## 3 Methodology
### Temporal Risk Predictor  
As shown in Figure 3, the Temporal Risk Predictor is designed to capture sequential dependencies in deformation time series by combining convolutional layers, fully connected (FC) layers, and LSTM mechanisms. The architecture refines temporal features through a series of operations, leveraging local feature extraction and global sequence modeling. Figure 2: Detailed structure of the Spatial Attention Encoder. The module processes multi-scale patch embeddings, utilizing channel cross-attention and spatial cross-attention mechanisms to extract meaningful spatial features and encode relationships between tokens. These operations refine spatial dependencies, enhancing downstream deformation risk prediction tasks. The module starts by applying a \(1\times 1\) convolutional layer to the input tensor \(\mathbf{X}_{t}\in\mathbb{R}^{C\times H\times W}\), where \(C\), \(H\), and \(W\) denote the number of channels, height, and width, respectively. The convolutional output is then elementwise multiplied with the original input tensor to emphasize meaningful temporal patterns:  
\[\mathbf{X}_{\text{conv}}=\text{Conv}_{1\times 1}(\mathbf{X}_{t}), \tag{10}\]  
\[\mathbf{X}_{\text{weighted}}=\mathbf{X}_{\text{conv}}\odot\mathbf{X}_{t}. \tag{11}\]  
Next, the weighted tensor is reshaped into a matrix \(\mathbf{X}_{\text{flat}}\in\mathbb{R}^{C\times D}\), where \(D=H\cdot W\). This reshaped representation is passed through a fully connected layer followed by a softmax activation to compute temporal attention weights:  
\[\mathbf{A}=\text{Softmax}(\text{FC}(\mathbf{X}_{\text{flat}})). \tag{12}\]  
These weights are used to aggregate temporal features:  
\[\mathbf{X}_{\text{attn}}=\mathbf{A}\odot\mathbf{X}_{\text{flat}}. \tag{13}\]  
The aggregated features are then transformed via another fully connected layer to produce the intermediate representation \(\mathbf{h}_{\text{temp}}\in\mathbb{R}^{D\times 1}\). This representation is processed further using an LSTM component, capturing sequential dependencies:  
\[\mathbf{h}_{t}=\sigma\big{(}\mathbf{W}_{h}\mathbf{h}_{\text{temp},t}+\mathbf{ U}_{h}\mathbf{h}_{t-1}+\mathbf{b}_{h}\big{)}, \tag{14}\]  
where \(\mathbf{h}_{t}\) represents the LSTM hidden state at time \(t\), and \(\mathbf{W}_{h}\), \(\mathbf{U}_{h}\), and \(\mathbf{b}_{h}\) are learnable parameters. The LSTM outputs are passed through a final \(1\times 1\) convolutional layer to generate the refined temporal features for downstream tasks:  
\[\mathbf{X}_{\text{final}}=\text{Conv}_{1\times 1}(\mathbf{h}_{t}). \tag{15}\]  
This multi-step process enables the Temporal Risk Predictor to extract both localized and global temporal dependencies, making it well suited for deformation risk prediction tasks. By combining convolutional and sequential learning mechanisms, the predictor achieves robust feature representation for complex temporal patterns. Figure 3: Structure of the Temporal Risk Predictor. The component processes sequential inputs through a combination of convolutional layers, fully connected layers, and LSTM mechanisms, capturing both local and global temporal dependencies for deformation risk prediction. As shown in Figure 4, the Feature Fusion Mechanism integrates spatial and temporal features to produce a unified representation that captures both low-scale and high-resolution information. The module consists of four primary stages: backbone network feature extraction, attention-based feature fusion, down-sampling layers, and final convolutional transformations. Spatial features are extracted from input imagery through a backbone network, which includes multiple convolutional and down-sampling layers. Low-scale spatial features are interpolated and passed through additional double convolution layers to align their resolutions with backbone features. The low-scale spatial features and backbone features are fused using an attention mechanism.