  Neural networks possess formidable representational power, rendering them
invaluable in solving complex quantum many-body systems. While they excel at
analyzing static solutions, nonequilibrium processes, including critical
dynamics during a quantum phase transition, pose a greater challenge for neural
networks. To address this, we utilize neural networks and machine learning
algorithms to investigate the time evolutions, universal statistics, and
correlations of topological defects in a one-dimensional transverse-field
quantum Ising model. Specifically, our analysis involves computing the energy
of the system during a quantum phase transition following a linear quench of
the transverse magnetic field strength. The excitation energies satisfy a
power-law relation to the quench rate, indicating a proportional relationship
between the excitation energy and the kink numbers. Moreover, we establish a
universal power-law relationship between the first three cumulants of the kink
numbers and the quench rate, indicating a binomial distribution of the kinks.
Finally, the normalized kink-kink correlations are also investigated and it is
found that the numerical values are consistent with the analytic formula.
