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arXiv · 2211.10344

Physics-informed neural networks for operator equations with stochastic data

Paul Escapil-Inchauspé·Gonzalo A. Ruz
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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 performance; raising a variety of new promising research avenues.

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Paul Escapil-Inchauspé, Gonzalo A. Ruz. 2022-11-15. Physics-informed neural networks for operator equations with stochastic data. https://arxiv.org/abs/2211.10344

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