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We investigate the ability of an ensemble reservoir computing approach topredict the long-term behaviour of the phase-space region in which the motionof charged particles in hadron storage rings is bounded, the so-called dynamicaperture. Currently, the calculation of the phase-space stability region ofhadron storage rings is performed through direct computer simulations, whichare resource- and time-intensive processes. Echo State Networks (ESN) are aclass of recurrent neural networks that are computationally effective, sincethey avoid backpropagation and require only cross-validation. Furthermore, theyhave been proven to be universal approximants of dynamical systems. In thispaper, we present the performance reached by ESN based on an ensemble approachfor the prediction of the phase-space stability region and compare it withanalytical scaling laws based on the stability-time estimate of the Nekhoroshevtheorem for Hamiltonian systems. We observe that the proposed ESN approach iscapable of effectively predicting the time evolution of the extent of thedynamic aperture, improving the predictions by analytical scaling laws, thusproviding an efficient surrogate model.

Ensemble Reservoir Computing for Dynamical Systems: Prediction of Phase-Space Stable Region for Hadron Storage Rings