Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning

• Published in: The journal of high energy physics Vol. 2025; no. 5; pp. 185 - 26
• Main Authors: von Hippel, Matt, Wilhelm, Matthias
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21.05.2025; Springer Nature B.V; SpringerOpen
• Subjects: Automation; Classical and Quantum Gravitation; Electroweak Precision Physics; Elementary Particles; Genetic algorithms; Gravitational waves; Heuristic; Heuristic methods; Integrals; Large language models; Machine learning; Mathematics; Mutation; Physics; Physics and Astronomy; Python; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Seeds; String Theory; Wave physics; Scattering Amplitudes; Automation; Electroweak Precision Physics
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP05(2025)185

A bstract 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.