Speaker
Description
We employ machine learning techniques to estimate the topological charge $Q$ of gauge configurations in SU(3) Yang-Mills theory. As a first trial, four-dimensional convolutional neural networks are trained to estimate the topological charge from the topological charge density on gauge configurations. The value of $Q$ measured by the gradient flow is used for the definition of the correct value. We, however, find that the neural network completely fails in the classification in this approach.
Next, we feed the topological charge density at nonzero but small flow times $t$ as inputs for the neural network. Dimensional reduction is also performed as well as the four-dimensional analysis. We find that, by the combination of the topological charge densities at $t/a^2\le0.3$, the trained neural network can estimate the correct value of $Q$ with more than $95\%$ accuracy, although the distribution of the $Q$ value at $t/a^2=0.3$ does not well converge to integer values. This result suggests that the value of $Q$ obtained at large gradient-flow time can be well estimated from the information obtained at small flow time, and thus the numerical costs to estimate the value of $Q$ in the gradient flow method can be substantially reduced with the aid of the machine learning.
It is also found that the best accuracy is obtained when the dimension of the input is reduced to zero, i.e. when the four-dimensinal integral of the topological charge density is used for inputs of the neural network. This result shows that the neural network cannot finds any useful feature from the spatial structure of the topological charge density.
The dependences on lattice spacing, spatial volume, and numerical costs for training will also be discussed.