Hamiltonian Generative Networks

Abstract

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.

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Cited by in corpus (21)

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• Deep learning of thermodynamics-aware reduced-order models from data
• Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• Symplectic Learning for Hamiltonian Neural Networks
• Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
• Deep Hamiltonian networks based on symplectic integrators
• Stochastic Normalizing Flows
• LagNetViP: A Lagrangian Neural Network for Video Prediction
• TorchDyn: A Neural Differential Equations Library
• Locally-symplectic neural networks for learning volume-preserving dynamics
• Learning Physical Constraints with Neural Projections
• Learning Group Structure and Disentangled Representations of Dynamical Environments
• Learning Potentials of Quantum Systems using Deep Neural Networks
• Kinematically consistent recurrent neural networks for learning inverse problems in wave propagation
• Physics-enhanced Neural Networks in the Small Data Regime
• Time-Reversal Symmetric ODE Network
• Rodent: Relevance determination in differential equations
• Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational $N$-body Problem
• Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control
• Learn Proportional Derivative Controllable Latent Space from Pixels
• Extracting Dynamical Models from Data