Optimal time sampling in physics-informed neural networks

arXiv:2404.18780v1 Announce Type: new
Abstract: Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which includes, when the equation is time-dependent, a time sampling. It was argued in the literature that the sampling need not be uniform but should overweight initial time instants, but no rigorous explanation was provided for these choice. In this paper we take some …

abstract applications arxiv computing cs.lg cs.na equation literature math.na networks neural networks paradigm part physics physics.comp-ph physics-informed pinn residual sampling scientific solve type