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We propose a systematic method for learning stable and physicallyinterpretable dynamical models using sampled trajectory data from physicalprocesses based on a generalized Onsager principle. The learned dynamics areautonomous ordinary differential equations parameterized by neural networksthat retain clear physical structure information, such as free energy,diffusion, conservative motion and external forces. For high dimensionalproblems with a low dimensional slow manifold, an autoencoder with metricpreserving regularization is introduced to find the low dimensional generalizedcoordinates on which we learn the generalized Onsager dynamics. Our methodexhibits clear advantages over existing methods on benchmark problems forlearning ordinary differential equations. We further apply this method to studyRayleigh-Benard convection and learn Lorenz-like low dimensional autonomousreduced order models that capture both qualitative and quantitative propertiesof the underlying dynamics. This forms a general approach to building reducedorder models for forced dissipative systems.

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