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

Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning