Identifying Generalized Neural Representation Across Hamiltonian Manifolds via Meta-learning

Recent advancements in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. However, these approaches are system-specific and do not allow for easy adaptation to new physical systems governed by different laws. For example, a neural network trained on a mass-spring system cannot accurately predict the behavior of a two-body system or any other system with different governing physics. In this work, we model our system with a graph neural network and employ a meta-learning algorithm to enable the model to gain experience over a distribution of tasks and make it adapt to new physics. Our approach aims to learn a general representation across the various Hamiltonian manifolds, which is a common feature of the data distribution of Hamiltonian systems. We train our model using a dataset of different physical systems, each governed by its own inherent dynamics, and evaluate its performance on a new type of dynamical system with unknown physics. Our results show that the meta-trained model effectively adapts to the new system, which was unseen during the meta-training phase. Furthermore, we analyze the representation learned by the meta-trained neural network to identify a generalizable representation of Hamilton's equation that is shared across various physical systems. Our findings suggest that the meta-learned model can capture the generalizable representation across Hamiltonian manifolds inherent in dynamical systems.Comment: 15 pages, 7 figure