@inproceedings{42163,
  abstract     = {{The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.}},
  author       = {{Offen, Christian and Ober-Blöbaum, Sina}},
  booktitle    = {{Geometric Science of Information}},
  editor       = {{Nielsen, F and Barbaresco, F}},
  keywords     = {{System identification, discrete Lagrangians, travelling waves}},
  location     = {{Saint-Malo, Palais du Grand Large, France}},
  pages        = {{569--579}},
  publisher    = {{Springer, Cham.}},
  title        = {{{Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}}},
  doi          = {{10.1007/978-3-031-38271-0_57}},
  volume       = {{14071}},
  year         = {{2023}},
}