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Solving forward and inverse problems of the nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II potential via PINN deep learning
Jiaheng Li,Biao Li
Figure 6. The activation function's influence on the learning ability of this complex-valued PINN in the self-focusing NLSE with the generalized PT-symmetric Scarf-II potential and initial boundary value conditions in Case 1 given in Section 3.1: the deep learning results in four different activation functions {ReLU,Leaky ReLUs,Sigmoid,Tanh} from the first row to the last row. Left column images : the magnitude of the approximate predicted solution |ˆψ(t,x)| with the initial and Dirichlet boundary training data and 10 000 collocation points. Right three columns : comparisons of the exact and predicted solutions at the three temporal snapshots described by the three dotted black lines in the panels in the first column corresponding to time instants t = 0.5, 1.0 and 1.5.