We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used for inputs of the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; the accuracy exceeds $99\%$ with the data at $t/a^2\le0.3$. High robustness against the change of simulation parameters is also confirmed. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out as a preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

中文翻译：

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用机器学习对 SU(3) Yang-Mills 理论中的拓扑荷进行分类

我们应用机器学习技术来识别四维 SU(3) Yang-Mills 理论中量子规范配置的拓扑电荷。在具有和不具有降维的原始和平滑规范配置上测量的拓扑电荷密度用于具有和不具有卷积层的神经网络 (NN) 的输入。梯度流用于规范场的平滑。我们发现，经过训练的神经网络可以根据小流量时间的数据高精度地预测在大流量时间确定的拓扑电荷；精度超过$99\%$，数据为$t/a^2\le0.3$。还证实了对仿真参数变化的高鲁棒性。