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arXiv · 2302.08232

Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves

Christian Offen·Sina Ober-Blöbaum
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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.

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Christian Offen, Sina Ober-Blöbaum. 2023-02-16. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. https://doi.org/10.1007/978-3-031-38271-0_57

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