Machine Learning Post-Minkowskian Integrals

TL;DR

This paper introduces a neural network-based method to enhance the numerical evaluation of Feynman integrals, significantly improving convergence and accuracy in complex physics calculations compared to traditional Monte Carlo techniques.

Contribution

The authors develop a neural network framework that improves importance sampling in Monte Carlo integration, advancing the computational efficiency for high-dimensional Feynman integrals in physics.

Findings

Neural network sampling outperforms VEGAS in convergence speed.

The method achieves higher precision in evaluating integrals for gravitational systems.

Neural importance sampling reduces computational time for complex integrals.

Abstract

We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine learning approach improves the convergence of the Monte Carlo algorithm for high-precision evaluation of multi-dimensional integrals compared to traditional algorithms. In particular, we use a neural network to improve the importance sampling. For a set of representative integrals appearing in the computation of the conservative dynamics for a compact binary system in General Relativity, we perform a quantitative comparison between the Monte Carlo integrators VEGAS and i-flow, an integrator based on neural network sampling.