Deep Learning Beyond Lefschetz Thimbles

TL;DR

This paper introduces a machine learning approach to efficiently approximate the integration manifold in complex field theories, significantly reducing the sign problem and computational cost compared to traditional methods.

Contribution

It proposes a neural network-based method to bypass solving expensive flow equations, enabling faster and more stable sampling in theories with sign problems.

Findings

Reduces sign problem in the 1+1D Thirring model

Speeds up sampling compared to traditional flow methods

Avoids Monte Carlo trapping issues

Abstract

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the $1+1$ dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parameterization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.