用分离转移法提升PINN对多激波问题的求解精度
Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks
- 分步处理强弱激波，利用迁移学习降低求解复杂度
- 在二维非定常激波折射问题上误差显著下降
- 适合研究复杂激波相互作用的流体力学研究者
尽管物理信息神经网络（PINNs）在科学计算中取得显著进展，但在求解含多个间断的流体动力学问题时仍面临挑战。本文提出分离-转移物理信息神经网络（ST-PINNs），通过从强到弱逐次解析间断，并在训练中引入迁移学习，显著降低问题复杂度并提升解的精度。据我们所知，这是首次将基于PINNs的方法应用于二维非定常平面激波折射问题，为PINNs在复杂激波界面相互作用中的应用提供了新视角。数值实验表明，ST-PINNs能更准确捕捉尖锐间断，大幅减少多间断流体问题的解误差。
原文摘要 · Abstract (English)
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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