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Flow Annealed Importance Sampling Bootstrap meets Differentiable Particle Physics

Annalena Kofler, Vincent Stimper, Mikhail Mikhasenko, Michael Kagan, Lukas Heinrich

TL;DR

The paper tackles efficient sampling from high-dimensional matrix-element densities $p(x)$ essential for HL-LHC event generation. It introduces Flow Annealed Importance Sampling Bootstrap (FAB), which trains normalizing flows by evaluating the differentiable target density through AIS with Hamiltonian Monte Carlo transitions and uses a replay buffer to reduce target evaluations. Compared against forward KL and reverse KL objectives, FAB—especially with a prioritized replay buffer—achieves higher importance sampling efficiency $\epsilon$ with far fewer target evaluations in both a 2D Dalitz-like scenario and an 8D collider ME. The approach demonstrates potential for accelerating ML-assisted event generation without domain-specific multi-channeling, with code and data openly available for reproducibility and further development.

Abstract

High-energy physics requires the generation of large numbers of simulated data samples from complex but analytically tractable distributions called matrix elements. Surrogate models, such as normalizing flows, are gaining popularity for this task due to their computational efficiency. We adopt an approach based on Flow Annealed importance sampling Bootstrap (FAB) that evaluates the differentiable target density during training and helps avoid the costly generation of training data in advance. We show that FAB reaches higher sampling efficiency with fewer target evaluations in high dimensions in comparison to other methods.

Flow Annealed Importance Sampling Bootstrap meets Differentiable Particle Physics

TL;DR

The paper tackles efficient sampling from high-dimensional matrix-element densities essential for HL-LHC event generation. It introduces Flow Annealed Importance Sampling Bootstrap (FAB), which trains normalizing flows by evaluating the differentiable target density through AIS with Hamiltonian Monte Carlo transitions and uses a replay buffer to reduce target evaluations. Compared against forward KL and reverse KL objectives, FAB—especially with a prioritized replay buffer—achieves higher importance sampling efficiency with far fewer target evaluations in both a 2D Dalitz-like scenario and an 8D collider ME. The approach demonstrates potential for accelerating ML-assisted event generation without domain-specific multi-channeling, with code and data openly available for reproducibility and further development.

Abstract

High-energy physics requires the generation of large numbers of simulated data samples from complex but analytically tractable distributions called matrix elements. Surrogate models, such as normalizing flows, are gaining popularity for this task due to their computational efficiency. We adopt an approach based on Flow Annealed importance sampling Bootstrap (FAB) that evaluates the differentiable target density during training and helps avoid the costly generation of training data in advance. We show that FAB reaches higher sampling efficiency with fewer target evaluations in high dimensions in comparison to other methods.

Paper Structure

This paper contains 30 sections, 14 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Method
  4. Training
  5. Forward KL Divergence (fKLD).
  6. Reverse KL Divergence (rKLD).
  7. FAB.
  8. Differentiable Matrix Elements
  9. $\Lambda_c^+ \rightarrow pK^-\pi^+$.
  10. $e^+e^- \rightarrow t\bar{t}, t\rightarrow W^+ b, \bar{t} \rightarrow W^- \bar{b}$.
  11. Experimental Setup
  12. Training Settings.
  13. Baseline.
  14. Performance Metrics.
  15. Results and Discussion
  16. ...and 15 more sections

Figures (9)

  • Figure 1: Training with fKLD
  • Figure 2: Training with rKLD
  • Figure 3: Training with FAB
  • Figure 5: The $\Lambda_c^+ \rightarrow pK^- \pi^+$ decay (left-most diagram) consists of three decay channels characterized by their resonances $\Lambda_0$ (center-left), $\Delta^{++}$ (center-right), and $K^*$ (right), each visualized in Feynman-like diagrams.
  • Figure 6: Comparison of the target density for the $\Lambda_c^+ \rightarrow pK^- \pi^+$ matrix element with histograms based on samples from VEGAS+ and the best normalizing flow for each method.
  • ...and 4 more figures