用斯温格-戴森关系高效学习格点规范理论的参数
Efficient Learning of Lattice Gauge Theories with Fermions
- 基于斯温格-戴森关系构造凸损失函数，实现参数恢复
- 方法可扩展至含费米子的真实格点量子色动力学模型
- 为规范场论中的机器学习提供通用框架，适合理论物理研究者
我们提出一种从格点场论中恢复作用量参数的学习方法。该方法基于利用斯温格-戴森关系构建的凸损失函数。我们证明了主流的得分匹配方法是这一无限族有效损失函数中的特例。重要的是，我们的斯温格-戴森基础构造适用于包含格拉斯曼值场（用于描述动力学费米子）的规范场论。特别地，该方法被拓展至包含量子色动力学（QCD）的真实格点场论。
原文摘要 · Abstract (English)
We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.
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