[HN Gopher] The beginning of the Monte Carlo method (1987) [pdf]
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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
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