## 2 The Proposed Methodology
### The Construction of Slope Stability Evaluation Model
#### 2.2.3 GNN-TreeNet Network Structure  
Graph neural networks (GNNs) are specialized neural network models designed for processing graph-structured data. By learning both the topological relationships between nodes and their inherent attribute features, GNNs enable effective modeling and prediction on graph data. Through iterative representation updates, these networks progressively enrich node features by aggregating information from neighboring nodes, thereby capturing global structural patterns through localized learning. The core mechanism involves graph convolution operations that systematically combine neighborhood information with node-wise features. This recursive aggregation process allows each node to accumulate multi-hop contextual information, enabling the network to develop increasingly comprehensive representations that reflect both local connectivity patterns and global graph characteristics. Therefore, based on the previously constructed ontology instance feature representation, the idea of a GNN network [43] was proposed to generate the final embedding vector of the top node. Through observation, it was found that, for a specific top node, its descendant nodes actually formed a tree. As a special case in the context of a graph, this tree was called the GNN-TreeNet network, as shown in Figure 3. The network could be of any depth, and its maximum number of layers was determined by the depth from the ontology instance to the top node. The input nodes of the ontology instance feature vector network generated in the previous section were used as the initial state. The ontology instance was set as Layer 0. The initial vector (initial embedding) of each node was constructed based \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instance Name** & **Value** & **Processing Method** & **Output Dimensions** \\ \hline \multirow{6}{*}{Slope structure type} & \multicolumn{2}{c}{Clastic rock slopes, soil slopes, gently} & \multirow{6}{*}{One-hot encoding} & \multirow{2}{*}{\(11\)} \\  & layered slopes, metamorphic rock slopes, & & \\  & along slopes, reverse slopes, oblique & & \\  & slopes, crystalline rock slopes, transverse & & \\  & slopes, special structural slopes, & & \\  & carbonate rock slopes & & \\  & Broken, loose, slightly dense, medium & & \\  & dense, dense, dense; dry, wet & & \\  & Pharetic water, figure water, & & \\  & karst water, fissure water, confined water, & & \\  & upper stagnant water & & \\  & & Convex, concave; left, right & & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subproperty Name** & **Value** & **Processing Method** & **Output Dimensions** \\ \hline Tendency to slide & 0–360 & /360 & 1 \\ Slide bed & & One-hot encoding & \\ inclination angle & Linear, arc, 0–90 & +/90 & 3 \\ Original slope height & 0–1500 & /1500 & 1 \\ Original slope & 0–90 & /90 & 1 \\ Slide belt thickness & 0–250 & /250 & 1 \\ Longitude & Real number & (v-70)/65 & 1 \\ Latitude & Real number & /50 & 1 \\ Tendency to slide & 0–360 & /360 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numeric instance encoding examples. on the characteristic data of the ontology, and it was established according to the general collection-update formula of the GNN propagation mechanism [44]:  
\[\mathrm{h_{v}(i)}=\sigma\Big{(}\Big{[}\mathrm{W_{i}\cdot AGG}\Big{(}\mathrm{h_{ u}^{i-1}},\forall u\in\mathrm{N(v)}\Big{)},\mathrm{B_{i}h_{v}(i-1)}\Big{]}\Big{)}, \mathrm{i}=0,1,\ldots\mathrm{n} \tag{1}\]  
Among them, \(\mathrm{h_{v}(i)}\) represents the embedding of node v; i represents the number of layers; \(\sigma\) represents the activation function; \(\mathrm{W_{i}}\) and \(\mathrm{B_{i}}\) are weight matrices; \(\mathrm{N(v)}\) is the set of child nodes of node v; and \(\mathrm{AGG(*)}\) represents the collection function. Since it was a tree structure, the subtree of each node was unique, which simplified the network structure. The aggregation function was defined as the weighted average of all nodes in the previous layer.