Learning the chaotic and regular nature of trajectories in Hamiltonian systems with Lagrangian descriptors

In this paper we investigate the use of Machine Learning techniques, specifically Support Vector Machines (SVMs), to classify chaotic and regular trajectories in Hamiltonian systems and symplectic maps through Lagrangian descriptors. Traditional chaos indicators, though effective, are computationally intensive and require exhaustive parameter space exploration to establish classification thresholds. By training SVMs on data from the dynamics of a double pendulum Hamiltonian system, we aim to streamline this process. Our SVM models achieve high accuracy in classifying trajectories across various dynamical systems, including the four-well Hamiltonian, the Hénon–Heiles system, and the Chirikov Standard Map. Results demonstrate that SVMs, combined with Lagrangian descriptors, provide a robust and efficient method for chaos classification in diverse dynamical systems. This approach not only simplifies classification but also highlights the potential of Machine Learning algorithms in advancing the study of nonlinear dynamics and chaos.