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In this paper, we focus on the inverse problem study of nonlinear Schrödinger (NLS) typed equations in optical fiber communicaitons. As an extension of the physics-informed neural network (PINN), multi-parallelized PINNs are constructed and trained for the discovery of diverse high-order terms and variable coefficients. We firstly study various constant-coefficient combinations of a generalized high-order NLS typed equation, where the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation and the Kundu-Eckhaus equation are included. With small amount of exact solutions available to us, we predict the value of multiple coefficients under different cases to deduce the undetermined terms of the generalized equation based on the multi-parallelized PINN. Different categories of NLS typed equations are then inferred. In the meantime, high accuracy numerical solutions on localized regions can be accordingly obtained. The parameter discovery of NLS typed equations with variable coefficients has also been carried out based on the extended network, including analysis on interaction behaviors and the periodic phenomenon of solutions. According to outputs of multi-parallelized PINNs, we compare the numerical solutions and the predicted variable coefficients with exact results. Error analysis are then performed to check the accuracy of prediction, where both the absolute error and the mean squared error are given. Compared with the traditional PINN, our model exerts its state-of-art power in the inverse problem study of nonlinear systems, where different high-order terms and variable-coefficient terms can be clearly predicted while deducing diverse types of localized numerical solutions with lower fitting error and less data consumption. As the self-steepening pulses without self-phase modulation and the Raman effect are closely related to the inferred high-order terms of NLS typed equations, our research will serve as experimental basis in the field of optical fiber communications. • Multi-parallelized PINNs are constructed for the study of inverse problem. • With small data available, we can deduce undetermined terms of a generalized NLS typed equation. • Nonlinear analysis are provided based on the parameter discovery of variable coefficients. • Compared with traditional PINNs, lower fitting error of solutions and parameters can be achieved. [ABSTRACT FROM AUTHOR]

Under investigation in this paper is the cubic–quintic nonlinear Schrödinger equation, which describes the propagation of optical on resonant-frequency fields in the inhomogeneous fiber. According to abundant previous researches on the model, exact soliton solutions and rogue wave solutions have been derived through Darboux transformation. The modulation instability phenomenon has been analyzed to evaluate the ability of an initially perturbed plane wave to split into localized energy packets when propagating in a dispersive and nonlinear medium. Numerical solutions with high accuracy are needed in fields of production and engineering. Nonetheless, the data acquisition costs of the optical pulse transmission system is high, which will limit the accuracy and the efficiency of typical numerical and data-driven methods. With the physical knowledge embedded into neural networks in the form of loss function, the problem of big data dependence has been solved. For dynamic analysis on optical pulses with small amount of known information, we strive to obtain high accuracy numerical solutions. Considering the case that the cubic–quintic nonlinear Schrödinger equation is converted to the Kundu–Eckhaus equation with simplified coefficient constraints through variable transformation, we construct modified physics-informed neural networks, where conversions on the input and output are attached to deep neural networks. Training networks with the given initial and boundary data, we effectively derive the expected soliton and rogue wave solutions, where the approximated one-soliton, two-soliton, first-order and second-order rogue waves are included. In general, the modified network reaches low prediction errors with small data available. With the coefficients of equations, the weights and the bias of networks combined as parameters to be trained, we deduce the corresponding value of condition settings for different systems. Moreover, we simulate diverse localized waves in the context of nonlinear electrical transmissions with different environment settings and compare the evolution process to reach conclusions on the parameter discovery. • Dynamic characteristics of optical pulses are analyzed when the frequency of field is near to the resonant frequency in the inhomogeneous fiber. • We apply data-driven algorithms to derive numerical solutions. • We construct the modified PINNs, where conversions on the input and output are attached to deep neural networks. [ABSTRACT FROM AUTHOR]