Fig. 4

Topological phase boundary shift of perturbed systems with perturbation strengths η = {3,6,9} (from bottom to top) identified with the trained DNN. The Chern number of the perturbed systems identified with our trained DNN are represented with the symbols “, , ” for \({\cal{C}} = 0,1, - 1\) respectively, and the coordinates of the symbols represent the system’s parameters {t₃, m}. The thin grey line is the phase boundary of unperturbed system (η = 0), the blue line is the theoretical prediction of phase boundary for the perturbed systems. The horizontal displacement of the blue lines from the grey line indicates the topological phase boundary shift of the corresponding perturbed system