Hybrid PINN–SSF Framework for Mode-Locked Fiber Laser Simulation: Comparative Assessment with SSF and FDM

Simulating intracavity pulse evolution in mode-locked fiber lasers (MLFLs) requires solving the generalized nonlinear Schrödinger equation (GNLSE), typically via the split-step Fourier (SSF) or finite-difference (FDM) methods, while physics-informed neural networks (PINNs) have recently emerged as a mesh-free alternative. Yet a quantitative benchmark of all three within a unified dissipative cavity model remains absent. Here we adopt a hybrid PINN-SSF strategy to overcome the limitations of standalone PINNs in gain-saturated dynamics, and compare its performance against SSF and FDM over fifty consecutive round trips. The results reveal distinct error-accumulation behaviors: Within the tested cavity configuration, SSF serves as the numerical reference supported by discretization-refinement tests; FDM exhibits increasing global field differences during repeated cavity propagation while retaining visible late-stage sideband-like structures; the hybrid PINN-SSF exhibits earlier temporal localization during the initial stage, yet suffers from high-frequency spectral degradation and a 50% energy drift from 10 pJ to approximately 5 pJ over 50 round trips, despite achieving a lower mean absolute error (MAE) of 1.275% versus 2.092% relative to SSF. In conclusion, within the tested ring-cavity configuration and under the investigated parameter set, SSF remains optimal for long-term high-fidelity modeling, FDM suits sideband-resolved analysis with adequate resolution, and the hybrid PINN-SSF, while promising for early-stage prediction, still requires improved stationary dissipative balance for extended cavity simulations.