Physics-Informed Neural Networks (PINNs): Algorithms, Applications, and Software
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. In this talk, I will first present an overview of physics-informed neural networks (PINNs) for solving forward and inverse PDEs, which embed a PDE into the loss of the neural network using automatic differentiation. I will then discuss several approaches to improve the accuracy and efficiency of PINN, including a residual-based adaptive refinement (RAR) method, gradient-enhanced PINN (gPINN), and PINN with hard constraints (hPINN). I will also demonstrate the effectiveness of PINN to diverse problems. The PINN algorithm can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, I will present a Python library for PINNs, DeepXDE.