A machine learning approach for efficient multi-dimensional integration

Abstract Many physics problems involve integration in multi-dimensional space whose analytic solution is not available. The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in s...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Boram Yoon
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/d6f6aeb2505749ccbcc8199689dc48fa
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:d6f6aeb2505749ccbcc8199689dc48fa
record_format	dspace
spelling	oai:doaj.org-article:d6f6aeb2505749ccbcc8199689dc48fa2021-12-02T18:14:30ZA machine learning approach for efficient multi-dimensional integration10.1038/s41598-021-98392-z2045-2322https://doaj.org/article/d6f6aeb2505749ccbcc8199689dc48fa2021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-98392-zhttps://doaj.org/toc/2045-2322Abstract Many physics problems involve integration in multi-dimensional space whose analytic solution is not available. The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in solving the physics problems. We propose a novel numerical multi-dimensional integration algorithm using machine learning (ML). After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral. Then, the difference between the approximation and the true answer is calculated to correct the bias in the approximation of the integral induced by ML prediction errors. Because of the bias correction, the final estimate of the integral is unbiased and has a statistically correct error estimation. Three ML models of multi-layer perceptron, gradient boosting decision tree, and Gaussian process regression algorithms are investigated. The performance of the proposed algorithm is demonstrated on six different families of integrands that typically appear in physics problems at various dimensions and integrand difficulties. The results show that, for the same total number of integrand evaluations, the new algorithm provides integral estimates with more than an order of magnitude smaller uncertainties than those of the VEGAS algorithm in most of the test cases.Boram YoonNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-8 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Boram Yoon A machine learning approach for efficient multi-dimensional integration
description	Abstract Many physics problems involve integration in multi-dimensional space whose analytic solution is not available. The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in solving the physics problems. We propose a novel numerical multi-dimensional integration algorithm using machine learning (ML). After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral. Then, the difference between the approximation and the true answer is calculated to correct the bias in the approximation of the integral induced by ML prediction errors. Because of the bias correction, the final estimate of the integral is unbiased and has a statistically correct error estimation. Three ML models of multi-layer perceptron, gradient boosting decision tree, and Gaussian process regression algorithms are investigated. The performance of the proposed algorithm is demonstrated on six different families of integrands that typically appear in physics problems at various dimensions and integrand difficulties. The results show that, for the same total number of integrand evaluations, the new algorithm provides integral estimates with more than an order of magnitude smaller uncertainties than those of the VEGAS algorithm in most of the test cases.
format	article
author	Boram Yoon
author_facet	Boram Yoon
author_sort	Boram Yoon
title	A machine learning approach for efficient multi-dimensional integration
title_short	A machine learning approach for efficient multi-dimensional integration
title_full	A machine learning approach for efficient multi-dimensional integration
title_fullStr	A machine learning approach for efficient multi-dimensional integration
title_full_unstemmed	A machine learning approach for efficient multi-dimensional integration
title_sort	machine learning approach for efficient multi-dimensional integration
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/d6f6aeb2505749ccbcc8199689dc48fa
work_keys_str_mv	AT boramyoon amachinelearningapproachforefficientmultidimensionalintegration AT boramyoon machinelearningapproachforefficientmultidimensionalintegration
_version_	1718378424091803648

A machine learning approach for efficient multi-dimensional integration

Ejemplares similares