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

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.