Physics-informed neural networks for operator equations with stochastic data
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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. This scheme can overcome the curse of dimensionality and covers 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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