Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
This addresses the need for more robust and stable data-driven models in scientific domains like fluid dynamics, though it is incremental as it builds on existing physics-informed methods.
The paper tackles the problem of improving neural network models for scientific problems by incorporating physics-informed prior knowledge, specifically Lyapunov stability for fluid flow prediction, resulting in improved generalization error and reduced prediction uncertainty.
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.