Optimization Using Pathwise Algorithmic Derivatives of Electromagnetic Shower Simulations

TL;DR

This paper integrates algorithmic differentiation into electromagnetic shower simulations to evaluate the accuracy of pathwise derivatives for energy deposition, demonstrating their effectiveness in certain conditions and their use in optimization.

Contribution

It introduces a method to compute pathwise derivatives in complex electromagnetic simulations and assesses their bias and convergence properties.

Findings

Pathwise derivatives converge when multiple scattering is disabled.

They closely approximate true derivatives in specific simulation conditions.

The method enables gradient-based optimization in electromagnetic modeling.

Abstract

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.