用神经网络求解量子电动力学中的动态质量函数，突破传统数值方法局限。
Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
- 将积分方程直接嵌入损失函数，实现连续可导的质量函数学习。
- 在兰道规范下成功生成非微扰的费米子动态质量函数。
- 为机器学习应用于高能理论物理提供新范式，适合相关领域研究者。
本文采用物理信息神经网络（PINNs）求解欧几里得空间中量子电动力学（QED）的杜森-施温格方程，重点在于兰道规范下费米子动态质量函数的非微扰生成。通过将积分方程直接引入损失函数，所提出的PINN框架使单一神经网络能够学习在动量谱上连续且可导的质量函数表示。我们还将该方法与传统数值算法进行了对比，揭示了二者的主要差异。这一创新策略有望推广至其他量子场论，是机器学习在前沿理论物理中应用的初步尝试。
原文摘要 · Abstract (English)
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.
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