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@PHDTHESIS{Koeppe:819355,
      author       = {Koeppe, Arnd},
      othercontributors = {Markert, Bernd and Herty, Michael},
      title        = {{D}eep learning in the finite element method},
      volume       = {IAM-11},
      school       = {Rheinisch-Westfälische Technische Hochschule Aachen},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2021-04990},
      series       = {Report. IAM, Institute of General Mechanics},
      pages        = {1 Online-Ressource : Illustrationen, Diagramme},
      year         = {2021},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, Rheinisch-Westfälische Technische
                      Hochschule Aachen, 2021},
      abstract     = {In mechanics and engineering, the Finite Element Method
                      (FEM) represents the predominant numerical simulation
                      method. It is extraordinarily modular and flexible since it
                      can simulate complex structures assembled from generic
                      elements and utilizing various constitutive models. However,
                      nonlinear problems, such as elastoplasticity, demand many
                      Degrees of Freedom (DOF) and numerous iterations, which make
                      the FEM numerically expensive. To increase numerical
                      efficiency, data-driven algorithms and Artificial
                      Intelligence (AI) offer an attractive approach to infer
                      accurate nonlinear solutions from reduced-order inputs,
                      thereby accelerating simulations. Inspired by the human
                      brain, deep learning algorithms, i.e., (artificial) neural
                      networks, organize and connect numerous neurons in layers
                      and cells to train universal function approximations. Neural
                      networks have demonstrated excellent performance and
                      efficiency through parallelization in various applications.
                      Because of the myriads of neurons and possible ways to
                      connect them, neural networks often elude human
                      understanding. Therefore, simpler models have been favored,
                      even if they exhibit inferior performance. This thesis aims
                      to integrate deep learning algorithms into the FEM,
                      accelerate computations, and interpret neural networks in
                      mechanics. Towards those objectives, a data-driven
                      methodology is developed that deducts strategies to design
                      neural networks for mechanics. Moreover, inductive
                      approaches search optimal neural network configurations and
                      explain neural network learning. Leveraging the fundamental
                      data structure in mechanical balance equations, the
                      data-driven methodology yields strategies and methods to
                      interface neural networks with the FEM at three integration
                      levels. At the highest level, intelligent surrogate models
                      substitute entire finite element models and achieve
                      efficient computations. At the lowest level, intelligent
                      constitutive models offer flexibility, modularity, and
                      straightforward integration. Combining the advantages of
                      both approaches, intelligent meta elements yield
                      considerable speed-ups and flexibility using substructuring.
                      Additionally, strategies for data generation, preprocessing,
                      and postprocessing translate and augmented mechanical data
                      to train new neural network architectures with convolutions
                      and recursions. Finally, a novel explainable AI approach
                      interprets the black box of Recurrent Neural Networks
                      (RNNs). Focusing on elastoplasticity, numerical
                      demonstrators establish the performance of the deducted
                      methods and strategies. Achieving considerable speed-ups by
                      several orders of magnitude, mechanical field quantities are
                      inferred accurately. Lastly, the new explainable AI approach
                      investigates RNNs trained for constitutive behavior.},
      cin          = {411110},
      ddc          = {620},
      cid          = {$I:(DE-82)411110_20140620$},
      typ          = {PUB:(DE-HGF)11 / PUB:(DE-HGF)3},
      doi          = {10.18154/RWTH-2021-04990},
      url          = {https://publications.rwth-aachen.de/record/819355},
}