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

arXiv: https://arxiv.org/abs/2605.16682 · HTML: https://mlsanity.com/paper/2605.16682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 13 of 13)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Mamba-3: Improved Sequence Modeling using State Space Principles](https://mlsanity.com/paper/2603.15569/) (2026)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Learning Latent Graph Dynamics for Visual Manipulation of Deformable Objects](https://mlsanity.com/paper/2104.12149/) (2021)
- [Self-supervised contrastive learning performs non-linear system identification](https://mlsanity.com/paper/2410.14673/) (2024)
- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)
- [PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting](https://mlsanity.com/paper/2602.17998/) (2026)

## Abstract (arXiv)

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.