[论文解读] Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction

N. Benjamin Erichson, Michael Muehlebach+1 more|arXiv (Cornell University)|May 26, 2019

Model Reduction and Neural Networks参考文献 36被引用 69

一句话总结

该论文研究将Lyapunov稳定性原则纳入基于自编码器的流体流动预测，以提升物理信息神经模型的泛化能力和对噪声的鲁棒性。

ABSTRACT

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.

研究动机与目标

• 在神经网络中结合稳定性以解决科学问题的物理信息建模的动力
• 探索Lyapunov稳定性作为先验，以提高流体流动预测的泛化性和鲁棒性
• 评估在有噪声数据下，Lyapunov稳定的模型是否给出更低的预测不确定性。

提出的方法

• 使用结合物理信息约束、聚焦Lyapunov稳定性的自编码器架构。
• 分析强制Lyapunov稳定性对模型条件数和对参数调整鲁棒性的影响。
• 评估对流体流动预测的泛化误差和不确定性的影响。

实验结果

研究问题

• RQ1 是否在自编码器中强制Lyapunov稳定性可以提高流体流动预测的泛化性？
• RQ2 Lyapunov信息方法是否降低对噪声数据或参数变化的敏感性？
• RQ3 Lyapunov稳定性如何影响数据驱动的流体流动模型的鲁棒性与条件性？

主要发现

• Lyapunov稳定的模型在流体流动预测的泛化性能得到提升。
• 稳定性感知的模型相比非稳定性感知的同类，在预测不确定性方面更低。
• 将Lyapunov先验引入有助于模型在数据变动下的鲁棒性。