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000906503 005__ 20230123101916.0
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000906503 037__ $$aFZJ-2022-01482
000906503 041__ $$aEnglish
000906503 1001_ $$0P:(DE-Juel1)187395$$aJohn, Chelsea Maria$$b0$$eCorresponding author
000906503 245__ $$aInvestigating Machine Learning methods to replace Hybrid Monte Carlo in simulations of Hubbard Model$$f - 2021-12-06
000906503 260__ $$c2021
000906503 300__ $$avi, 83
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000906503 3367_ $$02$$2EndNote$$aThesis
000906503 3367_ $$2BibTeX$$aMASTERSTHESIS
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000906503 502__ $$aMasterarbeit, Rheinische Friedrich-Wilhelms-Universität Bonn, 2021$$bMasterarbeit$$cRheinische Friedrich-Wilhelms-Universität Bonn$$d2021
000906503 520__ $$aThe 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.
000906503 536__ $$0G:(DE-HGF)POF4-5111$$a5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511)$$cPOF4-511$$fPOF IV$$x0
000906503 8564_ $$uhttps://juser.fz-juelich.de/record/906503/files/PhysicsMasterThesis.pdf$$yOpenAccess
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000906503 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)187395$$aForschungszentrum Jülich$$b0$$kFZJ
000906503 9131_ $$0G:(DE-HGF)POF4-511$$1G:(DE-HGF)POF4-510$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5111$$aDE-HGF$$bKey Technologies$$lEngineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action$$vEnabling Computational- & Data-Intensive Science and Engineering$$x0
000906503 9141_ $$y2022
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000906503 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
000906503 9201_ $$0I:(DE-Juel1)IAS-4-20090406$$kIAS-4$$lTheorie der Starken Wechselwirkung$$x1
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