Fig. 1. Schematic diagram of the simulated NOGM system: high-power pump pulses at 1064 nm and the continuous-wave seed at 1121 nm are coupled through a wavelength division multiplexer (WDM) into the Raman gain fiber.

Fig. 2. Architecture of the implemented fully connected neural network (FCNN): a four-layer structure with hidden layer widths of 256, 256, 512, and 512, employing ReLU activation functions. The input includes initial pump pulse parameters and propagation distances, while the output represents the predicted spectrum.

Fig. 3. Evolution of training and validation losses during the network training process, showing the convergence of both losses over training epochs.

Fig. 4. Comparison of simulated and FCNN predicted spectra for pulse propagation in PM 980 fiber with initial pump pulse parameters of 400 nJ and 10 ps: (a) GNLSE-simulated spectral evolution; (b) FCNN-predicted spectral evolution; (c) absolute error distribution; (d)–(i) spectral comparisons at specific propagation distances (z = 0.1, 0.2, 0.4, 0.6, 0.8, 1.0 m).

Fig. 5. Comparison of simulated and FCNN predicted spectra for pulse propagation in PM Raman fiber with initial pump pulse parameters of 300 nJ and 10 ps: (a) GNLSE-simulated spectral evolution; (b) FCNN-predicted spectral evolution; (c) absolute error distribution; (d)–(i) spectral comparisons at specific propagation distances (z = 0.02, 0.04, 0.08, 0.12, 0.16, 0.20 m).

Fig. 6. Evolution of NRMSE (−10 dB) with propagation distance for different initial pump pulse parameters: (a) PM 980 fiber; (b) PM Raman fiber. The NRMSE (−10 dB) is calculated for spectral regions above −10 dB relative to the maximum intensity of the generated spectrum.

Fig. 7. Performance comparison of neural networks with different architectures in predicting spectral evolution: (a) Net 1 with reduced parameters; (b) Net 2 with architecture shown in Fig. 2; (c) Net 3 with increased parameters. The NRMSE (−10 dB) values demonstrate the trade-off between model complexity and prediction accuracy.

Fig. 8. Heat map showing the neural network’s generalization capability for different input pulse parameters in PM Raman fiber. The color represents the mean NRMSE (−10 dB) values across all propagation distances (0–0.20 m).

Fig. 9. Comparison of simulated and FCNN predicted spectra for pulse propagation in PM Raman fiber with initial pump pulse parameters of 460 nJ and 36 ps: (a) GNLSE-simulated spectral evolution; (b) FCNN-predicted spectral evolution; (c) absolute error distribution; (d)–(i) spectral comparisons at specific propagation distances (z = 0.02, 0.04, 0.08, 0.12, 0.16, 0.20 m).