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@INPROCEEDINGS{FernandezCorral:601475,
      author       = {Fernandez Corral, Alvaro and Mendoza, Sebastian and
                      Yachmenev, Andrey and Iske, Armin and Küpper, Jochen},
      title        = {{L}earning phase-space flows using time-discrete implicit
                      {R}unge-{K}utta {PINN}s},
      reportid     = {PUBDB-2024-00205},
      pages        = {26},
      year         = {2024},
      note         = {https://bib-pubdb1.desy.de/record/603801},
      abstract     = {We present a computational framework for obtaining
                      multidimensional phase-space solutions of systems of
                      non-linear coupled differential equations, using high-order
                      implicit Runge-Kutta Physics-Informed Neural Networks
                      (IRK-PINNs) schemes. Building upon foundational work
                      originally solving differential equations for fields
                      depending on coordinates [J. Comput. Phys. 378, 686
                      (2019)],we adapt the scheme to a context where the
                      coordinates are treated as functions. This modification
                      enables us to efficiently solve equations of motion for a
                      particle in an external field. Our scheme is particularly
                      useful for explicitly time-independent and periodic fields.
                      We apply this approach to successfully solve the equations
                      of motion for a mass particle placed in a central force
                      field and acharged particle in a periodic electric field.},
      month         = {Mar},
      date          = {2024-03-19},
      organization  = {International Conference on Scientific
                       Computing and Machine Learning 2024,
                       Kyoto (Japan), 19 Mar 2024 - 23 Mar
                       2024},
      cin          = {FS-CFEL-CMI / UHH / UNI/CUI / UNI/EXP},
      cid          = {I:(DE-H253)FS-CFEL-CMI-20220405 / I:(DE-H253)UHH-20231115 /
                      $I:(DE-H253)UNI_CUI-20121230$ /
                      $I:(DE-H253)UNI_EXP-20120731$},
      pnm          = {631 - Matter – Dynamics, Mechanisms and Control
                      (POF4-631) / HIDSS-0002 - DASHH: Data Science in Hamburg -
                      Helmholtz Graduate School for the Structure of Matter
                      $(2019_IVF-HIDSS-0002)$ / AIM, DFG project
                      G:(GEPRIS)390715994 - EXC 2056: CUI: Advanced Imaging of
                      Matter (390715994)},
      pid          = {G:(DE-HGF)POF4-631 / $G:(DE-HGF)2019_IVF-HIDSS-0002$ /
                      G:(GEPRIS)390715994},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)8},
      url          = {https://bib-pubdb1.desy.de/record/601475},
}