Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
This provides a novel computational approach for theoretical physicists studying quantum field theories, though it is incremental as it applies an existing PINN method to a new physics problem.
The paper tackles solving the Dyson-Schwinger equations of quantum electrodynamics to generate the fermion's dynamical mass function non-perturbatively, using physics-informed neural networks (PINNs) that learn a continuous representation and benchmark against traditional numerical methods.
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.