[HN Gopher] Monte Carlo Long-Range Interacting System Simulations
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Monte Carlo Long-Range Interacting System Simulations
Author : sandoze
Score : 39 points
Date : 2023-07-30 16:34 UTC (6 hours ago)
(HTM) web link (www.uni-leipzig.de)
(TXT) w3m dump (www.uni-leipzig.de)
| conformist wrote:
| Arxiv: https://arxiv.org/abs/2207.14670
|
| If I understand correctly after skimming, one of the fundamental
| ideas behind this appears to be similar to the well-known Fast
| Multiple Method [1]. It's also a tree-based approach where far
| away points are aggregated into larger chunks?
|
| [1] https://en.m.wikipedia.org/wiki/Fast_multipole_method
| physicsguy wrote:
| It's exactly the same as the Barnes-Hut method from a quick
| glance, there's nothing particularly new in this paper as far
| as I can see. There are various papers which have merit on
| releasing specific codes that support this, but people have
| been using it in spin systems and even in micromagnetics for
| years. I did my PhD in this area years ago and implemented it
| in Monte Carlo and dynamical simulations at the time... and I
| cited papers going back to the 80s and 90s when I wrote up my
| thesis!
| conformist wrote:
| Ah, yes, and they do indeed cite Barnes-Hut, too. So the
| (claimed) novelty seems to be how they connect it to Monte
| Carlo steps.
| radioactivist wrote:
| While the spatial decomposition matches what is done in
| Barnes-Hut, the details of the underlying algorithm are
| somewhat different (they outline this in the introduction).
|
| In particular, their scheme using exact bounds on energy
| differences (evaluated using a hierarchical tree as in BH)
| but in such a way that no approximation is being made. The
| tree is evaluated to whatever depth is needed to decide
| whether to accept/reject the MC move (which in worse case
| could be a brute-force sum over the whole lattice/system) --
| this is different I think than BH or other multipole inspired
| methods (which have a kind of "truncation" or "tolerance"
| parameter).
|
| [This also works well with systems where update are local and
| not global, which I think is a difference from some other
| spatial partitioning schemes -- but I'm less conversant with
| that aspect].
| physicsguy wrote:
| I read the full paper after posting my initial comment. Not
| really - BH does use a "opening angle" parameter, but for
| FMM you use an order of expansion which provides a strict
| error bound in terms of accuracy which was derived in
| Greengard and Rohklin's original paper on but have been
| expanded to other potentials.
|
| To me it's just a minor (but nonetheless interesting)
| variation of an existing method; there have been many of
| these. They don't compare it to other tree based methods in
| performance in the paper which says to me that is merits
| aren't really that clear... with long range potentials FP
| inaccuracies mean none of this is exact anyway.
| Fede_V wrote:
| Isn't this a stochastic variant of Barnes-Hut:
| https://en.wikipedia.org/wiki/Barnes%E2%80%93Hut_simulation
| ckrapu wrote:
| Any commentary on what this means for the wider world of MCMC?
| tnecniv wrote:
| I imagine a similar scheme can be used for general inference if
| you have a way to cluster components of your model in a similar
| fashion even if the parameters are not spatial. Perhaps your
| model has some kind of natural tree structure.
| punnerud wrote:
| Duplicate? https://news.ycombinator.com/item?id=36930857
| phyalow wrote:
| Welcome to reinforcement learning
| whatever1 wrote:
| Really, communities should start talking to each other.
| angus-mackaiver wrote:
| Could you elaborate on that or point to any literature/websites
| because I'm curious to learn about what these have in common.
| Thank you!
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