Research on the Forward and Inverse Problem Fitting Method of Distributed Raman Amplifiers Based on Kolmogorov-Arnold Network

The Kolmogorov–Arnold network (KAN), as an alternative to the multilayer perceptron (MLP), offers high-precision modeling of complex nonlinear dynamics. In this paper, we propose a KAN-based method for fitting both the forward and inverse problems of the distributed Raman amplifier (DRA) to achieve improved predictive accuracy. The learnable B-spline activation function within KAN allows the activation curve to adapt across different input intervals, thereby capturing the input–output relationship with greater granularity. Comparative experiments with the MLP demonstrate that, whether employing the Tree-structured Parzen Estimator (TPE) for hyperparameter optimization or constraining the model to an equal floating-point operation (FLOP) budget, KAN substantially reduces both the root-mean-square error and the maximum error in DRA forward and inverse fitting tasks. Furthermore, a secondary optimization via gradient descent leverages the high-precision characteristic of KAN to deliver additional performance gains. The proposed approach provides an efficient modeling tool for real-time control in an optical network and advances the application of KAN in a complex physical system.