改进PINNs损失权重策略，提升流体模拟的稳定性和精度。
Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamics
- 设计双维度加权方案，兼顾可量化与不可量化项
- 高佩克莱数对流扩散问题下实现稳定准确预测
- 适合需要鲁棒数值解的流体力学研究者
物理信息神经网络（PINNs）为求解偏微分方程提供无网格框架，但对损失权重选择敏感。本文提出两种二维分析加权策略：一种基于可量化的项，另一种还纳入不可量化的项以实现更均衡训练。在热传导、对流扩散和盖式腔流等基准测试中，第二种方案显著优于均等加权，在高佩克莱数对流扩散问题中，传统求解器失效时，本方法仍能实现稳定且精确的预测，凸显其在计算流体力学问题中的鲁棒性与泛化能力。
原文摘要 · Abstract (English)
Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also incorporating unquantifiable terms for more balanced training. Benchmarks on heat conduction, convection diffusion, and lid driven cavity flows show that the second scheme consistently improves stability and accuracy over equal weighting. Notably, in high Peclet number convection diffusion, where traditional solvers fail, PINNs with our scheme achieve stable, accurate predictions, highlighting their robustness and generalizability in CFD problems.
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