Nonlinear embeddings for conserving Hamiltonians and other quantities with neural Galerkin schemes

DOI10.1137/23m1607799MaRDI QIDQ6623695

Philipp Schulze, Benjamin Peherstorfer, Jules Berman, Paul Schwerdtner

Publication date: 24 October 2024

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsmodel reductionstructure preservationDirac-Frenkel variational principledeep networksconservation of quantitiesneural Galerkin schemes

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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