Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
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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.
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.
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References · 10
- 2017Attention Is All You Needcited by 60,361
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
- 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 214
- 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 200
- 2021Equinox: neural networks in JAX via callable PyTrees and filtered transformationscited by 148
- 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
- 2022Neural Integral Equationscited by 23
- 2024A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systemscited by 2
- 2024Identifying phase transitions in physical systems with neural networks: a neural architecture search perspectivecited by 1
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