Abstract
<title>Abstract</title> <p>The determination of the extent of the phase-space region where bounded motion occurs for the case of non-linear beam dynamics in hadron storage rings, typically relies on computer simulations over a wide ensemble of initial conditions, which makes the procedure computationally demanding. In a previous work \cite{Casanova_2023}, we examined how well an ensemble reservoir computing scheme based on Echo State Networks can forecast the long-term evolution of the radius of the stable region in phase space. We benchmarked its performance against analytical scaling laws derived from the stability-time estimates provided by the Nekhoroshev theorem for Hamiltonian systems. In this paper, we study the dependence of the Echo State Networks’ predictive power on different ways of partitioning the original dataset into training, validation, and test subsets. With the goal of automating the data partitioning process, we investigate whether the derivative of the analytical scaling law can be used to determine the boundary between the combined training-and-validation set and the test set, and we report the outcomes of this investigation.</p>