A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations

Physics informed neural networks (PINNs) are a novel deep learning paradigm primed for solving forward and inverse problems of nonlinear partial differential equations (PDEs). By embedding physical information delineated by PDEs in feedforward neural networks, PINNs are trained as surrogate models for approximate solution to the PDEs without need of label data. Due to the excellent capability of neural networks in describing complex relationships, a variety of PINN-based methods have been developed to solve different kinds of problems such as integer-order PDEs, fractional PDEs, stochastic PDEs and integro-differential equations (IDEs). However, for the state-of-the-art PINN methods in application to IDEs,…