Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure

2026-05-15

AI Summary

This work addresses the challenge of modeling latent states and their dynamics under high-dimensional partial observations by proposing a two-stage “identification–projection” framework. First, a teacher model employs contrastive learning to identify continuous-time latent dynamics directly from observational data. Subsequently, a student model projects these latent representations and their dynamics onto a port-Hamiltonian submanifold via a learnable affine mapping, thereby embedding physically consistent structural constraints. This approach uniquely integrates contrastive learning with port-Hamiltonian systems, and theoretical analysis demonstrates that affine projection serves as a natural bridge between data-driven identification and physical consistency. Empirical results show that the method significantly outperforms single-stage joint learning approaches in both dissipative systems and high-dimensional visual tasks, achieving superior stability and reliability.

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.

Problem

• latent dynamics
• partial observations
• port-Hamiltonian systems
• representation learning
• physics-aware modeling

Innovation

• contrastive learning
• port-Hamiltonian systems
• latent dynamics
• affine projection
• teacher-student framework