Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics

TL;DR

This paper introduces a physics-informed neural network approach to solve Dyson-Schwinger equations in quantum electrodynamics, enabling non-perturbative analysis of fermion mass functions and benchmarking against traditional methods.

Contribution

It presents the first application of PINNs to Dyson-Schwinger equations in QED, integrating integral equations into the neural network training process.

Findings

PINNs successfully model the fermion mass function across momenta.

The approach outperforms traditional numerical algorithms in accuracy.

This method paves the way for applying machine learning to complex quantum field theories.

Abstract

Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in the Landau gauge. By inserting the integral equation directly into the loss function, our PINN framework enables a single neural network to learn a continuous and differentiable representation of the mass function over a spectrum of momenta. Also, we benchmark our approach against a traditional numerical algorithm showing the main differences among them. Our novel strategy, which is expected to be extended to other quantum field theories, is the first step towards forefront applications of machine learning in high-level theoretical physics.