ImPINN: Improved Physics-informed neural networks for solving inverse problems

Physics-informed learning methods have gained significant attention as a function approximator for solving partial differential equation problems. However, the vanilla PINN tends to provide inaccurate solutions when solving inverse problems of partial differential equations with characteristics such as strong nonlinearity. To address this problem, we introduce a new approach, the Improved Physics-informed Neural Network (ImPINN), which combines improvement strategies to enhance the convergence and accuracy of the vanilla PINN method for solving inverse problems. The ImPINN method adopts adaptive ideas in the activation function, loss function and sampling strategy. These strategies have significantly increased the efficiency and accuracy of the vanilla PINN method during the feature fitting process. Numerical experiments demonstrate that the improved PINN performs better on Burgers, Allen-Cahn, Korteweg-de Vries, heat transfer and Navier-Stokes equations and reduces the relative error of the unknown parameters by up to about two orders of magnitude.