Tropical sampling from Feynman measures

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-09-12 DOI:10.1016/j.cpc.2025.109846

Michael Borinsky , Mathijs Fraaije

{"title":"Tropical sampling from Feynman measures","authors":"Michael Borinsky , Mathijs Fraaije","doi":"10.1016/j.cpc.2025.109846","DOIUrl":null,"url":null,"abstract":"<div><div>We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an implementation, <span>momtrop</span>, and apply it to a series of relevant integrals from the loop-tree duality framework. Compared to naive sampling methods, we observe convergence speedups by factors of more than 10<sup>6</sup>.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> <span>momtrop</span></div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/v9mxr9dw2z.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://github.com/alphal00p/momtrop</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> MIT</div><div><em>Programming language:</em> <span>Rust</span></div><div><em>Nature of problem:</em> Efficient numerical evaluation of Feynman-type integrals (e.g. phase space or loop-tree duality integrals).</div><div><em>Solution method:</em> Efficient sampling of loop momenta distributed as the Feynman measure (i.e. the integrand of a scalar Euclidean Feynman integral) using tropical sampling [1]. The input to the library is the graph associated to the Feynman measure. From the graph a sampler is produced that takes as input a set of uniformly distributed random numbers and returns a (weighted) set of loop momenta.</div><div><em>Additional comments including restrictions and unusual features:</em> Memory usage is exponential in the number of propagators of the Feynman integral. There can be numerical instabilities if the parameters are close to a divergent configuration.</div></div><div><h3>References</h3><div><ul><li><span>[1]</span><span><div>M. Borinsky, Tropical Monte Carlo quadrature for Feynman integrals, Ann. Inst. H. Poincare D Comb. Phys. Interact. 10 (4) (2023) 635–685. <span><span>arXiv:2008.12310</span><svg><path></path></svg></span>, <span><span>https://doi.org/10.4171/aihpd/158</span><svg><path></path></svg></span>.</div></span></li></ul></div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"317 ","pages":"Article 109846"},"PeriodicalIF":3.4000,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525003480","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an implementation, momtrop, and apply it to a series of relevant integrals from the loop-tree duality framework. Compared to naive sampling methods, we observe convergence speedups by factors of more than 10⁶.

Program summary

Program Title: momtrop

CPC Library link to program files: https://doi.org/10.17632/v9mxr9dw2z.1

Developer's repository link: https://github.com/alphal00p/momtrop

Licensing provisions: MIT

Programming language: Rust

Nature of problem: Efficient numerical evaluation of Feynman-type integrals (e.g. phase space or loop-tree duality integrals).

Solution method: Efficient sampling of loop momenta distributed as the Feynman measure (i.e. the integrand of a scalar Euclidean Feynman integral) using tropical sampling [1]. The input to the library is the graph associated to the Feynman measure. From the graph a sampler is produced that takes as input a set of uniformly distributed random numbers and returns a (weighted) set of loop momenta.

Additional comments including restrictions and unusual features: Memory usage is exponential in the number of propagators of the Feynman integral. There can be numerical instabilities if the parameters are close to a divergent configuration.

References

[1]
M. Borinsky, Tropical Monte Carlo quadrature for Feynman integrals, Ann. Inst. H. Poincare D Comb. Phys. Interact. 10 (4) (2023) 635–685. arXiv:2008.12310, https://doi.org/10.4171/aihpd/158.

查看原文本刊更多论文

费曼测量的热带取样

我们介绍了一种算法，该算法对一组分布为给定费曼被积的环路动量进行采样。该算法采用热带采样方法，可以有效地求相空间型积分。我们提供了一个实现，momtrop，并将其应用于循环树对偶框架中的一系列相关积分。与朴素抽样方法相比，我们观察到收敛速度超过106倍。程序摘要程序标题：momtropCPC库链接到程序文件：https://doi.org/10.17632/v9mxr9dw2z.1Developer's存储库链接：https://github.com/alphal00p/momtropLicensing条款：mit编程语言：rust问题的性质：费曼型积分的有效数值评估（例如相空间或环树对偶积分）。求解方法：利用热带采样[1]对费曼测度分布的环路动量（即标量欧几里得费曼积分的被积）进行有效采样。库的输入是与费曼测量相关的图形。从图中产生一个采样器，它将一组均匀分布的随机数作为输入，并返回一组（加权）循环动量。额外的注释包括限制和不寻常的功能：内存使用是费曼积分的传播数的指数。如果参数接近发散构型，则可能存在数值上的不稳定性。费曼积分的热带蒙特卡罗积分，安。庞加莱研究所。理论物理。互动，10(4)(2023)635-685。arXiv: 2008.12310, https://doi.org/10.4171/aihpd/158。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.