OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle

TL;DR

This paper introduces OnsagerNet, a neural network-based approach for learning stable, interpretable dynamical models that incorporate physical principles, suitable for high-dimensional systems with slow manifolds, demonstrated on fluid dynamics and reduced order modeling.

Contribution

The paper presents a systematic method combining neural networks and a generalized Onsager principle to learn physically interpretable and stable dynamical systems from trajectory data.

Findings

Outperforms existing methods on benchmark ODE learning tasks.

Successfully models Rayleigh-Benard convection dynamics.

Learns Lorenz-like reduced models capturing key dynamics.

Abstract

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Benard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative systems.