A nonlocal physics-informed deep learning framework using the peridynamic differential operator

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well identification equation parameters. performance existing PINN approaches, however, may degrade in presence sharp gradients, result inability network to capture behavior globally. We posit that this shortcoming be remedied by introducing long-range (nonlocal) interactions network's input, addition short-range (local) space time variables. Following ansatz, here we develop nonlocal approach using Peridynamic Differential Operator (PDDO)---a numerical method which removes spatial derivatives governing equations. Because PDDO functions can readily incorporated neural architecture, nonlocality does not modern deep-learning algorithms. apply PDDO-PINN material parameters solid mechanics and, specifically, elastoplastic deformation domain subjected indentation rigid punch, mixed displacement--traction boundary condition leads localized gradients solution. document superior with respect local both accuracy parameter inference, illustrating its potential simulation discovery whose develops gradients.