Study of topological quantities of lattice QCD with a modified Wasserstein generative adversarial network

We propose a modified Wasserstein generative adversarial network (M-WGAN) to study the distribution of the topological charge in lattice QCD based on Monte Carlo simulations. We construct new generator and discriminator in M-WGAN to support the generation of high-quality distribution. Our results show that the M-WGAN scheme of machine learning should be helpful for us to calculate efficiently the 1D distribution of topological charge compared with the method by the Monte Carlo simulation alone.

Figure 1

The overall structure of M-WGAN.

Figure 2

The evolution of the average of plaquette under different initial conditions.

Figure 3

The distribution of topological charge based on the MC simulations with Wilson flow. A total number of Wilson flow time steps $N_{\mathrm{flow}}=600$ are chosen. The numbers of topological charge are 100 for the left plot and 300 for the right plot.

Figure 4

Comparison of models with 100, 200, 300 training data.

Figure 5

The fourth root of the topological susceptibility ${{\chi }_t}^{1/4}$ for MC and ML methods under different data size.

Figure 6

The distributions of topological charge for MC and ML methods.