Header

UZH-Logo

Maintenance Infos

A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec


Borowka, S; Heinrich, G; Jahn, S; Jones, S P; Kerner, M; Schlenk, J (2019). A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec. Computer Physics Communications, 240:120-137.

Abstract

The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.

Abstract

The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.

Statistics

Citations

Dimensions.ai Metrics
16 citations in Web of Science®
18 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

20 downloads since deposited on 20 Aug 2019
9 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Hardware and Architecture
Physical Sciences > General Physics and Astronomy
Uncontrolled Keywords:Hardware and Architecture, General Physics and Astronomy
Language:English
Date:1 July 2019
Deposited On:20 Aug 2019 13:02
Last Modified:29 Jul 2020 11:06
Publisher:Elsevier
ISSN:0010-4655
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.cpc.2019.02.015
Project Information:
  • : FunderH2020
  • : Grant ID739568
  • : Project TitlePRO-METROFOOD - Progressing towards the construction of METROFOOD-RI
  • : FunderFP7
  • : Grant ID340983
  • : Project TitleMCATNNLO - High Precision Simulation of particle collisions at the LHC
  • : FunderH2020
  • : Grant ID739568
  • : Project TitlePRO-METROFOOD - Progressing towards the construction of METROFOOD-RI
  • : FunderFP7
  • : Grant ID340983
  • : Project TitleMCATNNLO - High Precision Simulation of particle collisions at the LHC

Download

Hybrid Open Access

Download PDF  'A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec'.
Preview
Content: Published Version
Filetype: PDF
Size: 930kB
View at publisher
Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)