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

Step (N) 20000 30000 40000 50000 ${{\mathbb{L}}}_{2}$-norm error u 8.117321e-03 8.733681e-03 8.113012e-04 2.130153e-04 v 7.993082e-03 4.103771e-03 8.034227e-04 6.880915e-04 ψ 9.910189e-04 9.204713e-04 6.001371e-04 3.437614e-04 Loss function 4.421448e-03 5.101375e-03 1.121848e-03 9.857296e-04