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3-Dimensional Adaptive Unstructured Tessellated Look-up Tables for the Approximation of Compton Form Factors

Charles Hyde, Mitch Kerver, Christos Tsolakis, Polykarpos Thomadakis, Spiros Tsalikis, Kevin Garner, Angelos Angelopoulos, Wirawan Purwanto, Gagik Gavalian, Christian Weiss, Nikos Chrisochoides

TL;DR

This study tackles the computational bottleneck in DVCS simulations by constructing an iterative-adaptive, unstructured tessellation of Compton Form Factors (CFFs) in 3D to serve as a fast lookup table for Monte Carlo event generation. It develops and compares four mesh-generation strategies, with the iterative-adaptive pipeline achieving a maximum interpolation error of $5\%$ while using tens to hundreds of thousands of vertices, significantly reducing GPD-model evaluations. The LUT-based approach yields substantial speedups for MC event generation, reporting about a $23\times$ speedup for $10^7$ events on 40 cores (and extrapolated $\sim955\times$ for $10^{10}$ events), highlighting practical impact for nuclear femtography and enabling reuse across analyses. The work offers a path toward common denominator adaptive tessellations across CFFs and potential extensions to higher-dimensional cross sections, with software tools to be publicly released for community use.

Abstract

We describe an iterative algorithm to construct an unstructured tessellation of simplices (irregular tetrahedra in 3-dimensions) to approximate an arbitrary function to a desired precision by interpolation. The method is applied to the generation of Compton Form Factors for simulation and analysis of nuclear femtography, as enabled by high energy exclusive processes such as electron-proton scattering producing just an electron, proton, and gamma-ray in the final state. While producing tessellations with only a 1% mean interpolation error, our results show that the use of such tessellations can significantly decrease the computation time for Monte Carlo event generation by $\sim23$ times for $10^{7}$ events (and using extrapolation, by $\sim955$ times for $10^{10}$ events).

3-Dimensional Adaptive Unstructured Tessellated Look-up Tables for the Approximation of Compton Form Factors

TL;DR

This study tackles the computational bottleneck in DVCS simulations by constructing an iterative-adaptive, unstructured tessellation of Compton Form Factors (CFFs) in 3D to serve as a fast lookup table for Monte Carlo event generation. It develops and compares four mesh-generation strategies, with the iterative-adaptive pipeline achieving a maximum interpolation error of while using tens to hundreds of thousands of vertices, significantly reducing GPD-model evaluations. The LUT-based approach yields substantial speedups for MC event generation, reporting about a speedup for events on 40 cores (and extrapolated for events), highlighting practical impact for nuclear femtography and enabling reuse across analyses. The work offers a path toward common denominator adaptive tessellations across CFFs and potential extensions to higher-dimensional cross sections, with software tools to be publicly released for community use.

Abstract

We describe an iterative algorithm to construct an unstructured tessellation of simplices (irregular tetrahedra in 3-dimensions) to approximate an arbitrary function to a desired precision by interpolation. The method is applied to the generation of Compton Form Factors for simulation and analysis of nuclear femtography, as enabled by high energy exclusive processes such as electron-proton scattering producing just an electron, proton, and gamma-ray in the final state. While producing tessellations with only a 1% mean interpolation error, our results show that the use of such tessellations can significantly decrease the computation time for Monte Carlo event generation by times for events (and using extrapolation, by times for events).

Paper Structure

This paper contains 28 sections, 15 equations, 16 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Nuclear Femtography
  3. Tessellations and Monte Carlo Event Generation
  4. Background
  5. Physics
  6. Monte Carlo Event Generators
  7. Tessellations
  8. Types of Tessellations
  9. Mesh Generation
  10. Input
  11. Image-to-mesh conversion software
  12. Portability
  13. Interpolation Error
  14. Mesh generation approaches
  15. Structured Tessellation
  16. ...and 13 more sections

Figures (16)

  • Figure 1: Different types of tessellations applied on a dataset.
  • Figure 2: Cartesian Image of (a) the Im($H_u$) CFF and (b) Re($H_u$). Vertical axis is $\sqrt{t'/0.05 \text{GeV}^2}$. The horizontal axes are $\log_2(Q^2/\text{GeV}^2)$ (y) and $\log_{10}\xi$ (x).
  • Figure 3: (a) Structured grid of $Im(H_{u})$ CFF and (b) Mean, RMS, and Max interpolation error statistics of structured grids of different sizes
  • Figure 4: Uniform tessellation of $Im(H_{u})$ CFF (a) the 1st instance and (b) Mean, RMS, and Max interpolation error statistics of uniform tessellations of different sizes
  • Figure 5: (a) The adaptation rule applied on a 2D element, (b) an adaptive tessellation of $Im(H_{u})$ CFF using $SF_1$, (c) an adaptive tessellation of $Im(H_{u})$ CFF using $SF_2$.
  • ...and 11 more figures