{"title":"费曼测量的热带取样","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":"{\"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}","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}
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
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.
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.