Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction

TL;DR

This paper introduces physics-informed autoencoders that incorporate Lyapunov stability principles to enhance fluid flow prediction accuracy, robustness, and generalization by embedding physical stability constraints into neural network models.

Contribution

It presents a novel approach integrating Lyapunov stability into autoencoders for fluid dynamics, improving model robustness and generalization over traditional data-driven methods.

Findings

Models preserving Lyapunov stability improve generalization error.

Stability-aware models reduce prediction uncertainty.

Physics-informed autoencoders outperform standard models in fluid flow tasks.

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.