Research on the problem of spatial heterogeneity in row data and generalization capability for landslide susceptibility assessment using the physics-constrained U-net model

Landslide susceptibility research serves as the primary approach for analyzing the future development of landslides, and could provide the scientific reference for mountainous area development strategic decisions. The accuracy of landslide susceptibility assessment mainly depends on input data and evaluation methods. To address the issues of significant impacts from raw data defects and low spatial resolution in susceptibility assessment results within traditional deep learning evaluation models, this study establishes a physically constrained U-Net model (PCUM). This method selects ten landslide assessment factors, including slope gradient, profile curvature, slope aspect, landform, river distribution density, annual average precipitation, annual average temperature, fault distribution density, lithology, and seismic intensity. Through adjusting the weights of the model’s loss function by imposing explicit physical constraints, the model’s performance was ultimately enhanced. A comparison of the model evaluation results before and after applying the constraints is as follows: the AUC value increased from 0.871 to 0.877, the recall increased from 0.884 to 0.891, and the Kappa coefficient rose from 0.597 to 0.605. Meanwhile, the frequency ratio of the very high susceptibility zone increased from 5.64 to 5.80, while that of the very low susceptibility zone decreased from 4.77 × 10⁻² to 3.23 × 10⁻². Compared with other deep learning models, the evaluation results of PCUM demonstrate the advantage of maintaining spatial resolution consistent with the original input data, better revealing the spatial characteristics of landslide distribution, and higher accuracy. This study focuses on the southeastern region of Tibet and selects five typical regions to investigate the impact of spatial heterogeneity in raw data on the PCUM. The AUC values of the BP neural network model in the five typical regions are 0.905, 0.930, 0.871, 0.877, and 0.920, respectively, with relatively poor performance in typical regions 3 and 4. The AUC values of the residual neural network model are 0.874, 0.921, 0.915, 0.891, and 0.914, respectively, showing poor performance in typical region 1. In contrast, the PCUM achieves AUC values of 0.923, 0.940, 0.935, 0.915, and 0.899 across the five regions, demonstrating robust performance in all typical areas. The results indicate that the physically constrained U-Net model can effectively handle spatial heterogeneity in raw data and exhibits good generalization capabilities. This study may provide an effective reference for the generalizability research of landslide susceptibility assessment models.