Meta-learning Structure-Preserving Dynamics
This work addresses the limitation of many-query or parameter-varying scenarios in physical system modeling, offering a scalable solution for meta-learning across parametric families, though it is incremental as it builds on existing structure-preserving and meta-learning approaches.
The paper tackled the problem of training structure-preserving dynamics models for fixed system configurations, which requires costly retraining for new parameters, by introducing a modulation-based meta-learning framework that conditions models on latent representations of unknown parameters. The result is accurate predictions in few-shot learning settings without compromising physical constraints, as demonstrated on standard benchmarks.
Structure-preserving approaches to dynamics modeling have demonstrated great potential for modeling physical systems due to their strong inductive biases that enforce conservation laws and dissipative behavior. However, the resulting models are typically trained for fixed system configurations, requiring explicit knowledge of system parameters as well as costly retraining for each new set of parameters -- a major limitation in many-query or parameter-varying scenarios. Meta-learning offers a potential solution, but existing approaches like optimization-based meta-learning often suffer from training instability or limited generalization capability. Inspired by ideas from computer vision, we introduce a modulation-based meta-learning framework that directly conditions structure-preserving models on compact latent representations of potentially unknown system parameters, avoiding the need for gray-box system knowledge and explicit optimization during adaptation. Through the application of novel modulation strategies to parametric energy-conserving and dissipative systems, we enable scalable and generalizable learning across parametric families of dynamical systems. Experiments on standard benchmark problems demonstrate that our approach achieves accurate predictions in few-shot learning settings, without compromising on the essential physical constraints necessary for dynamical stability and effective generalization performance across parameter space.