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

• URL: http://arxiv.org/abs/2505.20361v1
• Date: Mon, 26 May 2025 08:55:04 GMT
• Title: Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks
• Authors: Chuanxing Wang, Hui Luo, Kai Wang, Guohuai Zhu, Mingxing Luo,
• Abstract summary: We propose Separation-Transfer Physics Informed Neural Networks (ST-PINNs) to address such problems.<n>By sequentially resolving discontinuities from strong to weak, ST-PINNs significantly reduce the problem complexity and enhance solution accuracy.<n>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.
• Score: 6.839965440704237
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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