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

TL;DR

PhaseFlow4D introduces a physics-constrained, feedback-guided latent diffusion model for real-time 4D beam distribution reconstruction from sparse 2D projections, significantly accelerating and improving accuracy over traditional methods.

Contribution

It presents a novel 4D VAE with projection-based physics constraints and an adaptive feedback loop for online, high-fidelity 4D beam reconstruction from limited observations.

Findings

Achieves 11000× faster reconstruction than physics simulations.

Accurately tracks time-varying 4D distributions in heavy-ion beam simulations.

Demonstrates robustness of generative models in physics-based inverse problems.

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 $\rho(x,p_x,y,p_y)$ 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.