[HN Gopher] The beginning of the Monte Carlo method (1987) [pdf] ___________________________________________________________________ The beginning of the Monte Carlo method (1987) [pdf] Author : swibbler Score : 113 points Date : 2022-09-18 11:15 UTC (11 hours ago) (HTM) web link (lib-www.lanl.gov) (TXT) w3m dump (lib-www.lanl.gov) | radford-neal wrote: | It's not a very good history. | | It says "In the late 1940s, Stanislaw Ulam invented the modern | version of the Markov Chain Monte Carlo method", but as far as I | know, this is incorrect. He invented a Monte Carlo method, but | not a Markov chain Monte Carlo method. Markov chain Monte Carlo | is generally attributed to Metropolis, Rosenbluth, Rosenbluth, | Teller, and Teller. See https://en.wikipedia.org/wiki/Metropolis- | Hastings_algorithm | | The article fails even to distinguish simple Monte Carlo based on | independently sampled points from Markov chain Monte Carlo. It | seems rather confused in other respects too, such as in its | discussion of "mean field" methods. | [deleted] | dang wrote: | This comment was posted when the URL at the top was | https://en.wikipedia.org/wiki/Monte_Carlo_method#History. | | We've since changed it to the URL suggested by sampo at | https://news.ycombinator.com/item?id=32889436. | sampo wrote: | Here is an article "The beginning of the Monte Carlo method" by | N. Metropolis: https://lib-www.lanl.gov/cgi- | bin/getfile?00326866.pdf | dang wrote: | Nice. We've changed to that from | https://en.wikipedia.org/wiki/Monte_Carlo_method#History | above. Thanks! | ckrapu wrote: | What do you think comes next after HMC/NUTS for general purpose | turn-key sampling? | bardcore wrote: | 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? | vasco wrote: | You should be able to model "infinite" complexity, the way | people design analog circuits is basically this. | BOOSTERHIDROGEN wrote: | Sorry for stupid question, what is infinite complexity in | analog circuit ? Any examples/model ? | RicoElectrico wrote: | I think it's an ad-hoc term. But basically, MC simulations | are needed because circuit elements such as transistors, | resistors may be mismatched, for example Vth in MOS | transistors. This can create input offsets in op-amps, or | timing differences in logic. You can run exactly the same | simulations as normally (DC operating point, AC transfer | function, time-domain with many thousands of points) just | over and over with new random parameters according to the | distribution estimated in device characterization (I think | mostly Gaussian). Transistors models like BSIM are crazy | complicated these days and there's no way to find an | analytical solution for all that. | mjb wrote: | > 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. | | Yes, this is exactly why I like it. At AWS, we've used Monte | Carlo simulations quite extensively to model the behavior of | complex distributed systems and distributed databases. These | are typically systems with complex interactions between many | components, each linked by a network with complex behavior of | its own. Latency and response time distributions are typically | multi-modal, and hard to deal with analytically. | | One direction I'm particularly excited by in this niche is | converging simulation tools and model checking tools. For | example, we could have a tool like P use the same specification | for exhaustive model checking, fuzzing invariants, and doing MC | (and MCMC) to produce statistical models of things like latency | and availability. | mjb wrote: | A while ago I wrote this as a simple introduction to applying | MC methods in distributed systems: | https://brooker.co.za/blog/2022/04/11/simulation.html | NohatCoder wrote: | It is hard to generalise about the suitability of Monte Carlo | methods. In practical applications it is almost always used in | hybrid systems, combined with analytical methods and problem | specific short cuts. How one should apply Monte Carlo methods | to a problem tends to be an open ended question. | aaron695 wrote: | atan2 wrote: | I cannot believe a raw link to Wikipedia made it to the top | stories. | melling wrote: | Some people on HN farm for karma points. They frequently post | Wikipedia articles. It seems somewhat effective. | | There are certain topics that attract a bit of quick attention. | psd1 wrote: | A high-karma Reddit account has monetary value, you can sell | it to a bot operator. | | Does an HN account have any value, or do you think karma | farmers are just in it for the ego boost? | dcminter wrote: | I'm sure that's true, but _also_ there 's a lot of very | interesting HN-relevant stuff on Wikipedia, and it's | perfectly reasonable to share it when you find something | pithy. | | I've certainly done it and contrariwise have often enjoyed | Wikipedia articles (including this one) from other users. | | Apropos of which I wish I'd had Wikipedia when I was a kid - | I recall being utterly baffled by Brittanica's "explanation" | of the term "parsec" and only much later reading a definition | that put it in the context of how stellar distances were | actually resolved. | | Edit: Looking at swibbler's submission history, they're | clearly not a karma farmer btw. | dang wrote: | Edit: as if to illustrate the below, someone found a more | specific third-party article so we've since switched the URL. | More at https://news.ycombinator.com/item?id=32890671. | | ------ | | Happens all the time! | https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... | | It's a good practice _not_ to link to wikipedia.org when a more | in-depth or specific third-party source is available, or if the | topic is a well known one (too generic). But that leaves a lot | of Wikipedia pages on more obscure topics, and those make fine | HN submissions, as long as the topic is of intellectual | interest and not particularly correlated with other things. And | as long as we don 't overdo it. | | Past explanations about this: | https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... | | https://news.ycombinator.com/item?id=30307077 | | https://news.ycombinator.com/item?id=23929687 | | https://news.ycombinator.com/item?id=23249978 | detaro wrote: | not unusual at all | warinukraine wrote: | speedylight wrote: | I've seen it happen quite a bit! | yesco wrote: | Wikipedia posts are my favorite kind of submission | blooalien wrote: | If it's properly fascinating, well written, and informative, | why not? | srvmshr wrote: | A while ago, I submitted a raw Wiki link to "Ligne Claire", a | drawing style adopted by Herge of "Adventures of Tintin" fame. | That made it to #1 and remained for a few hours. It is not very | unusual. | dang wrote: | 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._ | alhirzel wrote: | It should be noted that modern graphics rendering techniques are | a little more accessible and intuitive, while still having the | same basic challenges and solutions as the nuclear simulations | mentioned in this thread/in the Wikipedia article. Things get | even more interesting because quantities are spectral in nature, | can be polarized, etc. Wenzel Jakob is doing important work in | this area out of EPFL[1]. | | [1]: https://rgl.epfl.ch/people/wjakob/ | scubakid wrote: | It's also super useful for exploring the spectrum of potential | outcomes in financial projections / retirement scenarios. People | are sometimes tempted to think in the simpler terms of average | rates of return and not fully consider issues like sequence risk. | MC can help build better intuitions around the real chances of | success given a broader range of varying market conditions. | rahen wrote: | 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-... | | https://eniacinaction.com/wp-content/uploads/2014/02/LosAlam... | acidburnNSA wrote: | 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/ | dav_Oz wrote: | >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. | | Is it really easier to "believe" an answer on a purely | stochastical level? I'm kinda surprised, I would be way more | confident (if I were to choose) with answers from deterministic | descriptions/equations despite being more abstract and | potentially harder to "visualize". | | I find more often than not supposed 'comprehensibility' on the | surface level to be quite misleading. Of course if one doesn't | have clue where to start and enough processing power the Monte | Carlo method and alike certainly can help to jumpstart/brute | force the process. | fastneutron wrote: | MC tends to be more physically accurate (in the limit of a | large number of particle histories) because it can simulate | radiation transport in continuous space, energy, and angular | distribution. Deterministic methods can be faster, but the | discretization process is somewhat of a dark art because the | underlying distributions can be highly nonlinear and rapidly | varying. A combination of methods with varying levels of | fidelity are typically used in real nuclear engineering | applications, and are always referenced back to a common | suite of experimental benchmarks for validation. | wnkrshm wrote: | You can write down an equation for evaluating a ray-traced | picture with perfect mathematical precision, you just cannot | evaluate the integral for any scene that is non-trivial. MC | is the integration technique for it. | | Edit: so you know exactly what you get, if you keep it simple | - the gotchas start if you try to be clever and use fewer | samples (biased MC) | acidburnNSA wrote: | Yes, definitely. With deterministic methods you have to make | all sorts of approximations to discretize the spatial details | of the fuel assemblies, the energy space of the neutrons, the | angular directions of the neutrons, and so on. The | approximations are complex and sensitive. With monte carlo | methods you can treat all those things without | approximations. Under the hood, both deterministic and monte | carlo nucleonics methods are depending on the same | measured/interpolated nuclear interaction probability tables | (aka nuclear cross sections). | pixelpoet wrote: | That sounds super interesting, how does one get into simulating | reactor cores? I'm very familiar with MC methods from computer | graphics. | acidburnNSA wrote: | I would definitely start with some of the openmc tutorials. | | https://docs.openmc.org/en/stable/usersguide/beginners.html | | If you're asking at a higher level, you end up in nuclear | engineering school after having a nebulous interest in energy | issues. | eternalban wrote: | _An Exact MCNP Modeling of Pebble Bed Reactors_ : | | https://www.researchgate.net/publication/264537140_An_Exact_. | .. | | OP's link was a rabbit hole (in a v. good way), sent me down | some paper on the LCG random number generator used for MCNP | modelling, which somehow led to that. | | (https://mcnp.lanl.gov/pdf_files/la-ur-07-7961.pdf) | ur-whale wrote: | The one thing I love with Monte-Carlo is the way you can use it | very simply to give yourself some peace of mind that your | probability formula for a finite distribution, derived with sweat | and blood using very complicated combinatorics (the kind found in | here: | https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathemat...) | actually works. | xhkkffbf wrote: | I became a big fan of the Monte Carlo method when I watched an | economist torture a problem until he found a way to turn it into | the heat equation, a differential equation he knew how to solve. | He made so many bogus assumptions that the answer was pretty much | worthless. But, hey, he could claim he had a closed form | solution! | xxxtentachyon wrote: | Black-Scholes uses the heat equation, is that what you're | thinking of? | ur-whale wrote: | Here's one of the most successful use of MC outside of the field | of nuclear physics: | | https://graphics.stanford.edu/papers/veach_thesis/thesis.pdf ___________________________________________________________________ (page generated 2022-09-18 23:00 UTC)