Monte Carlo Long-Range Interacting System Simulations
uni-leipzig.de
uni-leipzig.de
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?
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].
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.
Sarle, Warren S. (1994). Neural Networks and Statistical Models. Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994.
If you want an in-depth discussion, these books relate ANNs and statistical methods:
Schürmann, Jürgen. (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches.
Raudys, Sarunas. (2001). Statistical and Neural Classifiers: An Integrated Approach to Design.