In addition to providing high-profile successes in computer vision and
natural language processing, neural networks also provide an emerging set of
techniques for scientific problems. Such data-driven models, however, typically
ignore physical insights from the scientific system under consideration. Among
other things, a physics-informed model formulation should encode some degree of
stability or robustness or well-conditioning (in that a small change of the
input will not lead to drastic changes in the output), characteristic of the
underlying scientific problem. We investigate whether it is possible to include
physics-informed prior knowledge for improving the model quality (e.g.,
generalization performance, sensitivity to parameter tuning, or robustness in
the presence of noisy data). To that extent, we focus on the stability of an
equilibrium, one of the most basic properties a dynamic system can have, via
the lens of Lyapunov analysis. For the prototypical problem of fluid flow
prediction, we show that models preserving Lyapunov stability improve the
generalization error and reduce the prediction uncertainty.

该论文探讨了如何将物理先验知识加入数据驱动模型，提高模型的质量和稳定性，并以 Lyapunov 分析为视角，通过研究液体流动预测的典型问题，验证了保持 Lyapunov 稳定性的模型可以提高泛化性能并减少预测不确定性。