Physics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Accelerators

TL;DR

This paper introduces a physics-informed neural network approach for accurately modeling charged particle beam dynamics in accelerators, leveraging Taylor maps and symplectic regularization for improved simulation and tuning.

Contribution

It presents a novel polynomial neural network architecture based on Taylor maps, incorporating symplectic regularization to ensure Hamiltonian system modeling and enhance training.

Findings

Accurately models beam dynamics in large accelerators.

Enables fine-tuning of beam optics with experimental data.

Demonstrated on PETRA III and PETRA IV storage rings.

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.