Meta-learning Structure-Preserving Dynamics

TL;DR

This paper explores modulation-based meta-learning techniques within structure-preserving models to enable accurate, few-shot adaptation and robust generalization in physical system dynamics without explicit parameterization.

Contribution

It introduces novel modulation strategies into Hamiltonian learning frameworks, improving generalization and adaptation in modeling physical systems.

Findings

Modulation techniques improve few-shot learning of dynamics.

Models generalize well across different system parameters.

Conservation laws are maintained during adaptation.

Abstract

Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative behavior. However, these models are typically trained on a per-configuration basis, requiring explicit knowledge of system parameters and costly retraining when these parameters vary. While meta-learning provides a potential remedy, optimization-based approaches can suffer from limited generalizability. Motivated by recent advances in modulation-based learning aimed at mitigating these drawbacks, we systematically investigate the use of modulation techniques in learning conservative dynamical systems. We study a range of existing modulation strategies alongside newly proposed variants, integrating them into a Hamiltonian learning framework without requiring an explicit system parameterization. Through extensive experiments on benchmark problems, we demonstrate that modulation-based meta-learning enables accurate few-shot adaptation, achieving robust generalization across parameter space without compromising the conservation of key invariants responsible for the dynamics.