MCNNTUNES: Tuning Shower Monte Carlo generators with machine learning

Abstract

The parameters tuning of event generators is a research topic characterized by complex choices: the generator response to parameter variations is difficult to obtain on a theoretical basis, and numerical methods are hardly tractable due to the long computational times required by generators. Event generator tuning has been tackled by parametrization-based techniques, with the most successful one being a polynomial parametrization. In this work, an implementation of tuning procedures based on artificial neural networks is proposed. The implementation was tested with closure testing and experimental measurements from the ATLAS experiment at the Large Hadron Collider.

Program summary

Program Title: MCNNTUNES

CPC Library link to program files: https://doi.org/10.17632/dmkydsxgd3.1

Developer’s repository link: https://github.com/N3PDF/mcnntunes

Licensing provisions: GPLv3

Programming language: Python

Nature of problem: Shower Monte Carlo generators introduce many parameters that must be tuned to reproduce the experimental measurements. The dependence of the generator output on these parameters is difficult to obtain on a theoretical basis.

Solution method: Implementation of a tuning method using supervised machine learning algorithms based on neural networks, which are universal approximators.

Introduction

Shower Monte Carlo (SMC) event generators are tools that apply shower algorithms to simulated collisions of particles at high energies. They introduce many parameters, mainly due to the usage of phenomenological models, like the hadronization model or the underlying event model, needed to describe the low-energy limit of quantum chromodynamics (QCD) which is not easily calculable from first principles. These parameters are difficult to obtain on a theoretical basis, so they must be carefully tuned in order to make the generators reproduce the experimental measurements. The procedure of estimating the best value for each parameter is called event generator tuning.

This tuning procedure is made more difficult by the high computational cost of running a generator, so it requires methods to study the dependence between a generator output and its parameters. Moreover, since the observables considered while analysing the generator output play a pivotal role in determining the tuning, one needs to model this dependence for different observables at the same time.

The current state-of-the-art tuning procedure is based on a polynomial parametrization of the generator response to parameter variations, followed by a numerical fit of the parametrized behaviour to experimental data. This is the procedure which is implemented in Professor [1], the primary tool for SMC event generator tuning at the Large Hadron Collider (LHC). However, the assumption that the dependence of the generator output on its parameters is polynomial is not always justified.

This paper investigates new tuning procedures based on artificial neural networks. Artificial neural networks are universal function approximators [2], [3], [4], providing accurate predictive models with a finite number of parameters, as shown in early attempts [5]. Two different tuning procedures are presented, called Per Bin and Inverse from now on. The former follows the same approach of Professor, but with a different parametrization model made of fully-connected neural networks and a different minimization algorithm: the evolutionary algorithm CMA-ES [6]. The latter takes a completely different approach: by using a fully-connected neural network, it learns to predict directly the parameters that the generator needs to output a given result. These two procedures were implemented in the Python package MCNNTUNES [7] and then tested with the event generator PYTHIA8 [8]. Two different datasets of Monte Carlo runs were generated, with three and four tunable parameters respectively. The procedures were tested with closure tests and with real experimental data taken from the ATLAS experiment [9], [10].

A description of the procedures and their technical implementation is presented in Section 2, while Section 3 contains the details of the testing phase. Finally, the conclusion of this work and future development directions are presented in Section 4.