FENN: Feature-enhanced neural network for solving partial differential equations involving fluid mechanics (2501.11957v1)

Abstract: Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving strongly nonlinear PDEs involving fluid dynamics. In this study, inspired by the input design in surrogate modeling, we propose a feature-enhanced neural network. By introducing geometric features including distance and angle or physical features including the solution of the potential flow equation in the inputs of PINNs, FENN can more easily learn the flow, resulting in better performance in terms of both accuracy and efficiency. We establish the feature networks in advance to avoid the invalid PDE loss in FENN caused by neglecting the partial derivatives of the features with respect to space-time coordinates. Through five numerical experiments involving forward, inverse, and parametric problems, we verify that FENN generally reduces the computational cost of PINNs by approximately four times. In addition, the numerical experiments also demonstrate that the proposed method can reduce the number of observed data for inverse problem and successfully solve the parametric problem where PINNs fail.