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

arXiv: https://arxiv.org/abs/2411.02177 · HTML: https://mlsanity.com/paper/2411.02177/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 69 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Neural Integral Equations](https://mlsanity.com/paper/2209.15190/) (2022)
- [A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systems](https://mlsanity.com/paper/2407.20669/) (2024)
- [Identifying phase transitions in physical systems with neural networks: a neural architecture search perspective](https://mlsanity.com/paper/2404.15118/) (2024)

## Built on by (most cited first, 2 of 2)

- [Unraveling particle dark matter with Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.17597/) (2025)
- [Spectral functions in Minkowski quantum electrodynamics from neural reconstruction](https://mlsanity.com/paper/2510.24728/) (2025)

## Abstract (arXiv)

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.