Discovering Phase Space Structure in Learned Hamiltonian Systems

The paper introduces Structured Phase Space GAN (SPS‑GAN), a conditional generative model that learns structured dynamics from Cartesian trajectories and video. SPS‑GAN integrates a port‑Hamiltonian backbone with adversarial conditional generation, enabling representation of conservative, dissipative, and forced systems within a single architecture. Using a cyclic‑coordinate loss, the model recovers system degrees of freedom and canonical coordinates from raw observations, achieving better trajectory accuracy than supervised dynamics baselines and improved video consistency over generative baselines while consistently identifying correct latent mechanical coordinates.

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