Passively mode-locked fiber lasers have significant application value in the field of ultrashort pulse generation due to their excellent parameter tunability. To elucidate the nonlinear relationship between cavity parameters and pulse characteristics in fiber lasers and optimize cavity structural design, this study employed an integrated approach combining stacking ensemble learning with Shapley additive explanations (SHAP) analysis to achieve laser performance prediction and design optimization.

This study adopted an integrated methodology combining theoretical modeling of fiber lasers, machine learning, and optimization algorithms, with the specific framework shown in Fig.1. First, a theoretical model of a mode-locked fiber laser with a saturable absorber (SA) was established based on the structure of a polarization-maintaining fiber. This study systematically investigated the influence of key parameters on pulse characteristics, including the length of dispersion-compensating fiber (DCF), second-order dispersion coefficient, nonlinear coefficient, gain saturation energy of erbium-doped fiber (EDF), and saturation absorption power and modulation depth of SA. A comprehensive mapping database between cavity parameters and pulse characteristics was established, and a high-precision prediction model was developed using a two-stage stacking ensemble learning framework. Additionally, SHAP analysis was then employed to analyze the contribution of cavity parameters to pulse characteristics and their interaction mechanisms. Six metaheuristic algorithms from the meta-heuristic algorithms in Python (MEALPY) platform were applied to perform multi-objective optimization of the stacking surrogate model, achieving inverse design optimization of the laser cavity parameters.

The results showed that the simulation achieved intracavity compression through dispersion management, compressing the pulse duration to the 400 fs level. The evolution of the laser pulses and spectra with the number of round trips was analyzed (Fig.2). Stable pulses were formed after approximately 36 round trips and remained in subsequent round trips. Before reaching stability, the pulse intensity gradually increased as the number of round trips increased. In the spectral evolution process in the frequency domain, the spectra broadened toward both sides from the 36th to the 70th round trips, forming multiple sidebands. To more clearly analyze the evolution process of the intracavity pulse, Fig.3 showed the evolution of the soliton pulse at different positions within the cavity during the 100th round trip. It could be observed that when the pulse passed through the output coupler (OC) and SA, the pulse energy decreased significantly, while the peak power decreased slightly. Subsequently, the influence of key parameters—such as DCF length, second-order dispersion coefficient, nonlinear coefficient, gain saturation energy of EDF, and saturation absorption power and modulation depth of SA—on pulse characteristics were analyzed, with specific results shown in Fig.4 and Fig.5. The study revealed that introducing DCF increased the pulse energy by about two times and the peak power by up to four times, providing clear insights into the relationship between cavity parameters and pulse performance. The laser was then simulated, randomly generating a dataset of 400 sets of cavity parameters and corresponding pulse characteristics. The mapping relationship was identified through a multi-model fused stacking regression model. As shown in Fig.6, the comparison between the stacking-predicted pulse characteristics and the target values demonstrated that the coefficient of determination (R²) for all prediction models was greater than 0.95, indicating excellent generalization ability.

The prediction performance of the first-stage learners showed that the stacking ensemble model significantly outperformed first-stage machine learning models such as random forest (RF), extreme gradient boosting (XGBoost), and categorical boosting (CatBoost) in predicting pulse characteristics. The SHAP analysis indicated that the gain saturation energy and DCF length exhibited wide ranges of SHAP value distributions, showing significant positive correlations with pulse energy, peak power, and spectral width, and a negative correlation with pulse duration. Finally, multiple optimization algorithms on the MEALPY platform were employed to optimize the cavity parameters for maximizing the pulse peak power and minimizing pulse duration based on the stacking model outputs. The performance comparison of different optimization algorithms for parameter optimization of the fiber laser peak power stacking ensemble model was achieved, as shown in Fig.8. The results showed that the wild horse optimizer (WHO), genetic algorithm (GA), and gradient-based optimizer (GBO) exhibited fast convergence speed and superior global search capability, while brain storm optimization (BSO), GA, evolutionary field optimization (EFO), and GBO demonstrated compact box-plot distributions, indicating good stability. Analysis by laser simulation further revealed a comparison of the parameter optimization results using different algorithms for fiber lasers (Table 2). The table showed that the cavity parameters found by the EFO algorithm achieved maximum peak power, closest to the reference value obtained by the control variable method.

The study integrates stacking ensemble learning with SHAP interpretability analysis, which deepens the understanding of the mechanism of ultrashort pulse regulation by cavity parameters, and establishes a novel intelligent design paradigm for fiber lasers. The findings provide valuable insights for the performance optimization and intelligent design of ultrashort pulse fiber lasers.