Identify then Realize: Contrastive Learning of Latent Port-Hamiltonian Dynamics from Partial Observations

Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We propose CIPHER, a two-stage identify-then-realize framework for learning latent port-Hamiltonian models of conservative and dissipative systems. First, a contrastive teacher jointly learns an encoder and a neural ODE to obtain predictive state representations from observation histories. Second, a student learns an invertible nonlinear coordinate transformation and port-Hamiltonian dynamics by matching encoded observed futures. We establish sufficient conditions for recovering the physical state up to a diffeomorphism and realizing its dynamics in port-Hamiltonian form. Across ten clean and noisy datasets, CIPHER is competitive with or outperforms state-of-the-art baselines by improving long-horizon forecast on complex systems. Further studies show robustness to over-specified latent dimensions and additional predictive gains from pH parameterization.