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@ARTICLE{Guo:905463,
      author       = {Guo, Yue and Dietrich, Felix and Bertalan, Tom and
                      Doncevic, Danimir and Dahmen, Manuel and Kevrekidis, Ioannis
                      G. and Li, Qianxiao},
      title        = {{P}ersonalized {A}lgorithm {G}eneration: {A} {C}ase {S}tudy
                      in {M}eta-{L}earning {ODE} {I}ntegrators},
      reportid     = {FZJ-2022-00704},
      year         = {2021},
      abstract     = {We study the meta-learning of numerical algorithms for
                      scientific computing, which combines the mathematically
                      driven, handcrafted design of general algorithm structure
                      with a data-driven adaptation to specific classes of tasks.
                      This represents a departure from the classical approaches in
                      numerical analysis, which typically do not feature such
                      learning-based adaptations. As a case study, we develop a
                      machine learning approach that automatically learns
                      effective solvers for initial value problems in the form of
                      ordinary differential equations (ODEs), based on the
                      Runge-Kutta (RK) integrator architecture. By combining
                      neural network approximations and meta-learning, we show
                      that we can obtain high-order integrators for targeted
                      families of differential equations without the need for
                      computing integrator coefficients by hand. Moreover, we
                      demonstrate that in certain cases we can obtain superior
                      performance to classical RK methods. This can be attributed
                      to certain properties of the ODE families being identified
                      and exploited by the approach. Overall, this work
                      demonstrates an effective, learning-based approach to the
                      design of algorithms for the numerical solution of
                      differential equations, an approach that can be readily
                      extended to other numerical tasks.},
      cin          = {IEK-10},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112) / HDS LEE - Helmholtz
                      School for Data Science in Life, Earth and Energy (HDS LEE)
                      (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1121 / G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2105.01303},
      howpublished = {arXiv:2105.01303},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2105.01303;\%\%$},
      url          = {https://juser.fz-juelich.de/record/905463},
}