Abstract: To address the challenges of high computational complexity in traditional full waveform inversion, limited nonlinear modeling capability, and insufficient utilization of physical features in existing deep learning methods for Ground Penetrating Radar (GPR) inversion, this paper proposes Hilbert-enhanced Unet with Kolmogorov-Arnold networks (HUKAN), a GPR permittivity inversion method integrating Hilbert feature enhancement and attention gating. Three key improvements are implemented based on the UKAN architecture: a Hilbert Feature Extraction and Spatial Adaptive Fusion module (HFE-SA) to enhance physical feature representation; a Spatial-Channel Attention Gating mechanism (SCAG) for adaptive feature selection and noise suppression at skip connections; and a Logarithmic Dynamic Range Compression (LDRC) strategy to improve reconstruction accuracy for low-value anomalies. Experimental results on simulated datasets containing various typical geological structures demonstrate that HUKAN reduces mean squared error by 45.5%, improves structural similarity index by 1.91%, and increases peak signal-to-noise ratio by 2.72 dB compared with the baseline Unet with Kolmogorov-Arnold networks(UKAN) model, outperforming mainstream methods including Unet and Attention Unet across all metrics with computational cost below 1 GFLOPs. Ablation studies validate the independent contributions and synergistic effects of each component, noise experiments confirm the method’s robustness under varying signal-to-noise ratio conditions, and attention visualization reveals the hierarchical feature selection mechanism of SCAG from coarse-grained semantic perception to fine-grained spatial localization. Validation on real GPR data from concrete test blocks with drilled cavities demonstrates that, through domain-adaptive fine-tuning, HUKAN achieves a mean target localization error of only 0.75 mm, a 73.4% reduction compared with UKAN, while accurately distinguishing permittivity characteristics of different medium types. Additionally, a continuous long-survey-line experiment on a 450 mm profile covering three test units demonstrated that HUKAN can accurately detect and reconstruct all heterogeneous targets through a segmented inversion strategy. Further environmental sensitivity analysis shows that the method is robust to sand-grain-scale surface roughness and maintains baseline-level accuracy under naturally-humid conditions, and quantitatively characterizes its generalization boundary under transient-absorption and long-term-soaking regimes via a two-stage physical interpretation. The results indicate that the synergistic integration of physical feature embedding, attention gating, and dynamic range compression can effectively improve the accuracy, robustness, and interpretability of GPR inversion, providing a feasible approach for high-precision intelligent subsurface parameter reconstruction.