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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用于带电粒子加速器中的束动力学的基于物理的深度神经网络

本文提出了一种构建带电粒子束动力学模型的神经网络的新方法。在我们的方法中，在动力学表示中出现的泰勒图被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态系统，并提供了在额外的实验数据上调整网络权重的可能性。我们为这种多项式神经网络提出了一种辛正则化方法，该方法总是将训练模型限制为哈密顿系统，并显着改进了训练过程。所提出的网络可用于光束动力学模拟或用于使用实验数据微调光束光学模型。该网络的结构允许对具有大量磁铁的大型加速器进行建模。我们在 DESY 现有 PETRA III 和计划中的 PETRA IV 存储环的示例中展示了我们的方法。