Physics-informed neural networks for operator equations with stochastic data

arXiv:2211.10344v2 Announce Type: replace
Abstract: We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and …

abstract application arxiv code computation cs.lg cs.na data enabling linear math.na moments networks neural networks non-linear physics physics-informed solve statistical stochastic tensor type