Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding
This work addresses a key bottleneck in high-precision calculations for particle and gravitational-wave physics, offering a practical improvement for multi-loop integral reduction.
The authors use machine learning to develop a tube-seeding strategy for integration-by-parts reduction of Feynman integrals, achieving linear growth in seed selection with numerator power instead of polynomial, and demonstrating reduction of non-planar 2-loop 5-point integrals of rank 20 and a complete set of top-level rank-10 integrals with lower time and memory footprint.
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.