Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
This work addresses a bottleneck in calculations for theoretical particle and gravitational-wave physics, providing an incremental improvement for physicists in these fields.
The authors tackled the problem of integration-by-parts reductions of Feynman integrals by using machine-learning techniques, resulting in the rediscovery of state-of-the-art heuristics and a small advance in one example. The approach led to a minor improvement over the current state of the art.
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.