FIESTA5: numerical high-performance Feynman integral evaluation

TL;DR

FIESTA5 tackles the numerical evaluation of multiloop Feynman integrals by enhancing sector decomposition with faster, more scalable integration. The key innovations include new integrators (Quasi Monte Carlo and Tensor Train), a codebase modernized to C++17, AVX-enabled evaluation, and improved contour transformation and sector balancing. Collectively, these changes enable significantly faster computations and extend the range of solvable integrals, including physically relevant kinematics that were previously intractable. The work demonstrates substantial speedups over FIESTA4 across multiple benchmarks and provides a practical framework for high-performance numerical Feynman integral evaluation on CPUs, GPUs, and clusters.

Abstract

In this paper we present a new release of the FIESTA program (Feynman Integral Evaluation by a Sector decomposiTion Approach). FIESTA5 is performance-oriented - we implemented improvements of various kinds in order to make Feynman integral evaluation faster. We plugged in two new integrators, the Quasi Monte Carlo and Tensor Train. At the same time the old code of FIESTA4 was upgraded to the C++17 standard and mostly rewritten without self-made structures such as hash tables. There are also several essential improvements which are most relevant for complex integrations - the new release is capable of producing results where previously impossible.