用神经网络求解胶子-鬼粒子的微分方程，精度达百分比级。
Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge
- 用神经网络直接拟合方程残差，无需标注数据
- 结果与固定点解一致，对初始化等变化稳定
- 可复现紫外行为和胶子自能符号变化
在四维兰道规范下，利用仅从重整化方程残差训练的神经表示求解了耦合的鬼粒子与胶子的戴森-施温格方程（DSE）。神经解与固定点解在百分比量级上一致，且对初始化、网络规模、积分网格及红外边界条件的变化保持稳定。不同三胶子顶点模型的影响远大于神经误差。在截断限制下，也成功再现了MiniMOM紫外运行行为以及胶子斯温格函数的符号变化。
原文摘要 · Abstract (English)
The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.
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