Physics-informed neural networks for operator equations with stochastic data

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 t...

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Authors: Paul Escapil-Inchauspé, Ruz, Gonzalo A
Format: Article
Language:English
Subjects:
Mathematical analysis
Neural networks
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422