Fig. 1. Schematic diagram of laser cavity

Fig. 2. Schematic diagram of PINNs

Fig. 3. Schematic diagrams of complex-valued laser and gain distributions at first plane along light propagation direction. (a) Real part of complex-valued laser distribution; (b) imaginary part of complex-valued laser distribution; (c) gain distribution; (d) local magnification of Fig. 3 (c)

Fig. 4. Residual distributions of real and imaginary parts of numerical results for complex-valued laser field. (a) Real part; (b) imaginary part

Fig. 5. Comparison of numerical results and PINNs prediction results of complex-valued laser distributions at seventh plane along light propagation direction

Fig. 6. Comparison of numerical result and PINNs prediction result of gain distribution. (a) Numerical result; (b) PINNs prediction result

Fig. 7. Comparison of numerical result and PINNs prediction result after adding gain label at boundary (marked area) . (a) Numerical result; (b) PINNs prediction result