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.
| Comments: | Accepted to ICML 2026; full camera-ready version will be updated later |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2508.11205 [cs.LG] |
| (or arXiv:2508.11205v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2508.11205 arXiv-issued DOI via DataCite |
From: Kookjin Lee [view email]
[v1]
Fri, 15 Aug 2025 04:30:27 UTC (22,283 KB)
[v2]
Sat, 2 May 2026 20:59:06 UTC (21,064 KB)
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