Identification of Loess Sinkholes Using a Gaussian Radial Basis Kolmogorov–Arnold Network

Sinkholes are a major type of geological hazard worldwide, commonly formed through collapse processes driven by hydrological dynamics. In the Loess Plateau region, sinkholes represent a distinctive loess subsurface erosion–related hazard and are widely distributed near tableland margins and slope areas. Once sinkholes reach a certain scale, they can significantly reduce slope stability, trigger cascading hazards, and threaten infrastructure such as roads, pipelines, industrial facilities, and residential buildings. Consequently, accurate identification of loess sinkholes is essential for disaster prevention and mitigation in loess regions. Traditional sinkhole identification relies mainly on field investigations, which are time-consuming and labor-intensive when applied at large scales. In recent years, high-resolution topographic data combined with machine learning techniques have been increasingly used for sinkhole detection. Approaches based on light detection and ranging (LiDAR)-derived digital elevation models (DEMs), including contour-based methods, random forests, and deep learning models trained on elevation, slope, and shaded relief images, have shown promising results, particularly for large-scale karst sinkholes with pronounced topographic relief. However, loess sinkholes are typically small in size and characterized by subtle micro-relief, making them difficult to distinguish in DEM imagery. To address this challenge, some studies have integrated unmanned aerial vehicle (UAV) thermal imagery with machine learning methods, while others have applied modified U-Net architectures with multi-scale filtering to improve identification accuracy. Recent investigations have also explored the use of unmanned aerial systems, handheld laser scanners, and point cloud learning networks such as PointNet++ for loess sinkhole detection. Despite their effectiveness, these methods are limited by high equipment costs, field survey constraints, and safety concerns. Moreover, the unique physical properties of loess and the distinct size, morphology, and spatial distribution of loess sinkholes further complicate their identification, leading to limited performance of existing methods. To overcome these limitations, this study employs wavelet transforms to decompose sinkhole data into multi-frequency components for enhanced feature learning. In addition, a Kolmogorov–Arnold network is introduced to strengthen nonlinear boundary representation. Experimental results demonstrate that the proposed method achieves high accuracy, efficiency, and strong generalization across multiple loess regions.