PINN-LPCDD: Physics-Informed Neural Network with Learnable and Physically Consistent Domain Decomposition for Compressible Multi-Medium Flows

Abstract

The physics-informed neural network (PINN) faces significant challenges when solving compressible multi-medium flows, including the inability to locate interface positions, poor approximation of discontinuities, and difficulty in handling high-pressure-ratio problems between media with large stiffness differences. To address these issues, we propose PINN with Learnable and Physically Consistent Domain Decomposition (PINN-LPCDD), a framework that incorporates the sharp interface method (SIM) into PINNs for solving compressible multi-medium flows. Firstly, we design separate sub-networks for each medium with learnable parameters to automatically learn interface positions, so that the domain decomposition is physically consistent, and the contact discontinuity at the interface is naturally sharp. Secondly, the Euler equations with artificial viscosity are solved to enhance robustness when handling problems involving shock waves. Lastly, the scaling invariance of the Euler equations is exploited to facilitate the solution of high pressure ratio problems. Numerical experiments on air-air, air-helium, air-water, and air-R22 problems demonstrate the acceptable accuracy of the proposed method in simulating multi-medium flows.