Reversely Exploring Higher-Order Effects in a Fiber Laser through Physics-Informed Recursive Neural Network

In ultrafast fiber lasers, the influence of higher-order effects on mode-locked pulses becomes increasingly notable as the pulse width decreases from the subpicosecond to the femtosecond level. However, accurately predicting the underlying higher-order effects in nonlinear nonconservative systems remains difficult with forward-calculating nonlinear partial differential equations. We propose a novel physics-informed recursive neural network (PIRNN) model to reversely explore the underlying higher-order effects in fiber lasers. Based on experimental data, the PIRNN can reversely deduce the coefficients of the group velocity dispersion, third- and fourth-order dispersion effects, and the third- and fifth-order nonlinearities in fibers to establish higher-order nonlinear Schrödinger equations and Ginzburg–Landau equations, which govern the theoretical model of a fiber laser. The PIRNN further demonstrates which higher-order effects are dynamically stimulated for different cases of 879 fs and 1.62 ps solitons in the experiments. Furthermore, the PIRNN-predicted spectrotemporal and phase information is verified by both experimental results and forward-calculating results of the theoretical model. Additionally, the physical rule of electromagnetic resonant radiation of bound electrons in SiO₂-based fibers is reversely deduced by constructing our self-designed dielectric neural network. Our novel approach for reversely exploring underlying higher-order effects introduces a novel perspective for investigating nonconservative systems.