Physics Informed Neural Networks for a Peridynamic Inverse Problem
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Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation. We show that the selection of a RBF is necessary to achieve meaningful solutions and that, with classical choices, non-admissible solutions are provided. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-PINN to the exact solutions.
