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math.NA2023★ 1 cited
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
Paul Schwerdtner, Philipp Schulze, Jules Berman +1
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear…
cs.LG2023★ 1 cited
Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks
Jules Berman, Benjamin Peherstorfer
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other p…