Hamiltonian Generative Networks

TL;DR

The paper introduces Hamiltonian Generative Networks (HGN), a novel deep learning model that learns Hamiltonian dynamics from high-dimensional data, enabling trajectory sampling, time manipulation, and density modeling, bridging physics formalism with machine learning.

Contribution

It presents the first neural network capable of learning Hamiltonian dynamics from high-dimensional observations without restrictive assumptions.

Findings

HGN can generate and manipulate trajectories in learned Hamiltonian systems.

HGN can be transformed into Neural Hamiltonian Flow for density modeling.

The approach demonstrates the practical integration of Hamiltonian formalism into deep learning.

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.