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| Home > Publications database > Investigating Machine Learning methods to replace Hybrid Monte Carlo in simulations of Hubbard Model |
| Master Thesis | FZJ-2022-01482 |
2021
Please use a persistent id in citations: http://hdl.handle.net/2128/30825
Abstract: The thesis research involves the application of machine learning (ML) to various parts of a Monte Carlo algorithm called Hybrid Monte Carlo (HMC–also referred to as Hamiltonian Monte Carlo), with the hopes that the neural network (NN), once properly trained, will speed up parts of the HMC algorithm. I implemented a NN that replaces the force calculations needed by HMC. The NN has been very successful for a large hyper-parameter space, and improves computational scaling from volume cube (N^3) scaling (w/o NN) to volume square (N^2) scaling (w/ NN), where volume here represents the total space-time dimension of the problem. The physics that motivates these calculations involves strongly correlated electrons described by the Hubbard model on two-dimensional lattices of various geometries. This model has broad applicability to solid-state and condensed matter systems. I have successfully applied my NN to hexagonal lattices (relevant for graphene), square lattices, and also more complicated lattices such as the kagome lattice (this exhibit topological behavior). In all cases I quantified the regions of parameter space where the NN adequately replaced the force calculations of HMC, thus providing improved scaling. For regions where the NN failed, I looked at alternative NN architectures (such as Bayesian NNs). I have also looked at the possibility of replacing the entire HMC algorithm (except for the Metropolis-Hastings step) with a modified NN leapfrog using unsupervised/reinforcement learning.
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