# Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal

arXiv: https://arxiv.org/abs/2408.07847 · HTML: https://mlsanity.com/paper/2408.07847/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems](https://mlsanity.com/paper/1809.08327/) (2018)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [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)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [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)
- [A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators](https://mlsanity.com/paper/2403.13858/) (2024)
- [Neural network based order parameter for phase transitions and its applications in high-entropy alloys](https://mlsanity.com/paper/2109.05598/) (2021)
- [Robust Errant Beam Prognostics with Conditional Modeling for Particle Accelerators](https://mlsanity.com/paper/2312.10040/) (2023)

## Built on by (most cited first, 6 of 6)

- [MORPH: PDE Foundation Models with Arbitrary Data Modality](https://mlsanity.com/paper/2509.21670/) (2025)
- [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)
- [Sim+Real: Joint Simulation-Experiment Training Improves Balanced Prediction in Physical Systems](https://mlsanity.com/paper/2610.01974/) (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)

Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally expensive, limiting their utility for solving inverse problems online. The problem of estimating upstream six-dimensional phase space given downstream measurements of charged particles in an accelerator is an inverse problem of growing importance. This paper introduces a reverse Latent Evolution Model (rLEM) designed for temporal inversion of forward beam dynamics. In this two-step self-supervised deep learning framework, we utilize a Conditional Variational Autoencoder (CVAE) to project 6D phase space projections of a charged particle beam into a lower-dimensional latent distribution. Subsequently, we autoregressively learn the inverse temporal dynamics in the latent space using a Long Short-Term Memory (LSTM) network. The coupled CVAE-LSTM framework can predict 6D phase space projections across all upstream accelerating sections based on single or multiple downstream phase space measurements as inputs. The proposed model also captures the aleatoric uncertainty of the high-dimensional input data within the latent space. This uncertainty, which reflects potential uncertain measurements at a given module, is propagated through the LSTM to estimate uncertainty bounds for all upstream predictions, demonstrating the robustness of the LSTM against in-distribution variations in the input data.