HIGH-PRECISION REGRESSORS FOR PARTICLE PHYSICS

Abstract

Monte Carlo simulations of physics processes at particle colliders like the Large Hadron Collider at CERN take up a major fraction of the computational budget. For some simulations, a single data point takes seconds, minutes, or even hours to compute from first principles. Since the necessary number of data points per simulation is on the order of 10 9 -10 12 , machine learning regressors can be used in place of physics simulators to significantly reduce this computational burden. However, this task requires high-precision regressors that can deliver data with relative errors of less than 1% or even 0.1% over the entire domain of the function. In this paper, we develop optimal training strategies and tune various machine learning regressors to satisfy the high-precision requirement. We leverage symmetry arguments from particle physics to optimize the performance of the regressors. Inspired by ResNets, we design a Deep Neural Network with skip connections that outperform fully connected Deep Neural Networks. We find that at lower dimensions, boosted decision trees far outperform neural networks while at higher dimensions neural networks perform significantly better. We show that these regressors can speed up simulations by a factor of 10 3 -10 6 over the firstprinciples computations currently used in Monte Carlo simulations. Additionally, using symmetry arguments derived from particle physics, we reduce the number of regressors necessary for each simulation by an order of magnitude. Our work can significantly reduce the training and storage burden of Monte Carlo simulations at current and future collider experiments.

1. INTRODUCTION

Particle physics experiments like those at the Large Hadron Collider at CERN, are running at progressively higher energies and are collecting more data than ever before. As a result, the experimental precision of the measurements they perform is continuously improving. However, to infer what these measurements mean for the interactions between the fundamental constituents of matter, they have to be compared with and interpreted in light of, our current theoretical understanding. This is done by performing first-principles computations for these high energy processes order by order in a power series expansion. After the computation, the resulting function is used in Monte Carlo simulations. The successive terms in the power series expansion, simplistically, become progressively smaller. Schematically, this can be written as: F (x) = f 00 (x) + α f 01 (x) + α 2 {f 11 (x) + f 02 (x)} + . . . . where α ≪ 1 is the small expansion parameter. The term of interest to our current work is the one enclosed by the curly braces in equation ( 1) which we will refer to as the second-order termfoot_0 . The function, F (x), must be evaluated on the order of 10 9 -10 12 times for each simulation. However, for many processes, evaluating the second-order term, specifically, f 02 , is computationally spaceand time-intensive and could take several seconds to compute a single data point. Moreover, these samples cannot be reused leading to an overall high cost of computation for the entire process under consideration. Building surrogate models to speed up Monte Carlo simulations is highly relevant not only in particle physics but in a very large set of problems addressed by all branches of physics using perturbative expansion like the one in equation ( 1). We give a broader overview of the physics motivation and applications in appendix A.



Here order refers to the power of the expansion coefficient α.1

