Discovering Phase Space Structure in Learned Hamiltonian Systems

Abstract:Mechanics-inspired neural dynamical models improve interpretability and physical consistency, but they usually assume a known configuration space, fixed physical parameters, and deterministic prediction from a prescribed initial condition. We introduce Structured Phase Space GAN (SPS-GAN), a conditional generative model that learns structured dynamics from both Cartesian trajectories and video. SPS-GAN combines a port-Hamiltonian backbone with adversarial conditional generation, allowing conservative, dissipative, and forced systems to be represented in a single architecture. To infer latent mechanical structure from raw observations, we use a cyclic-coordinate loss that recovers both the system degrees of freedom and canonical coordinates without access to the true phase space. Experiments on simulated and real-world systems show that SPS-GAN improves trajectory accuracy over supervised dynamics baselines and video consistency over generative baselines, while consistently recovering the correct latent mechanical coordinates across observation modalities and dynamical regimes.

Accept to The 40th Annual Conference on Neural Information Processing Systems (NeurIPS 2026). Camera-ready to come

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY)

arXiv:2509.23003 [cs.LG]

(or arXiv:2509.23003v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2509.23003 Focus to learn more arXiv-issued DOI via DataCite

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