Solving forward and inverse problems of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via PINN deep learning

Jiaheng Li,Biao Li

Table 2. Comparison between the ${{\mathbb{L}}}_{2}$-norm errors and the activation functions of the predicted solution $\hat{\psi }(t,x)$.

Activation function ReLU Leaky ReLUs Sigmoid Tanh ${{\mathbb{L}}}_{2}$-norm error u 5.786123e-01 5.000701e-01 6.347641e-03 4.195627e-03 v 6.045615e-01 6.477965e-01 4.094651e-03 2.428159e-03 ψ 4.509659e-01 5.020687e-01 3.260262e-03 1.350881e-03 Loss function 4.489665e-02 4.765688e-02 5.862674e-06 1.384692e-06