Learning partially observed systems with neural Hamiltonian ordinary differential equations

2026-05-22

AI Summary

This work proposes a modeling framework that integrates Hamiltonian neural networks with neural ordinary differential equations to address partially observable dynamical systems. By leveraging only supervisory signals from observable variables, the method jointly infers latent states and learns the complete system dynamics. The approach embeds physical priors—specifically symmetry-aware coordinate transformations and separable energy structures—to rigorously preserve Hamiltonian dynamical properties, thereby significantly enhancing long-term prediction stability and generalization. Evaluated across a range of systems—from linear oscillators to the chaotic three-body problem—the model accurately reconstructs both observed and unobserved states, consistently outperforming purely data-driven baselines.

Abstract

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially observed settings, where some state variables are completely unobserved and must be inferred without direct supervision. Here, we present neural Hamiltonian ordinary differential equations (NHODE), a framework that combines Hamiltonian neural networks (HNNs) with neural ordinary differential equations (neural ODEs) to learn partially observed dynamical systems from data. The Hamiltonian structure enforces energy conservation by construction, while the neural ODE framework enables a flexible training procedure that allows the loss to be defined only on observed variables. We also incorporate additional physical constraints through symmetry-aware coordinate transformations and separable energy formulations. The framework is evaluated on systems of increasing complexity, from linear and nonlinear mass-spring systems to the chaotic three-body problem. Across all examples, increasing the amount of embedded physical structure improves the accuracy and long-horizon stability of the predictions. Even in the most challenging regimes, the NHODE framework captures both observed and latent dynamics, whereas purely data-driven baselines become unstable.

Problem

• partially observed systems
• dynamical systems
• Hamiltonian systems
• neural ODEs
• latent dynamics

Innovation

• neural Hamiltonian ODE
• partially observed systems
• physics-informed learning
• energy conservation
• symmetry-aware modeling