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.

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 operators. In addition to being provably energy-conserving and entropy-stable, the proposed neural metriplectic systems (NMS) approach includes approximation results that demonstrate its ability to accurately learn metriplectic dynamics from data, along with an error estimate that indicates its potential for generalization to unseen timescales when the approximation error is low. Examples are provided to illustrate performance both with full state information available and when entropic variables are unknown, confirming that the NMS approach exhibits superior accuracy and scalability without compromising on model expressivity.

Primary Area: learning on time series and dynamical systems

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Submission Number: 8925