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.
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Acknowledgments
We thank Justin Berman, François Charton, Jordan Ellenberg, Garrett Merz, Maja Rudolph and Johann Usovitsch for fruitful discussions, Baptiste Rozière and Alexander Smirnov for communication, François Charton and Johann Usovitsch for comments on the manuscript as well as Cynthia Rodríguez for initial collaboration. Parts of the computations done for this project were performed on the UCloud interactive HPC system, which is managed by the eScience Center at the University of Southern Denmark. Other parts were performed on SCIENCE AI Centre’s GPU cluster at the University of Copenhagen. The work of MvH and MW was supported by the research grant 00025445 from Villum Fonden. MW was further supported by the Sapere Aude: DFF-Starting Grant 4251-00029B. MW moreover acknowledges the warm hospitality of the Data Science Institute, University of Wisconsin.
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von Hippel, M., Wilhelm, M. Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning. J. High Energ. Phys. 2025, 185 (2025). https://doi.org/10.1007/JHEP05(2025)185
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DOI: https://doi.org/10.1007/JHEP05(2025)185