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

arXiv: https://arxiv.org/abs/2007.03555 · HTML: https://mlsanity.com/paper/2007.03555/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators](https://mlsanity.com/paper/2403.13858/) (2024)
- [Physics-constrained 3D Convolutional Neural Networks for Electrodynamics](https://mlsanity.com/paper/2301.13715/) (2023)
- [Physics-informed neural network method for modelling beam-wall interactions](https://mlsanity.com/paper/2112.11323/) (2021)
- [TMPNN: High-Order Polynomial Regression Based on Taylor Map Factorization](https://mlsanity.com/paper/2307.16105/) (2023)
- [Toward a Fully Autonomous, AI-Native Particle Accelerator](https://mlsanity.com/paper/2602.17536/) (2026)
- [Advancing accelerator virtual beam diagnostics through latent evolution modeling: an integrated solution to forward, inverse, tuning, and UQ problems](https://mlsanity.com/paper/2602.22618/) (2026)

## Abstract (arXiv)

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.