PhaseFlow4D: Physically Constrained 4D Beam Reconstruction via Feedback-Guided Latent Diffusion

2026-04-04

AI Summary

Reconstructing the four-dimensional (4D) phase-space evolution of charged particle beams from sparse 2D projections is highly challenging due to the inaccessibility of the full high-dimensional distribution. This work proposes a feedback-guided latent diffusion model that enforces projection consistency as an architectural prior rather than a soft constraint and embeds hard physical constraints, enabling online 4D reconstruction and tracking using only incomplete 2D data. The approach integrates a 4D variational autoencoder, analytical projection computation, and an adaptive feedback mechanism, allowing it to adapt to time-varying distributions without retraining. Validated on FRIB heavy-ion beam simulations, the method achieves high-fidelity reconstructions over 11,000 times faster than conventional high-performance computing (HPC) simulations and accurately captures distribution drifts induced by changes in source conditions.

Abstract

We address the problem of recovering a time-varying 4D distribution from a sparse sequence of 2D projections - analogous to novel-view synthesis from sparse cameras, but applied to the 4D transverse phase space density $ρ(x,p_x,y,p_y)$ of charged particle beams. Direct single shot measurement of this high-dimensional distribution is physically impossible in real particle accelerator systems; only limited 1D or 2D projections are accessible. We propose PhaseFlow4D, a feedback-guided latent diffusion model that reconstructs and tracks the full 4D phase space from incomplete 2D observations alone, with built-in hard physics constraints. Our core technical contribution is a 4D VAE whose decoder generates the full 4D phase space tensor, from which 2D projections are analytically computed and compared against 2D beam measurements. This projection-consistency constraint guarantees physical correctness by construction - not as a soft penalty, but as an architectural prior. An adaptive feedback loop then continuously tunes the conditioning vector of the latent diffusion model to track time-varying distributions online without retraining. We validate on multi-particle simulations of heavy-ion beams at the Facility for Rare Isotope Beams (FRIB), where full physics simulations require $\sim$6 hours on a 100-core HPC system. PhaseFlow4D achieves accurate 4D reconstructions 11000$\times$ faster while faithfully tracking distribution shifts under time-varying source conditions - demonstrating that principled generative reconstruction under incomplete observations transfers robustly beyond visual domains.

Problem

• 4D phase space reconstruction
• charged particle beams
• sparse projections
• time-varying distribution
• phase space density

Innovation

• latent diffusion
• physics-constrained reconstruction
• 4D phase space
• projection consistency
• feedback-guided adaptation