Efficiently Parameterized Neural Metriplectic Systems

TL;DR

This paper introduces a scalable neural approach for learning metriplectic systems that guarantees energy conservation and entropy stability, with proven approximation capabilities and strong empirical performance.

Contribution

It presents a novel neural parametrization method for metriplectic systems that is both scalable and provably stable, improving upon previous approaches.

Findings

Achieves quadratic scaling with state size and data rank

Proven to conserve energy and maintain entropy stability

Demonstrates superior accuracy and scalability in experiments

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.