Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
Abstract Integration-by-parts reductions of Feynman integrals pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts identities, whose quality heavily influences the perfo...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)185 |
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| author | Matt von Hippel Matthias Wilhelm |
| author_facet | Matt von Hippel Matthias Wilhelm |
| author_sort | Matt von Hippel |
| collection | DOAJ |
| description | Abstract Integration-by-parts reductions of Feynman integrals pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts identities, whose quality heavily influences the performance. In this paper, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art. |
| format | Article |
| id | doaj-art-795282bf820f4dd9b2daca6d3badcccd |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-795282bf820f4dd9b2daca6d3badcccd2025-08-20T03:25:15ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025512610.1007/JHEP05(2025)185Refining Integration-by-Parts Reduction of Feynman Integrals with Machine LearningMatt von Hippel0Matthias Wilhelm1Niels Bohr International Academy, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy, Niels Bohr Institute, University of CopenhagenAbstract Integration-by-parts reductions of Feynman integrals pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts identities, whose quality heavily influences the performance. In this paper, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art.https://doi.org/10.1007/JHEP05(2025)185Scattering AmplitudesAutomationElectroweak Precision Physics |
| spellingShingle | Matt von Hippel Matthias Wilhelm Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning Journal of High Energy Physics Scattering Amplitudes Automation Electroweak Precision Physics |
| title | Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning |
| title_full | Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning |
| title_fullStr | Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning |
| title_full_unstemmed | Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning |
| title_short | Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning |
| title_sort | refining integration by parts reduction of feynman integrals with machine learning |
| topic | Scattering Amplitudes Automation Electroweak Precision Physics |
| url | https://doi.org/10.1007/JHEP05(2025)185 |
| work_keys_str_mv | AT mattvonhippel refiningintegrationbypartsreductionoffeynmanintegralswithmachinelearning AT matthiaswilhelm refiningintegrationbypartsreductionoffeynmanintegralswithmachinelearning |