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A fast Bayesian surrogate for the photon flux in ultra-peripheral collisions

Simone Ragoni, Janet Seger

TL;DR

The paper addresses the bottleneck of computing the photon flux in ultraperipheral collisions with nuclear-structure uncertainties. It introduces a physics-informed Bayesian neural-network surrogate trained on analytical flux integrals, employing MC dropout and an active-learning loop to concentrate computations where uncertainties are largest. The approach yields a ~100× speedup, propagates priors such as neutron-skin thickness and diffuseness from PREX-II, and provides a modular framework for updating uncertainties in UPC analyses. This enables robust end-to-end uncertainty propagation and rapid sensitivity studies, with potential applicability to other flux models and future nuclear-density constraints.

Abstract

We present a fast surrogate for the Equivalent Photon Approximation (EPA) flux in ultraperipheral collisions (UPCs), based on a Bayesian neural network (BNN) trained over analytical flux integrals with an iterative procedure focused on regions of high relative uncertainties to minimise the number of integrations. The surrogate propagates experimentally available uncertainties on the neutron skin thickness and surface diffuseness. Once trained, this surrogate technique brings an estimated gain of two orders of magnitude in CPU time. The implementation provides a modular framework for rapidly propagating updated nuclear priors and assessing uncertainties for photon flux in future UPC analyses.

A fast Bayesian surrogate for the photon flux in ultra-peripheral collisions

TL;DR

The paper addresses the bottleneck of computing the photon flux in ultraperipheral collisions with nuclear-structure uncertainties. It introduces a physics-informed Bayesian neural-network surrogate trained on analytical flux integrals, employing MC dropout and an active-learning loop to concentrate computations where uncertainties are largest. The approach yields a ~100× speedup, propagates priors such as neutron-skin thickness and diffuseness from PREX-II, and provides a modular framework for updating uncertainties in UPC analyses. This enables robust end-to-end uncertainty propagation and rapid sensitivity studies, with potential applicability to other flux models and future nuclear-density constraints.

Abstract

We present a fast surrogate for the Equivalent Photon Approximation (EPA) flux in ultraperipheral collisions (UPCs), based on a Bayesian neural network (BNN) trained over analytical flux integrals with an iterative procedure focused on regions of high relative uncertainties to minimise the number of integrations. The surrogate propagates experimentally available uncertainties on the neutron skin thickness and surface diffuseness. Once trained, this surrogate technique brings an estimated gain of two orders of magnitude in CPU time. The implementation provides a modular framework for rapidly propagating updated nuclear priors and assessing uncertainties for photon flux in future UPC analyses.
Paper Structure (10 sections, 11 equations, 3 figures)

This paper contains 10 sections, 11 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Photon flux formalism
  3. Nuclear density model
  4. Point‐charge kernel
  5. Implementing a BNN surrogate
  6. Active‐learning training loop
  7. Convergence of the active learning loop
  8. Results
  9. Customizing Nuclear Priors
  10. Conclusion

Figures (3)

  • Figure 1: Figures \ref{['fig:al_r1_before']}, \ref{['fig:al_r2_before']}, and \ref{['fig:al_r3_before']} show the training samples, before round 1, after round 1, and after round 2, respectively, used for the active-learning iterations, with the new incoming points in yellow, in regions of high uncertainty. Figures \ref{['fig:al_r1_unc']}, \ref{['fig:al_r2_unc']}, and \ref{['fig:al_r3_unc']} show the corresponding relative uncertainties after each round.
  • Figure 2: Negative log‐likelihood (NLL) on the training set (blue) and on a held‐out evaluation set (orange) as a function of the active‐learning round. The horizontal axis is plotted on a logarithmic scale to emphasize early‐round behavior.
  • Figure 3: Surrogate photon flux $N(\omega,b{=}20~\mathrm{fm})$ and $68\%$ credible interval compared to the direct numerical integration.