Learning Feynman Diagrams using Graph Neural Networks

TL;DR

This paper applies graph neural networks to Feynman diagrams, achieving high-accuracy matrix element predictions rapidly, and proposes a method to advance quantum field theory analysis through learned diagram construction.

Contribution

It introduces a novel application of geometric deep learning to Feynman diagrams, demonstrating fast, accurate predictions and a new approach for quantum field theory analysis.

Findings

Matrix element predictions reach 90% accuracy within 1 significant figure.

Peak performance with 3 significant figures achieved in over 10% of cases.

Training converges in fewer than 200 epochs.

Abstract

In the wake of the growing popularity of machine learning in particle physics, this work finds a new application of geometric deep learning on Feynman diagrams to make accurate and fast matrix element predictions with the potential to be used in analysis of quantum field theory. This research uses the graph attention layer which makes matrix element predictions to 1 significant figure accuracy above 90% of the time. Peak performance was achieved in making predictions to 3 significant figure accuracy over 10% of the time with less than 200 epochs of training, serving as a proof of concept on which future works can build upon for better performance. Finally, a procedure is suggested, to use the network to make advancements in quantum field theory by constructing Feynman diagrams with effective particles that represent non-perturbative calculations.