  In this paper, we explore the application of Machine Learning techniques,
specifically Support Vector Machines (SVM), to unveil the chaotic and regular
nature of trajectories in Hamiltonian systems using Lagrangian descriptors.
Traditional chaos indicators, while effective, are computationally expensive
and require an exhaustive study of the parameter space to establish the
classification thresholds. By using SVMs trained on a dataset obtained from the
analysis of the dynamics of the double pendulum Hamiltonian system, we aim at
reducing the complexity of this process. Our trained SVM models demonstrate
high accuracy when it comes to classifying trajectories in diverse Hamiltonian
systems, such as for example in the four-well Hamiltonian, the H\'enon-Heiles
system and the Chirikov Standard Map. The results indicate that SVMs, when
combined with Lagrangian descriptors, offer a robust and efficient method for
chaos classification across different dynamical systems. Our approach not only
simplifies the classification process but also is highlighting the potential of
Machine Learning algorithms in the study of nonlinear dynamics and chaos.
