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@MASTERSTHESIS{John:906503,
      author       = {John, Chelsea Maria},
      title        = {{I}nvestigating {M}achine {L}earning methods to replace
                      {H}ybrid {M}onte {C}arlo in simulations of {H}ubbard
                      {M}odel},
      school       = {Rheinische Friedrich-Wilhelms-Universität Bonn},
      type         = {Masterarbeit},
      reportid     = {FZJ-2022-01482},
      pages        = {vi, 83},
      year         = {2021},
      note         = {Masterarbeit, Rheinische Friedrich-Wilhelms-Universität
                      Bonn, 2021},
      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.},
      cin          = {JSC / IAS-4},
      cid          = {I:(DE-Juel1)JSC-20090406 / I:(DE-Juel1)IAS-4-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)19},
      url          = {https://juser.fz-juelich.de/record/906503},
}