## 5 Conclusions  
In this study, we proposed a novel approach to tackle the challenges of predicting complex InSAR subsidence time series by building on deep learning models and integrating time-series decomposition algorithms. Specifically, we introduced the MC-TCGRU model, which leverages CEEMDAN to decompose the original nonlinear, periodic, and non-stationary InSAR time series into more stable components, enabling the deep neural networks to make more accurate predictions. Our results demonstrate that the MC-TCGRU model significantly reduces the complexity of the data, and by predicting each decomposed component separately, we achieved a high level of accuracy in InSAR subsidence sequence predictions. The integration of these component-level predictions leads to a robust overall predictive model. Compared to traditional deep learning models like the TCGRU, which do not account for time-series complexity, the MC-TCGRU model improves the performance by reducing the RMSE values by up to 27.76%. In addition to this, we expanded our analysis by evaluating the individual predictive performance of each decomposed component and studying their combined effect on the final result. This not only provided new insights into the importance of data complexity decomposition, but it also highlighted how breaking down complex time series into simpler components enhances the prediction accuracy. The model was tested on the five InSAR time series of the points with the highest subsidence rates in the Kunming city area, and the experimental results confirmed that the  
Figure 14: Comparison of five AMEs on five LS points. (**a**) P1. (**b**) P2. (**c**) P3. (**d**) P4. (**e**) P5. MC-TCGRU model outperformed not only the TCGRU model, but also models based on STL and EMD. Specifically, our model demonstrated an enhanced capability to capture subtle variations in time-series data, further improving the prediction outcomes in comparison to the STL- and EMD-based methods. Furthermore, beyond the improvements in accuracy, the MC-TCGRU model offers a broader applicability by being adaptable to various complex time-series problems beyond subsidence prediction. It represents a significant advance in how we handle nonlinear and non-stationary time-series data, making it a valuable contribution to future research in this field. This model serves as a reference framework for improving the predictive performance of other complex time-series datasets, and it offers practical guidance for researchers working on subsidence time-series predictions and similar applications. Overall, the MC-TCGRU model not only surpasses the performance of traditional deep neural network models, but it also provides a superior alternative to subsidence prediction models incorporating STL and EMD decomposition. Its ability to effectively reduce data complexity while maintaining its predictive accuracy makes it a promising tool for advancing subsidence time-series prediction research and applications. Conceptualization, T.C. and Y.L. ; methodology, T.C. and Y.L. ; validation, D.N. and Y.L. ; formal analysis, Y.L. ; investigation, D.N. and Y.L. ; resources, T.C. ; writing--original draft preparation, T.C. and Y.L. ; writing--review and editing, T.C., Y.L. and D.N. ; project administration, D.N. All authors have read and agreed to the published version of the manuscript. This research was funded by the Open Fund of Hebei Cangzhou Groundwater and Land Subsidence National Observation and Research Station (No. CGLOS-2023-02). Not applicable. The raw data supporting the conclusions of this article will be made available by the authors on request. The authors declare no conflicts of interest.