A deep classifier of chaos and order in Hamiltonian systems of two degrees of freedom

TL;DR

This paper introduces a deep convolutional neural network that effectively classifies chaos versus order in Hamiltonian systems using Poincaré maps, with applications to geodesic motion around compact objects.

Contribution

The paper presents a novel deep learning approach employing convolutional networks to distinguish chaos from order in Hamiltonian systems, demonstrating good generalization and practical application.

Findings

High accuracy in classifying chaos and order in unseen datasets

Effective generalization to geodesic motion in non-Kerr spacetimes

Potential for applying deep learning to complex dynamical systems

Abstract

Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of classifying chaos from order in the discretised dynamics of Hamiltonian systems of two degrees of freedom, through the machinery of Poincar\'{e} maps. Our deep network is based predominantly on a convolutional architecture, and generalises with good accuracy on unseen datasets, thanks to the universal features of a perturbed pendulum learned by the deep network. We discuss in detail the significance and the preparation of our training set, and we showcase how our deep network can be applied to the dynamics of geodesic motion in an axi-symmetric and stationary spacetime of a compact object deviating from the Kerr black hole paradigm. Finally, we discuss current challenges and some promising future directions.