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.
Author indications on fulfilling journal expectations
Provide a novel and synergetic link between different research areas.
Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
Detail a groundbreaking theoretical/experimental/computational discovery
Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing
Reports on this Submission
Report #1 by
Anonymous
(Referee 1) on 2025-6-3
(Invited Report)
Strengths
modern machine-learning method for efficient solution of a numerical problem in field theory
clearly written
convincing numerical results after revision
Weaknesses
generality of the method and transferability to other, similar problems unclear and uncommented
Report
I think the paper in its revised form meets the publication criteria in SciPost. In particular the updated figures convey in a much better way the numerical accuracy, which was difficult to follow in the previous version.
Recommendation
Publish (meets expectations and criteria for this Journal)
