  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 peridynamic kernel in the nonlocal
formulation of classical wave equation, resulting in what we call RBF-iPINN. We
show that the selection of an RBF is necessary to achieve meaningful solutions,
that agree with the physical expectations carried by the data. We support our
results with numerical examples and experiments, comparing the solution
obtained with the proposed RBF-iPINN to the exact solutions.
