Research map / Probabilistic and scientific modeling / Dynamical systems

Discovering Phase Space Structure in Learned Hamiltonian Systems

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Physics-informed dynamics learning

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes SPS-GAN, a conditional GAN with a port-Hamiltonian latent phase-space backbone and a port-Hamiltonian cyclic-coordinate loss, that generates trajectories and videos and recovers active degrees of freedom and canonical coordinates.

Problem

Mechanics-inspired neural dynamics models assume known configuration spaces and parameters and are deterministic predictors, while generative models do not recover active phase-space structure from non-canonical observations (Cartesian trajectories or video).

Approach

Combine a conditional GAN with a port-Hamiltonian latent dynamics model and extend the cyclic-coordinate loss to account for dissipation and forcing, so that redundant coordinate-momentum pairs become dynamically inactive and active DoFs can be identified via PCA.

Key results

• SPS-GAN achieves the lowest trajectory MSE on four of five conservative systems (e.g., double pendulum 3.25e-2 vs HNN 1.25e-1) and on both non-conservative systems (e.g., damped pendulum 4.57e-4 vs pHNN 4.76e-4).
• SPS-GAN attains the lowest FVD on all five rendered conservative systems (e.g., mass-spring 25.63 vs HGAN 45.68; three-body 89.08 vs HGAN 1981.10).
• PCA on learned coordinates recovers the ground-truth DoF on all reported systems, e.g., one for single pendulum and two for double pendulum.

Surprising findings

• On the damped pendulum and single-pendulum conservative control, differences from baselines are small, and LatentODE/NeuralODE beat SPS-GAN on the mass-spring system.

Limitations

• Assumes the observed dynamics are port-Hamiltonian and does not extend to systems lacking this representation.
• Trajectory evaluation aligns generated initial conditions to the simulator, so it is not a direct comparison to predictive baselines.
• Real-world video energy checks depend on centroid extraction error.

Experimental setup

Datasets: simulated mass-spring, pendulum, double pendulum, two-body, three-body, damped pendulum, forced Duffing real pendulum trajectory recordings real double pendulum trajectory recordings real pendulum and double pendulum video recordings

Benchmarks: simulated trajectory MSE suites FVD on rendered and real pendulum videos PCA percentage variance explained on learned coordinates

Metrics: MSE FVD energy variance PVE

Baselines: HNN SymODEN TRS-ODEN NeuralODE LatentODE pHNN HGN HGAN SympNet GRU

Builds on: Hamiltonian Neural Networks port-Hamiltonian neural networks Hamiltonian Generative Networks HGAN SymODEN

Closest papers by meaning

• SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision (NeurIPS 2021 · similarity 0.87)
• Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics (ICML 2023 · similarity 0.86)
• Stiffness-aware neural network for learning Hamiltonian systems (ICLR 2022 · similarity 0.86)
• A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics (ICLR 2025 · similarity 0.85)
• Hamiltonian Score Matching and Generative Flows (NeurIPS 2024 · similarity 0.85)
• Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning (NeurIPS 2026 · similarity 0.85)