Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations

arXiv:2404.01145v1 Announce Type: cross
Abstract: Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that sequential-in-time training methods can be understood broadly as either optimize-then-discretize (OtD) or discretize-then-optimize (DtO) schemes, which are well known concepts in numerical analysis. The unifying perspective leads to novel stability and a posteriori error analysis results that provide insights into theoretical and numerical aspects that …

abstract arxiv cs.lg cs.na differential math.na networks neural networks shows solution solve training type work