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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!
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…
>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 a…
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)
Earlier quoted context omitted.
>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 a…
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)
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 MAN…
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…
As a cool bit of additional history, check out the FERMIAC. An analog Monte Carlo device for doing neutron transport in two dimensions. https://en.m.wikipedia.org/wiki/FERMIAC
https://www.semanticscholar.org/paper/A-self-trimming-14-b-1...
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...
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...
Thank you for these links! I do a lot of scientific computation using MC and MCMC. It’s great to read that history and see the care they invested in their flow diagrams, the versions that got more capable, etc.
The ENIAC is a fascinating machine as well, from its initial modular, parallel, dataflow layout to an actual CPU running code a couple years later.
I wish the Wikipedia article would dive more into the birth of its processor. Interestingly, the French article is the most exhaustive regarding this topic.
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!
Black-Scholes uses the heat equation, is that what you’re thinking of?
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 relationshi…
> 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 man…