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.

中文翻译：

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基于物理学的深度神经网络，用于带电粒子加速器中的束动力学

本文提出了一种新的构造带电粒子束动力学模型的神经网络的方法。在我们的方法中，将由动力学表示产生的泰勒映射映射到多项式神经网络的权重上。生成的网络在训练之前以完美的精度逼近动力学系统，并提供了根据其他实验数据调整网络权重的可能性。我们为此类多项式神经网络提出了辛正则化方法，该方法总是将训练后的模型限制在哈密顿系统中，并显着改善了训练过程。所提出的网络可用于束动力学仿真或具有实验数据的束光学模型的微调。网络的结构允许对带有大量磁铁的大型加速器进行建模。我们以DESY现有PETRA III和计划中的PETRA IV存储环为例演示我们的方法。