Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks

TL;DR

This paper introduces ST-PINNs, a novel neural network approach that sequentially addresses multiple discontinuities in hydrodynamic problems, significantly improving accuracy in complex shock-interface interactions.

Contribution

The paper presents the first application of PINNs to 2D unsteady shock refraction problems, using a sequential separation-transfer method to handle multiple discontinuities.

Findings

ST-PINNs accurately capture sharp discontinuities.

ST-PINNs reduce solution errors in complex hydrodynamic problems.

First PINNs application to 2D shock refraction problems.

Abstract

Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose Separation-Transfer Physics Informed Neural Networks (ST-PINNs) to address such problems. By sequentially resolving discontinuities from strong to weak and leveraging transfer learning during training, ST-PINNs significantly reduce the problem complexity and enhance solution accuracy. To the best of our knowledge, this is the first study to apply a PINNs-based approach to the two-dimensional unsteady planar shock refraction problem, offering new insights into the application of PINNs to complex shock-interface interactions. Numerical experiments demonstrate that ST-PINNs more accurately capture sharp discontinuities and substantially reduce solution errors in hydrodynamic problems involving multiple discontinuities.