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Learning discrete Lagrangians for variationalPDEs from data and detection of travelling waves

by   Christian Offen, et al.
Universität Paderborn

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.


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Learning of Lagrangian densities from data

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