Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms.

Australia

Csaba Balázs

United Kingdom

Melissa Beekveld

Netherlands

Sascha Caron

Germany

Barry Dillon

Ben Farmer

China

Andrew Fowlie

Spain

Eduardo Garrido-Merchán

Will Handley

Luc Hendriks

Sweden

Iceland

Guðlaugur Jóhannesson

Adam Leinweber

Judita Mamužić

United States

Gregory Martinez

Sydney Otten

Roberto Austri

Pat Scott

Zachary Searle

Bob Stienen

Joaquin Vanschoren

Martin White

A comparison of optimisation algorithms for high-dimensional particle and astrophysics applications

Constraining the parameters of physical models with $$&gt;5-10$$ <math><mrow><mo>&gt;</mo><mn>5</mn><mo>-</mo><mn>10</mn></mrow></math>  parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of computational resources. The commonly used solution of reducing the number of relevant physical parameters hampers the generality of the results. In this paper we show that this problem can be alleviated by the use of active learning. We illustrate this with examples from high energy physics, a field where simulations are often expensive and parameter spaces are high-dimensional. We show that the active learning techniques query-by-committee and query-by-dropout-committee allow for the identification of model points in interesting regions of high-dimensional parameter spaces (e.g. around decision boundaries). This makes it possible to constrain model parameters more efficiently than is currently done with the most common sampling algorithms and to train better performing machine learning models on the same amount of data. Code implementing the experiments in this paper can be found on GitHub

Tom Heskes

Constraining the parameters of high-dimensional models with active learning

A key research question at the Large Hadron Collider is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: it requires time consuming generation of scattering events, simulation of the detector response, event reconstruction, cross section calculations and analysis code to test against several hundred signal regions defined by the ATLAS and CMS experiments. In the BSM-AI project we approach this challenge with a new idea. A machine learning tool is devised to predict within a fraction of a millisecond if a model is excluded or not directly from the model parameters. A first example is SUSY-AI, trained on the phenomenological supersymmetric standard model (pMSSM). About 300,Â 000 pMSSM model sets â each tested against 200 signal regions by ATLAS â have been used to train and validate SUSY-AI. The code is currently able to reproduce the ATLAS exclusion regions in 19 dimensions with an accuracy of at least 93% . It has been validated further within the constrained MSSM and the minimal natural supersymmetric model, again showing high accuracy. SUSY-AI and its future BSM derivatives will help to solve the problem of recasting LHC results for any model of new physics. SUSY-AI can be downloaded from http://susyai.hepforge.org/ . An on-line interface to the program for quick testing purposes can be found at http://www.susy-ai.org/ .

Jong Soo Kim

Poland

Krzysztof Rolbiecki

Roberto Ruiz de Austri

The BSM-AI project: SUSY-AI–generalizing LHC limits on supersymmetry with machine learning