GPU Implementation of Zippel Method for Feynman Integral Reconstruction

2025/05/30 by Smirnov, Alexander V., Rozhnov, Boris I., Voevodin, Vadim V.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2505.24256

Abstract

The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in elementary particle physics. In some cases with multiple variables it might become a bottleneck for the whole evaluation so that different optimizations are required. In this paper we describe how we ported the classical Zippel algorithm together with its balanced version for rational functions to graphical processor units and perform its evaluation on several GPUs.

Citations

• Kira 3: integral reduction with efficient seeding and optimized equation selection
• Feynman integral reduction: balanced reconstruction of sparse rational functions and implementation on supercomputers in a co-design approach
• Rational Tracer: a Tool for Faster Rational Function Reconstruction
• Kira 1.2 Release Notes
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Integration by parts: The algorithm to calculate β-functions in 4 loops

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