Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure
Authors: Peilun Li, Kaiyuan Tan, Daniel Moyer, Thomas Beckers
Abstract
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 study this problem for latent port-Hamiltonian systems, a structured class encompassing both conservative and dissipative dynamics. We propose a two-stage identify-then-project framework. First, a contrastive teacher learns continuous-time latent dynamics from partial observations. Then, a student projects the identified teacher representation and dynamics onto a port-Hamiltonian submanifold via a learned affine chart, yielding a physically consistent realization. As a conceptual counterfactual, we also consider a single-stage variant that jointly learns latent identification and port-Hamiltonian structure, but find it to be less reliable, motivating the proposed two-stage teacher-student framework. We show theoretically that affine projection is the natural bridge between the affine gauge of contrastive latent identification and the port-Hamiltonian systems. Empirically, we demonstrate that the proposed two-stage approach preserves the teacher's dynamics while enforcing physical structure, and performs more reliably than the single-stage alternative, particularly in dissipative regimes and high-dimensional visual settings.
World models built on recurrent state space architectures enable efficient latent imagination, yet remain physically unstructured, producing dynamics that violate conservation and dissipative principles. We introduce a unified Port-Hamiltonian framework that remedies this through three synergistic mechanisms. First, we embed implicit physical priors into recurrent transitions by modeling projected latent evolution as action controlled energy routing governed by flow and dissipation, biasing the projected PH phase space toward a more compact and physically structured representation. Second, we develop a kinematics aware energy world model that estimates the Hamiltonian and power balance from proprioceptive observations, providing an explicit physical signal for thermodynamic reasoning. Third, leveraging these energy gradients, we establish an energy guided Actor-Critic that uses Lagrangian multipliers to regularize policy optimization toward lower energy and smoother control. Across visual control benchmarks, this paradigm not only attains superior asymptotic returns but also elevates internal simulator fidelity by establishing a tighter, lower variance alignment between imagined and real rewards, all while reducing latent phase space volume by 4.18-8.41%, energy consumption by up to 7.80%, and mean squared jerk by up to 9.38%.
Identifying latent dynamical systems from noisy, high-dimensional measurements is a central problem at the intersection of representation learning, system identification, and scientific discovery. We present DYSCO, a multi-view temporal contrastive learning algorithm that jointly recovers latent trajectories and the governing dynamics from such observations, by leveraging multiple independent noisy views of the same underlying process to disentangle signal from noise. By parameterizing the dynamics in a structured functional basis, our framework further enables symbolic recovery of the governing equations within an affine gauge. We offer theoretical guarantees for strong identification up to an affine indeterminacy, extending prior identifiability results to the realistic setting of noisy nonlinear observations. Empirically, we demonstrate accurate recovery of both latent trajectories and flow fields across a diverse set of dynamical regimes (e.g., chaotic, oscillatory, and metastable) under both Gaussian and Poisson observation noise, the latter being particularly relevant for neural recordings.
We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach co-learns a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-aware data collection. At each iteration, the system model is refined using trajectory data collected under the current control policy, and the controller is re-optimized on the updated model. Both components are parameterized by neural networks that embed the pH dynamics and EB-PBC structure, ensuring interpretability in terms of energy interactions. The learned controller renders the closed-loop system inherently passive and provably stable, and exploits passive plant dynamics without canceling the natural potential. A dissipation regularization enforces strict energy decay during training, thereby enhancing robustness to sim-to-real gaps. The proposed framework is validated on state-regulation and swing-up tasks for planar and torsional pendulum systems.