Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian

TL;DR

This paper introduces a novel deep learning approach that incorporates Hamiltonian structures on Lie group manifolds to improve modeling of complex astrophysical dynamics, especially for non-Newtonian systems.

Contribution

It extends Hamiltonian-based deep learning models to non-Euclidean Lie group manifolds, enabling better handling of rotational dynamics in astrophysics.

Findings

Enhanced training stability with symplectic integrators

Improved prediction accuracy for non-Newtonian celestial interactions

Demonstrated effectiveness on astrophysical data

Abstract

Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their extension to the Lie group manifold is needed when rotations form a key component of the dynamics, such as the higher-order physics beyond simple point-mass dynamics for N-body celestial interactions. Moreover, the multiscale nature of these processes presents a challenge to existing methods as a long time horizon is required. By leveraging a symplectic Lie-group manifold preserving integrator, we present a method for data-driven discovery of non-Newtonian astronomy. Preliminary results show the importance of both these properties in training stability and prediction accuracy.