We employ physics-informed neural networks (PINNs) to solve fundamental Dyson-Schwinger integral equations in the theory of quantum electrodynamics (QED) in Euclidean space. Our approach uses neural networks to approximate the fermion wave function renormalization, dynamical mass function, and photon propagator. By integrating the Dyson-Schwinger equations into the loss function, the networks learn and predict solutions over a range of momenta and ultraviolet cutoff values. This method can be extended to other quantum field theories (QFTs), potentially paving the way for forefront applications of machine learning within high-level theoretical physics.

翻译：我们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）理论的基本Dyson-Schwinger积分方程。该方法利用神经网络逼近费米子波函数重整化函数、动力学质量函数以及光子传播子。通过将Dyson-Schwinger方程嵌入损失函数，网络能够学习并预测动量与紫外截断值范围内的解。此方法可扩展至其他量子场论（QFTs），有望为机器学习在尖端理论物理领域的应用开辟新途径。