Abstract
This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of dynamics are mapped onto the weights of a polynomial neural network. The resulting network approximates the dynamical system with perfect accuracy prior to training and provides a possibility to tune the network weights on additional experimental data. We propose a symplectic regularization approach for such polynomial neural networks that always restricts the trained model to Hamiltonian systems and significantly improves the training procedure. The proposed networks can be used for beam dynamics simulations or for fine-tuning of beam optics models with experimental data. The structure of the network allows for the modeling of large accelerators with a large number of magnets. We demonstrate our approach on the examples of the existing PETRA III and the planned PETRA IV storage rings at DESY.
Highlights
Machine learning (ML) techniques are finding increasing usage in various aspects of particle accelerators, including fault prediction, performance optimization, and virtual diagnostics
Many applications could benefit from having a beam optics model which on the one hand accurately represents the beam dynamics of the accelerator, and on the other hand, can be trained or adjusted on the limited amount of experimental data to serve as a model of the real machine with various imperfections
Machine learning methods and neural networks (NN) in particular hold a promise for constructing such models
Summary
Machine learning (ML) techniques are finding increasing usage in various aspects of particle accelerators, including fault prediction, performance optimization, and virtual diagnostics. Applying ML methods for learning the behavior of dynamical systems such as those describing linear and nonlinear dynamics in charged particle accelerators can in some cases require a prohibitively large amount of training data. NNs are often employed for system learning and control [2,3], when models are trained either with large measured or simulated datasets. All studies related to PNNs regard the polynomial architectures as black-box models, and they do not indicate the architectures’ connection to the ODEs. We propose to incorporate the physics constraints on the single-particle beam dynamics in accelerators by introducing NN architecture which is directly derived from the Taylor maps corresponding to the accelerator components and imposing symplectic constraints on the network. We first introduce the polynomial neural network (PNN) architecture incorporating Taylor map (TMPNN) information. The results of fine-tuning the TM-PNN based on experimental data at the PETRA III [14] storage ring and simulations for the proposed PETRA IV [15] ring at DESY are presented
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