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

TL;DR

This paper explores machine learning methods, including genetic programming and large language models, to improve heuristics for integration-by-parts reductions of Feynman integrals, achieving state-of-the-art results and slight improvements.

Contribution

It introduces machine learning techniques to discover and enhance heuristics for Feynman integral reduction, surpassing traditional approaches.

Findings

Re-discovery of existing heuristics using ML methods

Achieved a small improvement over current heuristics

Demonstrated the potential of ML in complex physics calculations

Abstract

Integration-by-parts reductions of Feynman integrals pose a frequent bottle-neck 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.