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

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.

@article{terin2025_2411.02177,
  title={ Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics },
  author={ Rodrigo Carmo Terin },
  journal={arXiv preprint arXiv:2411.02177},
  year={ 2025 }
}