Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge
2026-07-23 • Machine Learning
Machine Learning
AI summaryⓘ
The authors solved complex mathematical equations from particle physics (called Dyson--Schwinger equations) using a neural network trained to minimize errors. Their neural network results matched traditional solutions closely and stayed consistent under various conditions. They found that changing a specific part of the model (the three-gluon vertex) had a bigger impact than the neural network's own inaccuracies. Additionally, their method captured some known behaviors of the theory within expected limitations.
Dyson–Schwinger equationsLandau gaugeYang–Mills theoryneural networksthree-gluon vertexMiniMOM schemegluon Schwinger functionultraviolet runninginfrared boundary conditionfixed-point solution
Authors
Rodrigo Carmo Terin
Abstract
The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.