Physics-informed neural networks for operator equations with stochastic data

• URL: http://arxiv.org/abs/2211.10344v2
• Date: Fri, 3 May 2024 21:35:02 GMT
• Title: Physics-informed neural networks for operator equations with stochastic data
• Authors: Paul Escapil-Inchauspé, Gonzalo A. Ruz,
• Abstract summary: We consider the computation of statistical moments to operator equations with data. PINNs -- referred to as TPINNs -- allow to solve the induced tensor operator equations under minimal changes of existing PINNs code. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations.
• Score: 0.6445605125467572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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