Fig. 1. (a) Schematic of the FNN-based nonlinear model and the iteration of prediction; (b) detailed principle of the FNN model and reconstruction testing.

Fig. 2. Comparison between GNLSE simulation and FNN inverse prediction with initial pulse duration of 125.9 fs and peak power of 1 kW. (a) Temporal intensity evolution simulated by GNLSE; (b) temporal intensity evolution inversely predicted by FNN; (c) intensity and phase profiles at z = 0.05 and 0.15 m. The arrow in (b) points toward the predicted direction.

Fig. 3. Comparison of SCG (a) spectral and (b) temporal evolutions between GNLSE simulation (left panel) stimulated by a 94.8 fs, 1.26 kW TL pulse and the corresponding reconstruction map (middle panel). The right panels show the intensity and phase profiles at z = 0 and 0.2 m.

Fig. 4. Influence of the initial pulse deviation between GNLSE simulation and FNN model on reconstruction results. (a) Spearman correlation coefficients (r_ρ); (b) reconstructed NRMSEs (sorted in ascending order) of 100 testing samples; scatter diagrams show (c) predicted NRMSE, (d) SNIP, and (e) PPD versus the reconstructed NRMSE. The solid lines are the polynomial fitting curves. SNIP, similarity of normalized intensity profile; PPD, peak power difference.

Fig. 5. Comparison of SCG (a) spectral and (b) temporal (b) evolutions between GNLSE simulation (left panel) stimulated by a 96.7 fs, 1.43 kW chirped pulse with the chirp value of 1.58 and the corresponding reconstruction map (middle panel). The right panels show the intensity and phase profiles at z = 0 and 0.2 m.