Targeting Multi-Loop Integrals with Neural Networks

TL;DR

This paper introduces neural network-based methods to optimize integration contours for multi-loop Feynman integrals, significantly improving numerical precision in complex contour deformation techniques.

Contribution

It proposes a novel approach combining global complex shifts and normalizing flows to enhance contour optimization for multi-loop integral evaluations.

Findings

Significant gain in numerical precision achieved

Effective contour optimization using neural networks demonstrated

Applicable to complex multi-loop Feynman integrals

Abstract

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. They can lead to a significant gain in precision.