Kolmogorov–Arnold Networks for System Identification of First- and Second-Order Dynamic Systems

System identification—originating in the 1950s from statistical theory—has since developed a wealth of algorithms, insights, and practical expertise. We introduce Kolmogorov–Arnold neural networks (KANs) as an interpretable alternative for model discovery. Leveraging KANs’ inherent property to approximate data and interpret it by employing learnable activation functions and decomposition of multivariate mappings into univariate transforms, we test its ability to recover the step responses of first- and second-order systems both numerically and symbolically. We employ synthetic datasets, both noise-free and with Gaussian noise, and find that KANs can achieve very low RMSE and parameter error with simple architectures. Our results demonstrate that KANs combine ease of implementation with symbolic transparency, positioning them as a compelling bridge between classical identification and modern machine learning.