对比两种无需时间积分的参数化降维模型，解决溃坝问题。
Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem
- 用PINN和张量型降阶模型直接学习参数到状态的映射
- 在参数外推时，张量模型精度更高且更稳定
- 引入激波感知采样可显著提升PINN鲁棒性
我们构建了两种参数化数据驱动降维模型：物理信息神经网络（PINN）与非侵入式张量型降阶模型（TROM），并应用于一维浅水溃坝问题。两种模型均无需时间积分，直接学习从空间、时间及溃坝参数到物理状态的映射关系。我们详细比较了模型在样本外及参数外推情况下的表现。结果表明，引入激波感知采样对提升PINN模型的鲁棒性至关重要。
原文摘要 · Abstract (English)
We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break problem. Both reduced models do not require time integration and learn a direct solution map from space, time, and dam-break parameters to the physical state. We present a detailed comparison for out-of-sample and extrapolated parameter values. In addition, we demonstrate that it is essential to introduce shock-aware collocation to improve the robustness of the PINN model.
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