数学2022lib-www.lanl.gov编辑精选
蒙特卡洛方法的开端
The beginning of the Monte Carlo method (1987)
入门 · 约 45 分钟读完前置知识：概率论基础、蒙特卡洛方法基本概念
导读
这是 Nicholas Metropolis 1987 年的回顾文章，讲述蒙特卡洛方法在洛斯阿拉莫斯国家实验室的起源：如何借助随机抽样和早期计算机（如 MANIAC）解决核物理中难以确定性求解的复杂问题。文章回顾了该方法从核武器与反应堆计算起步，逐渐成为跨领域通用数值工具的历史。
HN 关注点：HN 读者对计算历史的经典文献感兴趣，讨论聚焦于蒙特卡洛方法的核物理起源及其在现代各领域的广泛应用。
后来怎么样
这篇回顾文章记录的蒙特卡洛方法已成为跨领域通用数值方法，在核工程中衍生出 MCNP 等标准工具，是计算科学史上公认的基础性工作。
HN 评论精选
这几条评论里：质疑 1 补充 2 亲历 1
亲历核工程师视角：蒙特卡洛源自 LANL，虽比确定性方法慢，但因结果可信而在概念设计中广泛使用
我是核工程师（专攻堆芯设计/仿真）。看到蒙特卡洛方法如今被用于这么多领域很有趣。即使在核领域，对于常见构型的'常规'反应堆分析，确定性方法仍比蒙特卡洛快几个数量级；但计算机太快了，在概念设计阶段人们常用蒙特卡洛，因为得到的结果更容易让人信服。MCNP 仍是最常用的核分析代码，直接源自 LANL 的这些原始代码；ANL 还有一个强大的开源研究代码 OpenMC，任何人都可以在自己的（性能足够的）电脑上运行。
acidburnNSA查看英文原文
Nuclear engineer here (specialty in core design/simulation). It's fun to see the Monte Carlo method be used in so many other fields now. Even in nuclear, deterministic methods are still orders of magnitude faster for most 'normal' reactor analyses on reactor configurations that are common enough to have all the important deterministic effects known. But with computers so fast, it's quite common for people, especially in conceptual design space, to use Monte Carlo methods since it's a lot easier to believe the answer once you get it. The code MCNP is still the most common nuclear analysis code, and it's directly descended from these original codes from LANL. [1] There is also a very powerful research code called OpenMC from ANL that anyone can run on their (powerful) computer. [2] [1] https://mcnp.lanl.gov/reference_collection.html [2] https://docs.openmc.org/en/stable/
质疑提问：蒙特卡洛的效力是否随问题复杂度增加而衰减，还是采样密度可以弥补
我之前没意识到蒙特卡洛仿真对早期核技术进步如此关键。不过这说得通——它让你能'越级'去测量和预测那些太复杂或确定性建模成本太高的现象。我的直觉是，随着输入输出关系的复杂度上升，它的有效性会下降。这是真的吗？还是说足够的采样密度能克服任意程度的这种复杂性？
bardcore查看英文原文
I didn't realize how integral Monte Carlo sims were to our early advances in nuclear technology. It makes sense to me though- it seems like the Monte Carlo method lets you punch above your weight class in terms of measuring and predicting phenomena that are too complex, or too expensive to deterministically model. My intuition tells me that it's effectiveness would fall off as the complexity of the in/out relationship scales. Is this true? Or can sufficient sample density overcome arbitrary levels of that type of complexity?
补充补充史料：首个蒙特卡洛程序在 ENIAC 上运行，也是第一个存储程序
感兴趣的人可以看：第一个蒙特卡洛程序（运行于 ENIAC，共 840 条指令）已被找到并整理成文档。它也是有史以来第一个运行的存储程序。
rahen查看英文原文
For those interested, the first Monte Carlo program, which ran on the ENIAC, has been found and documented (840 instructions long). It was also the first stored program ever run. https://eniacinaction.com/the-articles/3-los-alamos-bets-on-eniac-nuclear-monte-carlo-simulations-1947-8/ https://eniacinaction.com/wp-content/uploads/2014/02/LosAlamosBetsOnENIAC.pdf
补充补充作者背景：Metropolis 是曼哈顿计划元老、MANIAC 计算机的设计者
文章末尾的作者简介很精彩：Metropolis 1937 年和 1941 年在芝加哥大学获物理学学士和博士，1943 年 4 月作为最初五十位科学家之一来到洛斯阿拉莫斯。1948 年重返 LANL 组建了设计建造 MANIAC I 和 II 的小组。（他取名 MANIAC 是希望遏制机器名称滥用缩写的风气，但可能反而助长了这种风气。）1965 年回到 LANL，1980 年成为实验室资深研究员。
dang查看英文原文
Pretty cool author bio from the end of the article: N. Metropolis received his B.S. (1937) and his Ph.D. (1941) in physics at the University of Chicago. He arrived in Los Alamos, April 1943, as a member of the original staff of fifty scientists. After the war he returned to the faculty of the University of Chicago as Assistant Professor. He came back to Los Alamos in 1948 to form the group that designed and built MANIAC I and II. (He chose the name MANIAC in the hope of stopping the rash of such acronyms for machine names, but may have, instead, only further stimulated such use.) From 1957 to 1965 he was Professor of Physics at the University of Chicago and was the founding Director of its Institute for Computer Research. In 1965 he returned to Los Alamos where he was made a Laboratory Senior Fellow in 1980. Although he retired recently, he remains active as a Laboratory Senior Fellow Emeritus.
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