## 4 Results
### Multi-Point Joint Predictions  
A nonlinear least squares algorithm was applied to integrate data from all 120 monitoring points. Predicted failure times under Case 1, Case 2, and Case 3 were 449.3 h (\(-\)8.7 h error), 450.7 h (\(-\)7.3 h error), and 458.3 h (\(+\)0.3 h error), respectively, demonstrating Case 3's superior accuracy (Figure 10).  
Figure 11 depicts the statistical distribution of the percentage of data exclusion at each monitoring point under Case 3. Despite data exclusion exceeding 50% at numerous monitoring points, the prediction accuracy remains uncompromised. Computations at this scale are not time-intensive, typically requiring only a few seconds.  
Figure 10: Schematic diagram of multi-point joint prediction results under 3 cases. The dots of different colors represent the inverse velocity data of different monitoring points, and the corresponding color lines are the fitted lines of these dots.  
Similar to single-point forecasting, the robustness and reliability of multi-point joint predictions necessitate rigorous validation. To this end, sensitivity analyses were conducted to evaluate: (1) Temporal Variability: The impact of prediction timing using temporal nodes consistent with Figure 10; and (2) Spatial Sampling Density: The influence of monitoring point inclusion ratios, tested at 10-90% increments (10% intervals).  
For each density level (e.g., 90%), a non-repetitive 90% subset of monitoring points was randomly selected to generate ensemble predictions. This subsampling process was iterated 1000 times per density level to compute the mean prediction error and standard deviation across trials. The resultant error distributions, illustrating the interplay between spatial sampling density and temporal prediction stability, are presented in Figure 12.  
As demonstrated in Figure 12, Case 1 exhibits mean prediction errors ranging from \(-8\) h to \(+2\) h, with standard deviations spanning 0-20 h, indicative of substantial uncertainty. Case 2 shows improved yet systematic prediction (mean error: \(-6\) h to \(-3\) h; standard deviation: 0-8 h). Notably, increasing the spatial sampling density in Cases 1 and 2 paradoxically amplifies mean errors while marginally reducing standard deviations. This counterintuitive behavior arises from the inherent limitations of rudimentary data exclusion and fitting strategies, where expanded datasets inadvertently propagate low-quality measurements, exacerbating prediction inaccuracies.  
In stark contrast, Case 3 achieves exceptional stability, with mean errors confined to 0-2 h and standard deviations less than 3 h. Furthermore, prediction robustness improves with larger datasets: even at 10% sampling density, prediction errors remain within \(\pm 1\) h, while higher data volumes further minimize standard deviations. These findings conclusively demonstrate that multi-point ensemble predicting delivers reliable and stable outcomes only when underpinned by rigorously selected data (Case 3), validating the necessity of advanced data-quality control protocols in operational landslide prediction systems.  
Figure 11: Statistical distribution of the percentage of data exclusion at each monitoring point under Case 3.