KAN-Based Parameter Estimation of the FitzHugh–Nagumo Model Under Noisy Conditions

This study proposes a two-stage algorithm combining the Kolmogorov-Arnold Network (KAN) surrogate models and segmented Huber fitting for identifying nonlinear dynamical systems, particularly the FitzHugh-Nagumo (FHN) model with piecewise parameters. This is followed by a refinement stage driven by a physics-based solver, which leverages the noise-resilient properties of piecewise Huber fitting and a sliding-window strategy to perform a surgically precise search within the high-dimensional, non-convex parameter space. Our contributions extend further: by quantifying the performance trade-offs associated with segmentation strategies and network architectures (depth, width, regularization), we provide a first-of-its-kind quantitative roadmap for surrogate model selection in complex problems. Under a gauntlet of extreme stress tests—including dual-frequency excitation, heavy-tailed noise, and sparse sampling—the framework demonstrated remarkable robustness. The experimental findings demonstrate that when noise intensity escalated by three orders of magnitude ($\sigma = 10^{-1} \to 10^{-4}$), the baseline model ($D_1$) experienced a marginal rise in Root Mean Square Error (RMSE) from 0.0028 to 0.0983. Despite this increase, its coefficient of determination ($R^2$) consistently stayed above 0.99. In conclusion, our experimental findings effectively demonstrate the efficacy of the proposed approaches.