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Hamiltonian Generative Networks
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Hamiltonian Generative Networks
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The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks. In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions. Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time and even speed up or slow down the learned dynamics. We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities. We hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to deep learning.
Forward citations
Cited by 8 Pith papers
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When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models
Shell-horizon certificates bound rollout steps on decoded physical invariants from measurable model defects in latent world models, showing some geometric priors survive representation learning while others do not.
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When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models
Shell-horizon certificates are derived for decoded physical invariants in latent models, allowing conservation laws to survive representation learning via a monotone alignment from soft witnesses, with empirical suppo...
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Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure
A two-stage contrastive teacher-student framework learns and then projects latent dynamics onto port-Hamiltonian submanifolds from partial observations.
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Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
Neural ODEs reproduce 2RDM dynamics from data only when three-particle cumulant correlations are strong, mapping the validity regime of cumulant expansions.
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Symplectic Neural Networks for learning Generalized Hamiltonians
Symplectic neural networks enable efficient training of Hamiltonian models with implicit integrators for improved energy conservation in chaotic systems.
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Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on m...
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Differential-Integral Neural Operator for Long-Term Turbulence Forecasting
DINO decomposes turbulent evolution into parallel local differential and global integral operators to achieve stable autoregressive forecasting on 2D Kolmogorov flow.
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PhysRAG: Enhancing Physics-Awareness in Video Generation via Retrieval-Augmented Generation
PhysRAG curates 7K videos from WISA-80K, builds a physical video database, and injects knowledge via learnable queries into a diffusion model to reach SOTA visual quality and physical compliance on PhyGenBench and VBench.
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