个车来说过路口的时间比最理想的状态慢了一点。
不知道是否可行：在循环调用的mpirun时我用python/shell做的流程控制，以python为例，先写一个run.sh脚本，其中含有单次mpirun，在python脚本中循环调用subprocess.run执行这个脚本。如果在运行python脚本之初就配置好mpi环境，每次调用时只传递这一个环境给run.sh脚本，就不再需要在每个循环中都调mpirun，而只需要在执行python脚本时调用一次即可。
修改需要mpirun的程序，使得需要的循环可以放在mpi_init里面。这个我干不来，别人写好的巨型程序，我半天都找不到mpi入口。

Liouville 方程的导出及一些性质讨论

Mon, 24 Mar 2025 00:00:00 +0000

1 Liouville 方程的导出

1.1 Liouville 方程回顾及基于输运定理的导出

1.2 基于 Liouville 定理导出输运定理

1.3 Liouville 定理的导出

2 Liouville 方程的解及其验证

2.1 Liouville 方程解的导出：特征线法

2.2 Liouville 方程解的验证

3 概率密度性质的讨论：基于 Liouville 方程的解

3.1 从概率密度的视角理解吸引子

3.2 概率密度增加一定意味着吸引子吗？

3.3 耗散系统中概率密度一定增大吗？

3.4 概率密度增大，与维数，自由度的随想

概率分布随时间的演化研究-线性情形

Wed, 18 Sep 2024 00:00:00 +0000

1 Liouville 方程

1.1 Liouville 方程的导出分析

2 线性自治动力系统的性质讨论

2.1 N=1时

2.2 N=2时

2.3 N=3时

2.4 N=4时

2.5 线性系统的 Liouville 方程解的性质

3 线性情形的具体例子

3.1 最简单的情况

3.2 二阶系统

3.3 四阶系统

4 对线性自治系统的小结

LMD MARS PCM相关整理

Thu, 01 Sep 2022 00:00:00 +0000

如题，使用notion记录整理。

2020春伯克利访学记

Mon, 25 May 2020 00:00:00 +0000

介绍了2020年春季在伯克利访学一学期的见闻，包括出行前准备，上课吃饭等。

金工实习新闻稿

Sat, 04 Jan 2020 00:00:00 +0000

关于金工实习这门课程动手实践过程的回顾，也有在雁栖湖的一些乐事。

之前经编辑同学加工后发在学校公众号上，但是我一时半会找不着链接了，谁找到了可以email我一下。

北京安家楼F1本科访学面签记录

Fri, 06 Dec 2019 00:00:00 +0000

介绍了2019年为了Berkeley访学去北京安家楼办理F1美签的经历。

昼长与太阳方位的计算

Sun, 08 Sep 2019 00:00:00 +0000

在空间中考察太阳与地球，根据定义，通过简单的数学方法得出计算昼长和太阳方位的公式，从而计算出给定地点时间的昼长及太阳方位等要素，进而导出一些常见结论。

热力学偏导数计算法与热力学地图

Fri, 06 Sep 2019 00:00:00 +0000

热力学中各类偏导数的推导方法，如何从最基本的偏导数导出其他偏导数，应用于迈耶公式，内能公式，TdS方程等。

利用洛必达证明极限