Ensemble Reservoir Computing for Dynamical Systems: Prediction of Phase-Space Stable Region for Hadron Storage Rings
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Model-Free Prediction of Chaotic Systems Using High Efficient Next-generation Reservoir Computing
To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving m…
Reservoir computing with logistic map
Recent studies on reservoir computing essentially involve a high dimensional dynamical system as the reservoir, which transforms and stores the input as a higher dimensional state, for temporal and nontemporal data proce…
Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing
Machine learning recently proved efficient in learning differential equations and dynamical systems from data. However, the data is commonly assumed to originate from a single never-changing system. In contrast, when mod…
Continual LearningReservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study…
Higher order quantum reservoir computing for non-intrusive reduced-order models
Forecasting dynamical systems is of importance to numerous real-world applications. When possible, dynamical systems forecasts are constructed based on first-principles-based models such as through the use of differentia…