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. Hence, we hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to machine learning. More results and video evaluations are available at: http://tiny.cc/hgn We have presented HGN, the first deep learning approach capable of reliably learning Hamiltonian dynamics from pixel observations. We have evaluated our approach on four classical physical systems and demonstrated that it outperformed the only relevant baseline by a large margin. Hamiltonian dynamics have a number of useful properties that can be exploited more widely by the machine learning community. For example, the Hamiltonian induces a smooth manifold and a vector field in the abstract phase space along which certain physical quantities are conserved. The time evolution along these paths is also completely reversible. These properties can have wide implications in such areas of machine learning as reinforcement learning, representation learning and generative modelling. We have demonstrated the first step towards applying the learnt Hamiltonian dynamics as normalising flows for expressive yet computationally efficient density modelling. We hope that this work serves as the first step towards a wider adoption of the rich body of physics literature around the Hamiltonian principles in the machine learning community. A SUPPLEMENTARY MATERIALS
We introduce a class of generative models that reliably learn Hamiltonian dynamics from high-dimensional observations. The learnt Hamiltonian can be applied to sequence modeling or as a normalising flow.
{"src": "scitldr-AIC_train", "paper_id": "HJenn6VFvB"}