Physics-informed neural networks for operator equations with stochastic data
This work addresses the problem of efficiently computing statistical moments in stochastic operator equations for researchers in computational science and engineering, offering an incremental extension of existing PINNs methods.
The paper tackled the computation of statistical moments for operator equations with stochastic data by proposing Tensorized Physics-Informed Neural Networks (TPINNs), which solve induced tensor operator equations with minimal code changes and handle non-linear and time-dependent operators, demonstrating applicability and performance through exhaustive numerical experiments.
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.