## 3 Key Processes for Deep Learning-Based Seepage Field Prediction
### Comparative Framework for Deep Learning Architectures in Seepage Modeling
#### 3.4.2 Capacity Boundary Matrix  
1. Capacity to deal with spatial and temporal dependencies: The ability of Deep Learning models to process spatio-temporal data directly determines their applicability in seepage field prediction. FeedForward Neural (FFN) networks, as an infrastructure, only process independent sample points through a fully connected layer and lack explicit modeling of spatial correlations or temporal evolution ([PERSON] et al. [10]). For example, in single-well pressure prediction, although FFN networks can capture wellbore dynamics, they cannot reconstruct the pressure gradient between wells, resulting in distorted global field predictions. In contrast, Convolutional Neural Networks (CNNs) extract local spatial features by sliding convolutional kernels, which are naturally adapted to gridded data. [PERSON] et al. [3] successfully reconstructed a 3D saturation field of a complex fracture-block reservoir using 3D CNNs, which was critically dependent on the spatial perception mechanism of the convolutional kernel to identify hyper-permeable channels and hypo-permeable barriers. Graph Neural Networks (GNNs) further break through the Euclidean spatial limitation by abstracting the fracture network as a topology of nodes and edges, which simulates the flow path of fluid in an unstructured medium through message passing ([PERSON] et al. [16]). Physical Information Neural Networks (PINNs), on the other hand, directly characterize the spatio-temporal continuous evolution of field variables by embedding the governing equations, e.g., [PERSON] et al. [5] inverted the full-field pressure distribution based on partial flow rate observations only. 2. Physical constraint embedding capability: The incorporation of physical laws is the key to improving the reasonableness of model predictions. FeedForward Neural (FFN) networks, as purely data-driven models, rely solely on the statistical laws of the training data and are prone to produce results that violate mass conservation or Darcy's law (e.g., negative pressure prediction). Convolutional Neural Networks (CNNs) can be partially embedded with physical laws beforehand by customized convolution kernels, such as the Physical Difference Convolution Neural Network (PD-CNN) kernel designed by [PERSON] et al. [2], which incorporates the residuals of Darcy's equation in finite difference form into the convolution operation, so as to make the prediction results satisfy the conservation of mass. Graph Neural Networks (GNNs), on the other hand, encode physical connectivity relations through the natural properties of graph structures: in [PERSON] et al. 's [16] \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **Structural Implication** & **Data Dependency** & **Physics Integration** \\ \hline FFN & Black-box function approximator & High & None \\ CNN & Spatial feature extractor & Medium & Convolution-based scheme \\ GNN & Relationship expansion analyzer & Low & Graph structure encoding physics linkage \\ PINNs & Physics equation solver & Very low & Loss function physics constraint \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of Deep Learning models in physics applications. microscopic seepage model, pore nodes are characterized by containing geometric parameters (e.g., aperture diameter, curvature), and edge weights characterize the flow impedance to implicitly satisfy Darcy-Weisbach equations. Physical Information Neural Networks (PINNs) are \"hard\" physically driven by directly constraining the residuals of the control equations through loss functions. For example, [PERSON] et al. [2] forced the partial differential equations for single-phase seepage during training, allowing the model to remain physically consistent (violation rate < 5%) with only 10% of the observed data. 3. Small sample generalization capability: Data scarcity is a common challenge in oilfield development, and the small-sample fitness of different models varies significantly.