Regularized Action-conditioned Hamiltonian Generative Networks for with External Control

Abstract

Recent advancements in physics-informed machine learning have successfully leveraged Hamiltonian mechanics to learn system dynamics from data. In this work, we build upon Action-Conditioned Hamiltonian Generative Networks (ACHGN), a framework that extends these principles to non-canonical inputs and systems subject to external control. We identify a set of architectural changes from recent literature which contribute to significantly improved dynamics predictions. This novel ACHGN++ architecture generally outperforms ablations and baselines on a set of seven dissipation-free classical control tasks with dynamics of varying complexity. In addition, we highlight a limitation of the architecture and propose physics-informed regularization to enforce separation between the learned dynamics and external forces. We demonstrate that this regularization not only improves long-term prediction but also ensures the learned dynamics align more strongly with the intended Hamiltonian structure, as quantified by two novel evaluation metrics introduced in this work. Finally, we show that ACHGN++ is capable of learning an interpretable latent phase space which behaves similarly to real canonical coordinates on a pendulum system.