Fig. 1. The basic structure of PINN consists of four parts: neural network, derivative calculation, partial differential equation calculation, and minimization loss function

Fig. 2. Predicted evolution results and error density of Gaussian pulse under various physical effects such as (a) GVD and SPM; (b) TOD and SPM; (c) GVD, SPM, and self-steepening; Predicted evolution results and error density of (d) first-order optical solitons and (e) second order optical solitons under the effect of GVD and SPM

Fig. 3. Schematic diagram of PDE loss for solving SRS ordinary differential evolution equations using PINN, with a total number of channels N=96

Fig. 4. Results obtained by numerical method and PINN at transmission distance of 20/40/60/80 km

Fig. 5. PINN-based solving scheme

Fig. 6. Evolution process of LP₀₁ and LP_11o modes in the y-z plane of tapered fiber obtained by FD and PINN by solving the PHE

Fig. 7. Mode speckle of five LP modes at different propagation distances in bent fibers obtained by FD and PINN by solving the PHE

Fig. 8. MSE variation curve with propagation distance for five LP modes in three geometric structures of optical fibers by PINN corresponding to FD-BPM

Fig. 9. Comparison of computational complexity (a) and running time (b) between PINN and finite difference method