## 3 Methodology  
### Overview  
Our proposed framework, named InSAR-RiskLSTM, integrates spatial and temporal modeling techniques to predict railway deformation risks with high precision. The model is designed to leverage advanced image-based spatial attention and temporal sequential learning to address the complexities of railway deformation prediction. At a high level, the framework consists of three core modules: a Spatial Attention Encoder, a Temporal Risk Predictor, and a Feature Fusion Mechanism. The Spatial Attention Encoder processes InSAR images and generates attention maps to highlight risk-prone regions. The Temporal Risk Predictor utilizes a specialized LSTM structure to model sequential dependencies in the deformation time series. Finally, the Feature Fusion Mechanism combines spatial and temporal features, aligning them into a unified representation that enhances predictive accuracy. As shown in Figure 1, the workflow begins with preprocessing InSAR imagery data to extract deformation patterns, which serve as input for the Spatial Attention Encoder. The encoder outputs spatial attention vectors that are subsequently fed into the LSTM-based temporal predictor. The predictor models temporal dependencies across sequential risk factors, including historical deformation trends and environmental conditions. These features are then fused using the feature fusion module to generate comprehensive risk scores. The outputs are used for predictive tasks, such as assessing deformation magnitudes and identifying high-risk railway segments. The Spatial Attention Encoder extracts spatial features from InSAR imagery, emphasizing regions that are prone to deformation risks. The Temporal Risk Predictor models sequential dependencies within deformation trends, leveraging LSTM-based structures for capturing long-term temporal patterns. The Feature Fusion Mechanism integrates the spatial and temporal features, aligning them into a cohesive representation to enhance predictive accuracy. This structure ensures that the approach effectively captures the spatial and temporal complexities inherent in deformation risk prediction. Figure 1: Framework of the InSAR-RiskLSTM model. The framework consists of three primary components: the Spatial Attention Encoder, the Temporal Risk Predictor, and the Feature Fusion Mechanism. It incorporates spatiotemporal priors, geophysical dependency tokenization, and Multi-Task Optimization to enhance predictive accuracy and interpretability. To provide a structured representation of the proposed methodology, the workflow of InSAR-RiskLSTM is formulated as Algorithm 1. The framework consists of six key steps, ensuring an effective integration of spatial and temporal modeling for railway deformation risk prediction. The process begins with data preprocessing, where deformation patterns are extracted from InSAR imagery, temporal features are normalized, and external environmental conditions are incorporated. Following this, the Spatial Attention Encoder processes the input InSAR imagery, generating attention maps to highlight high-risk regions and extracting spatial feature representations. Next, the Temporal Risk Predictor models sequential dependencies in deformation time series using an LSTM-based structure, capturing long-term trends and extracting temporal feature representations. These spatial and temporal features, along with external environmental factors, are then combined in the Feature Fusion Mechanism, aligning multi-source information into a unified representation that enhances predictive accuracy. The fused features are subsequently used to generate risk scores, assessing deformation magnitudes and identifying high-risk railway segments. Finally, the model outputs comprehensive risk assessments, providing decision support for railway maintenance and risk mitigation. This structured workflow ensures that InSAR-RiskLSTM effectively captures both spatial and temporal complexities, leading to improved predictive performance in railway deformation monitoring.