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

Perturbative Quantum Field Theory has proven to be a vastly successful theoretical framework for calculating precision predictions, with applications ranging from collider physics to gravitational-wave physics. A crucial step in the calculation of precision predictions is the reduction of the occurring Feynman integrals to a much smaller set of so-called master integrals, using integration-by-parts (IBP) identities [1-3]. This IBP reduction is a major bottleneck in precision calculations, requiring hundred thousands of CPU hours in current applications [4] and obstructing other applications altogether. IBP identities relate Feynman integrals with different integer exponents of the propagators as well as irreducible scalar products (ISP) in the numerator. They can easily be derived for general values of the exponents, see e.g.