Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding

In this paper, we use machine learning to discover a new seeding strategy for integration-by-parts reduction of Feynman integrals, which is a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. Our strategy allows us to reduce multi-loop integrals with large numerator powers via essentially the standard Laporta algorithm but with a sparse selection of seed integrals that grows only linearly with the numerator power, whereas existing strategies lead to growth with a polynomial power that increases with the complexity of the integral being reduced.

The seeds are restricted to a thin tube-like region that connects the target integral to the master integrals along a zigzag path. We demonstrate the power of our approach by reducing non-planar 2-loop 5-point integrals of rank 20 with numerical kinematics over a finite field, which is prohibitively difficult for the Laporta algorithm with conventional seeding.

Going beyond individual integrals, we further demonstrate the reduction of a complete set of top-level rank-10 integrals by dividing the target integrals into several chunks, each of which can be solved by our sparse seeding strategy with considerably less time and a significantly lower memory footprint than other state-of-the-art strategies, making the approach well-suited for phenomenological applications. We provide a proof-of-principle implementation on GitHub at https://github.com/andreslunagodoy/tube_seeding.