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

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.

References in corpus (4)

• Variational Learning of Euler-Lagrange Dynamics from Data
• Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems
• Hamiltonian Neural Networks with Automatic Symmetry Detection
• Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body

Cited by in corpus (2)

• Hamiltonian Neural Networks with Automatic Symmetry Detection
• Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery