# A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators

arXiv: https://arxiv.org/abs/2403.13858 · HTML: https://mlsanity.com/paper/2403.13858/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 77 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Neural Autoregressive Distribution Estimation](https://mlsanity.com/paper/1605.02226/) (2016)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D](https://mlsanity.com/paper/2012.11893/) (2020)
- [Accelerated, Scalable and Reproducible AI-driven Gravitational Wave Detection](https://mlsanity.com/paper/2012.08545/) (2020)
- [Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network](https://mlsanity.com/paper/2004.00707/) (2020)
- [Superconducting radio-frequency cavity fault classification using machine learning at Jefferson Laboratory](https://mlsanity.com/paper/2006.06562/) (2020)
- [Physics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Accelerators](https://mlsanity.com/paper/2007.03555/) (2020)
- [High-fidelity Prediction of Megapixel Longitudinal Phase-space Images of Electron Beams using Encoder-Decoder Neural Networks](https://mlsanity.com/paper/2101.10437/) (2021)
- [Learning to Forecast Aleatoric and Epistemic Uncertainties over Long Horizon Trajectories](https://mlsanity.com/paper/2302.08669/) (2023)
- [Neural network based order parameter for phase transitions and its applications in high-entropy alloys](https://mlsanity.com/paper/2109.05598/) (2021)
- [Adaptive Machine Learning for Time-Varying Systems: Low Dimensional Latent Space Tuning](https://mlsanity.com/paper/2107.06207/) (2021)
- [Explainable Machine Learning for Breakdown Prediction in High Gradient RF Cavities](https://mlsanity.com/paper/2202.05610/) (2022)
- [Inverse characterization of composites using guided waves and convolutional neural networks with dual-branch feature fusion](https://mlsanity.com/paper/2204.10486/) (2022)
- [Physics-constrained 3D Convolutional Neural Networks for Electrodynamics](https://mlsanity.com/paper/2301.13715/) (2023)
- [Delamination prediction in composite panels using unsupervised-feature learning methods with wavelet-enhanced guided wave representations](https://mlsanity.com/paper/2204.09764/) (2022)

## Built on by (most cited first, 8 of 8)

- [MORPH: PDE Foundation Models with Arbitrary Data Modality](https://mlsanity.com/paper/2509.21670/) (2025)
- [Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal](https://mlsanity.com/paper/2408.07847/) (2024)
- [Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading](https://mlsanity.com/paper/2603.04354/) (2026)
- [PDE foundation model-accelerated inverse estimation of system parameters in inertial confinement fusion](https://mlsanity.com/paper/2603.04606/) (2026)
- [Classifier-pruned Bayesian optimization for particle accelerator tuning: Exploring temporally structured manifold of 6D beam phase space](https://mlsanity.com/paper/2412.01748/) (2024)
- [Robust Anomaly Detection through Multi-Modal Autoencoder Fusion for Small Vehicle Damage Detection](https://mlsanity.com/paper/2509.01719/) (2025)
- [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)
- [Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution](https://mlsanity.com/paper/2610.14537/) (2026)

## Abstract (arXiv)

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding simulations, and inherent uncertainties in the system. We propose a two-step unsupervised deep learning framework named as Conditional Latent Autoregressive Recurrent Model (CLARM) for learning the spatiotemporal dynamics of charged particles in accelerators. CLARM consists of a Conditional Variational Autoencoder (CVAE) transforming six-dimensional phase space into a lower-dimensional latent distribution and a Long Short-Term Memory (LSTM) network capturing temporal dynamics in an autoregressive manner. The CLARM can generate projections at various accelerator modules by sampling and decoding the latent space representation. The model also forecasts future states (downstream locations) of charged particles from past states (upstream locations). The results demonstrate that the generative and forecasting ability of the proposed approach is promising when tested against a variety of evaluation metrics.