## 3 Key Processes for Deep Learning-Based Seepage Field Prediction
### Neural Network Construction Methods
[16] constructed a multi-scale nonlinear seepage simulation model based on Graph Neural Networks for predicting microscopic seepage paths in DCSs. They reconstructed the core CT image into a pore node graph, with node features including pore size, width of connecting channels, etc., and with edge weights representing the infiltration fluxes between neighboring pores. The transfer of physical information between nodes was realized by graph convolution layers and combined with a multilayer message aggregation strategy to predict the local velocity field and saturation evolution process. Experiments showed that the model has strong accuracy and spatial sensitivity in reconstructing microchannel flow paths and identifying residual oil-rich zones. Although the GNN model is still in the preliminary exploration stage in the field of oil and gas engineering, its potential in digital core analysis, fracture network simulation, and spatial coupling prediction has been initially shown [8], and it is expected to be fused with physical modeling, image recognition, and other technologies in the future, to construct a seepage intelligent simulation system with more generalized capability [23]. * Physical information neural network model: Physics-Informed Neural Networks (PINNs) are a class of Deep Learning methods that have emerged in recent years, which embed physical control equations into the neural network training process [56]. Unlike the traditional \"physical modeling followed by numerical solution\" approach,PINNs transform the control equations (e.g., Darcy's law, mass conservation equation) into the loss terms of neural networks, so that the model automatically satisfies the basic physical laws while fitting the data [57]. In the field of reservoir seepage, PINNs provide a novel modeling paradigm for prediction, inversion, and continuous field reconstruction of seepage response variables (e.g., pressure, saturation, velocity, etc. ), which is especially suitable for problem scenarios with incomplete data, restricted observations, and high nonlinearity. For example, [PERSON] et al. first systematically proposed the Hidden Fluid Mechanics (HFM) framework, which inverts complete fluid dynamics variables (e.g., pressure, velocity, vorticity, etc.) from partially observable velocity fields based on PINNs. Although this study did not focus on oil reservoirs, the modeling idea of image-variable mapping and physical constraints laid a methodological foundation for the subsequent application of PINNs in seepage [5,58]. [PERSON] et al. [2] introduced the idea of PINNs into the pressure field modeling of inhomogeneous reservoirs and proposed the physics-regularized DNN, which is a methodology to model the pressure field of non-homogeneous reservoirs that enables the model to learn both physical laws and numerical data in the training stage by embedding the residuals of the Darcy flow control equation. Their experiments showed that the PINN model has stronger stability and physical consistency than the traditional DNN in the case of sparse boundary data and complex well control. [PERSON] et al. [21] constructed a complete three-dimensional multiphase seepage PINN model to predict the pressure-saturation evolution process in a non-homogeneous pore medium. They embedded the coupled governing equations of two-phase flow in the loss function and introduced a regular term to constrain the WC evolution trajectory, which significantly improved the smoothness and physical interpretability of the prediction results. PINNs, with their embedded representation of the control equations, provide a new way of thinking for modeling reservoir seepage fields by integrating physical-driven and data-driven approaches. Combined with the research progress of [PERSON] [2], [PERSON] [21], and [PERSON] et al. [5], it has been shown that PINNs are not only suitable for pressure and saturation prediction under complex boundary conditions but also show significant advantages in small-sample inverse modeling and continuous field reconstruction [26].