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@PHDTHESIS{Rodekamp:1030406,
      author       = {Rodekamp, Marcel},
      title        = {{M}achine {L}earning for {P}ath {D}eformation and
                      {B}ayesian {D}ata {A}nalysis in {S}elected {L}attice {F}ield
                      {T}heories},
      school       = {Bonn},
      type         = {Dissertation},
      address      = {Bonn},
      publisher    = {Universitäts- und Landesbibliothek Bonn: bonndoc},
      reportid     = {FZJ-2024-05279},
      pages        = {151},
      year         = {2024},
      note         = {Dissertation, Bonn, 2024},
      abstract     = {Our collective understanding of the laws of nature has a
                      long history of an intricate interplay between theoretical
                      considerations and experimental falsification. As
                      computational power increases, simulations, at the interface
                      between theory and experiment, have taken an increasing role
                      in scientific discovery. In particular, first-principles
                      calculations are indispensable for systems with
                      non-perturbative behavior, requiring simulations to test
                      models against experiment. One widely accepted and deployed
                      method involves formulating the theory on a finite lattice
                      and then applying a Monte Carlo simulation. However, with
                      increasing interest in such simulations practical and
                      fundamental challenges arise, such as computational demand
                      and the numerical sign problem. In the following, I discuss
                      selected aspects for simulations of strongly correlated
                      systems, namely the Hubbard model and lattice quantum
                      chromodynamics. This encompasses methods to mitigate the
                      numerical sign problem and (Bayesian) analysis of simulation
                      results, in particular fitting methods and the treatment of
                      excited state contamination.The Hubbard model describes
                      systems of strongly correlated electrons and is used often
                      in studying chemical compounds. First principle studies of
                      this model are almost exclusively done using Monte Carlo
                      techniques, with the exception being very small systems
                      where direct diagonalization methods are feasible. However,
                      away from half filling, Monte Carlo methods struggle because
                      of the numerical sign problem. While the sign problem is
                      unlikely to be completely solved, methods that reduce its
                      impact are very valuable in expanding the computable
                      parameter space. Leveraging theoretical developments on path
                      deformations, I demonstrate that machine learning techniques
                      can be used to mitigate the sign problem. In particular, I
                      train complex-valued neural networks to serve as a
                      parameterization of a sign-optimized manifold related to
                      Lefschetz thimbles. These methods were developed and tested
                      on doped graphene sheets, modelled by a small number of ions
                      with periodic boundary conditions, at fixed temporal
                      discretization and temperature.Renewable energy is a
                      critical aspect of modern research to reduce effects of
                      climate change. Despite the enormous energy cost of
                      producing solar panels, they are a valuable element in the
                      electricity production. Organic solar cells show great
                      promise in reducing costs and allowing for flexibility.
                      Unfortunately, to date their efficiency falls behind their
                      silicon-based competitors. By studying the electronic
                      structure of certain chemical compounds that are usable for
                      organic solar cells, further development in this area can be
                      fostered. This motivates my work in the molecule C20 H12
                      perylene, which can be used as an acceptor material in
                      organic solar cells. This molecule is typically not at half
                      filling, so any simulation requires methods to mitigate the
                      sign problem.The study of perylene shown here requires the
                      analysis of a large data set, of the order of O (2000)
                      correlators, which is only feasible with an automated
                      analysis procedure. In this thesis I present such an
                      automatic routine based on Bayesian analysis using the
                      Akaike information criterion.Finally, I shift the focus to
                      particle physics to calculate aspects of the internal
                      structure of hadrons. Hadrons are primarily governed by the
                      strong interaction, i.e. described by quantum chromodynamics
                      (QCD). In this theory, the internal structure is modelled by
                      the correlation between spatial and momentum distributions
                      of all constituents. Many details of these distributions
                      remain to be calculated. In this thesis, I use lattice QCD
                      to calculate the 2nd moment of parton distribution functions
                      (PDFs) for the nucleon. These are the average momentum
                      fractions carried by the considered parton of the nucleon. I
                      analyze two ensembles at the physical pion mass to obtain
                      the moments of unpolarized, polarized, and transversity PDF
                      for the nucleon.},
      cin          = {JSC / CASA},
      cid          = {I:(DE-Juel1)JSC-20090406 / I:(DE-Juel1)CASA-20230315},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / SDS005 - Towards an
                      integrated data science of complex natural systems
                      (PF-JARA-SDS005)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(DE-Juel-1)PF-JARA-SDS005},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.34734/FZJ-2024-05279},
      url          = {https://juser.fz-juelich.de/record/1030406},
}