FiberKAN: Kolmogorov-Arnold Networks for Nonlinear Fiber Optics

Abstract: Scientific discovery and dynamic characterization of the physical system play a critical role in understanding, learning, and modeling the physical phenomena and behaviors in various fields. Although theories and laws of many system dynamics have been derived from rigorous first principles, there are still a considerable number of complex dynamics that have not yet been discovered and characterized, which hinders the progress of science in corresponding fields. To address these challenges, artificial intelligence for science (AI4S) has emerged as a burgeoning research field. In this paper, a Kolmogorov-Arnold Network (KAN)-based AI4S framework named FiberKAN is proposed for scientific discovery and dynamic characterization of nonlinear fiber optics. Unlike the classic multi-layer perceptron (MLP) structure, the trainable and transparent activation functions in KAN make the network have stronger physical interpretability and nonlinear characterization abilities. Multiple KANs are established for fiber-optic system dynamics under various physical effects. Results show that KANs can well discover and characterize the explicit, implicit, and non-analytical solutions under different effects, and achieve better performance than MLPs with the equivalent scale of trainable parameters. Moreover, the effectiveness, computational cost, interactivity, noise resistance, transfer learning ability, and comparison between related algorithms in fiber-optic systems are also studied and analyzed. This work highlights the transformative potential of KAN, establishing it as a pioneering paradigm in AI4S that propels advancements in nonlinear fiber optics, and fosters groundbreaking innovations across a broad spectrum of scientific and engineering disciplines.