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 performance; raising a variety of new promising research avenues.
@article{arxiv.2211.10344,
title = {Physics-informed neural networks for operator equations with stochastic data},
author = {Paul Escapil-Inchauspé and Gonzalo A. Ruz},
journal= {arXiv preprint arXiv:2211.10344},
year = {2024}
}