GPU Implementation of Zippel Method for Feynman Integral Reconstruction

TL;DR

This paper presents a GPU-based implementation of the Zippel algorithm for efficient rational reconstruction of multivariate polynomials, addressing computational bottlenecks in Feynman integral reduction in particle physics.

Contribution

It introduces a novel GPU port of the classical and balanced Zippel algorithms, enhancing performance for multivariate polynomial reconstruction.

Findings

GPU implementation accelerates Zippel algorithm evaluation

Improves efficiency in Feynman integral reduction workflows

Demonstrates scalability on multiple GPU architectures

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.