Ensemble Reservoir Computing for Dynamical Systems: Prediction of Phase-Space Stable Region for Hadron Storage Rings
This provides an efficient surrogate model for predicting stability in hadron storage rings, addressing a resource-intensive simulation problem in particle accelerator physics, though it is incremental as it builds on existing Echo State Networks.
The paper tackled predicting the phase-space stable region (dynamic aperture) for charged particles in hadron storage rings, using an ensemble reservoir computing approach, and found it effectively predicted time evolution and improved upon analytical scaling laws.
We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture. Currently, the calculation of the phase-space stability region of hadron storage rings is performed through direct computer simulations, which are resource- and time-intensive processes. Echo State Networks (ESN) are a class of recurrent neural networks that are computationally effective, since they avoid backpropagation and require only cross-validation. Furthermore, they have been proven to be universal approximants of dynamical systems. In this paper, we present the performance reached by ESN based on an ensemble approach for the prediction of the phase-space stability region and compare it with analytical scaling laws based on the stability-time estimate of the Nekhoroshev theorem for Hamiltonian systems. We observe that the proposed ESN approach is capable of effectively predicting the time evolution of the extent of the dynamic aperture, improving the predictions by analytical scaling laws, thus providing an efficient surrogate model.