Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks
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.
Cite
@article{arxiv.2505.20361,
title = {Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks},
author = {Chuanxing Wang and Hui Luo and Kai Wang and Guohuai Zhu and Mingxing Luo},
journal= {arXiv preprint arXiv:2505.20361},
year = {2025}
}