Ensemble reservoir computing for dynamical systems: prediction of phase-space stable region for hadron storage rings

Abstract We investigate the ability of an ensemble reservoir computing approach to predict long-term behaviour phase-space region in which motion charged particles hadron storage rings is bounded, so-called dynamic aperture. Currently, calculation stability performed through direct computer simulations, are resource- and time-intensive processes. Echo State Networks (ESN) a class recurrent neural networks that computationally effective, since they avoid backpropagation require only cross-validation. Furthermore, have been proven be universal approximants dynamical systems. In this paper, we present performance reached by ESN based on for prediction compare it with analytical scaling laws stability-time estimate Nekhoroshev theorem Hamiltonian observe proposed capable effectively predicting time evolution extent aperture, improving predictions laws, thus providing efficient surrogate model.