报告题目：Asymptotic-preserving PINNs for relaxation systems of conservation laws: Applications to the Euler equations
报 告 人：雷昕
工作单位：中国地质大学（北京）
报告时间：2026年11月3日上午8:00 -10:00.
地点：数信学院3412
报告摘要：We presents an innovative Asymptotic-Preserving Physics-Informed Neural Networks (APPINNs) framework for solving conservation law systems with enhanced numerical stability. The proposed methodology introduces relaxation terms to transform the original conservation laws into relaxation systems, effectively mitigating numerical oscillations when solving discontinuous solutions, particularly shock waves. A key aspect of solving relaxation systems involves maintaining rigorous attention to the long-term convergence and stability of the system state, ensuring strict adherence to the AP property. Through the incorporation of AP physics constraints, the proposed AP-PINNs demonstrate superior performance over traditional PINNs in solving complex wave phenomena. We provide rigorous theoretical proofs establishing the AP property of our network architecture. The methodology’s effectiveness is validated through comprehensive testing across multiple one- and two-dimensional cases, demonstrating exceptional capability in capturing various wave phenomena including shocks, rarefaction waves, contact discontinuities, and their complex interactions. Furthermore, we also analyze the impact of varying relaxation rates on AP-PINN performance, accompanied by detailed error quantification. The results indicate that AP-PINNs not only significantly enhance predictive performance but also enable robust and efficient simulations in compressible fluid dynamics applications.
报告人简介：雷昕，中国地质大学（北京）数理学院副教授、博士生导师。长期从事计算流体力学相关的研究工作，包括可压缩多相流问题的数值方法（涉及数值模拟多相流物质界面处的物理过程、抑制物质界面处的数值不稳定性现象）、基于物理信息神经网络的守恒律求解方法等。相关论文已发表于 J. Comput. Phys.、Phys. Fluids等本领域知名期刊。
