# Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution

arXiv: https://arxiv.org/abs/2610.14537 · HTML: https://mlsanity.com/paper/2610.14537/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 73 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Latent Neural Operator for Solving Forward and Inverse PDE Problems](https://mlsanity.com/paper/2406.03923/) (2024)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [CViT: Continuous Vision Transformer for Operator Learning](https://mlsanity.com/paper/2405.13998/) (2024)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)

## Abstract (arXiv)

Particle-in-cell (PIC) simulation is indispensable for modeling beam dynamics in particle accelerators, but its computational cost limits many-query workflows, such as configuration exploration, virtual diagnostics, and controller design. We introduce GLOBE, a physics-constrained Generative Latent Operator for Beam Evolution, modeling the nonlinear, control-dependent, multiscale evolution of 3D beam--field dynamics covering 107 spatial cells. GLOBE compresses beam--field states into a compact latent space and factors their evolution into two components. A control-conditioned neural operator learns the dominant dynamics, while an amplitude-normalized generative model captures the residual distribution, recovering fine-scale structures and conditional variations. GLOBE enforces field constraints by regime-specific, parameter-free operators: a Poisson solve reconstructs the electric field in the electrostatic regime, and a spectral projection imposes Gauss's law and a divergence-free magnetic field in the electromagnetic regime. On two high-resolution 3D particle-accelerator benchmarks, bunched-beam transport and plasma-wakefield acceleration, GLOBE lowers relative-L2 error by 9% and 13%, low-frequency spectral error by 69% and 51%, and mid-frequency spectral error by 54% and 20% relative to the strongest baseline (DPOT), satisfies field constraints, and reduces hours of PIC simulation to a minute per rollout.