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

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.

@article{wang2025_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 }
}