Efficiently Parameterized Neural Metriplectic Systems

Anthony Gruber, Kookjin Lee, Haksoo Lim, Noseong Park, Nathaniel Trask

Keywords: metriplectic systems, structure preservation, energy conservation, entropy stability, neural ODEs

TL;DR: General metriplectic systems are parameterized in a way which is universally approximating, bounded in error, and scales quadratically with the size of the system. This is leads to improvements over previous state of the art.

Abstract: Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with approximation results demonstrating its ability to accurately learn metriplectic dynamics from data as well as an error estimate indicating its potential for generalization to unseen timescales when approximation error is low. Examples are provided which illustrate performance in the presence of both full state information as well as when entropic variables are unknown, confirming that the proposed approach exhibits superior accuracy and scalability without compromising on model expressivity.

Primary Area: Machine learning for physical sciences (for example: climate, physics)

Submission Number: 7239