Fig. 1. Neural network dataset generation process. WDM, wavelength division multiplexer; EDF, erbium-doped fiber; SMF, single-mode fiber; SA, saturable absorber; OC, 10%/90% coupler.

Fig. 2. Schematic diagram of the DFNN for mode-locked fiber laser dynamic prediction.

Fig. 3. Training, validation, and test losses across epochs.

Fig. 4. Temporal evolution modeling of no soliton formation propagation dynamics under g₀ = 1.145 m⁻¹, L_EDF = 0.263 m, and L_SMF = 1.563 m. (a) The temporal evolution dynamics of the SSFM (top), the DFNN (middle), and the LSTM (bottom). (b) Temporal intensity at selected roundtrips predicted by the DFNN (dashed black lines), simulated with the SSFM (solid red lines).

Fig. 5. Temporal evolution modeling of single soliton formation propagation dynamics under g₀ = 2.658 m⁻¹, L_EDF = 0.293 m, and L_SMF = 1.552 m. (a) The temporal evolution dynamics of the SSFM (top), the DFNN (middle), and the LSTM (bottom). (b) Temporal intensity at selected roundtrips for detuned steady state predicted by the DFNN (dashed black lines), simulated with the SSFM (solid red lines).

Fig. 6. Temporal evolution modeling of soliton molecule formation with narrow temporal separation propagation dynamics under g₀ = 4.030 m⁻¹, L_EDF = 0.364 m, and L_SMF = 1.178 m. (a) The temporal evolution dynamics of the SSFM (top), the DFNN (middle), and the LSTM (bottom). (b) Temporal intensity at selected roundtrips from detuned steady state to steady state predicted by the DFNN (dashed black lines), simulated with the SSFM (solid red lines).

Fig. 7. Temporal evolution modeling of soliton molecule formation with wide temporal separation propagation dynamics under g₀ = 4.322 m⁻¹, L_EDF = 0.357 m, and L_SMF = 1.406 m. (a) The temporal evolution dynamics of the SSFM (top), the DFNN (middle), and the LSTM (bottom). (b) Temporal intensity at selected roundtrips from detuned steady state to steady state predicted by the DFNN (dashed black lines), simulated with the SSFM (solid red lines).

Table 1. Performance Comparison Between the DFNN, the LSTM^[27], and the SSFM