SciPost Submission Page
Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
by Rodrigo Carmo Terin
Submission summary
| Authors (as registered SciPost users): | Rodrigo Carmo Terin |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202503_00026v1 (pdf) |
| Date submitted: | 2025-03-18 10:02 |
| Submitted by: | Carmo Terin, Rodrigo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational, Phenomenological |
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 can be extended to other quantum field theories, paves the way for 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:
Reports on this Submission
Strengths
1. clearly written
2. interesting application
3. PINN for integral equations as a novel method
Weaknesses
1. numerical validity difficult to asses
2. approximations made cast doubt on generality of the method
Report
The paper "physics-informed neural network's viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics" presents a machine learning-method based on PINNs for solving the DSEs. I appreciate the novel character to apply PINNs to integral equations and DSEs as a highly-relevant application case in theoretical physics. The paper is clearly written, gives a nice summary of PINN applications in the introduction, and is very explicit in outlining the numerical method and the PINN application. I'm doubtful, however, about the numerical validity of the method, as exemplified by the figures, and wonder how restrictive simplifying assumptions ultimately are. I'd like to ask the author to clarify these points, before an actual publication can be considered.
Requested changes
My specific points are
1. The numerics relies on the "rainbow approximation" for treating the implicit/coupled integral equations. I'm wondering whether this restrict the generality of the PINN method to this type of problem. I'd like the author to comment on this.
2. Similarly, the assumption of Landau gauge simplify the equations, but the method itself should work independent of gauge- a argument would be likewise appreciated.
3. The author should include a comment on the choice of loss function in equation 22. In addition, it'd be great to know whether the author has encountered the fall-back of PINNs onto trivial solutions, for instance B=0, instead of the physically wanted solution.
4. My largest issue are the figures: First of all, I'd like to suggest merging the figures 1 and 3, and 2 and 4 into pairs, as they show show the same results and are thought to demonstrate the validity of the PINN as a numerical method. Then, I'd be important to give A(p^2) in a more meaningful representation. I'm a bit surprised by the differences between the results shown in figures 2 and 4: they are very different, and I can't read the y-axis label clearly. To my view, a comparison between a standard numerical technique and the PINN results is necessary before embarking on conclusions.
Recommendation
Ask for major revision