Identifying Hamiltonian manifold in neural networks

Abstract

Recent studies to learn physical laws via deep learning attempt to find the shared representation of the given system by introducing physics priors or inductive biases to the neural network. However, most of these approaches tackle the problem in a system-specific manner, in which one neural network trained to one particular physical system cannot be easily adapted to another system governed by a different physical law. In this work, we use a meta-learning algorithm to identify the general manifold in neural networks that represents Hamilton's equation. We meta-trained the model with the dataset composed of five dynamical systems each governed by different physical laws. We show that with only a few gradient steps, the meta-trained model adapts well to the physical system which was unseen during the meta-training phase. Our results suggest that the meta-trained model can craft the representation of Hamilton's equation in neural networks which is shared across various dynamical systems with each governed by different physical laws.