## 2 Development of Seepage Field Prediction Methods
### A Machine Learning-Based Method for Seepage Field Prediction
The analysis results showed that XGBoost and Random Forest had the best performance, in terms of prediction accuracy, stability, and training efficiency, and that both of them achieved prediction accuracy of R\({}^{2}\) greater than 0.95 [10]. [PERSON] et al. [14] constructed a permeability coefficient prediction model based on the Random Forest-Secretary Bird Optimization Algorithm (SBO-RF) to solve the problem of parameter inversion under pumping test data, which combined the modeling ability of Random Forest for complex nonlinear mapping relations with the efficiency advantage of the SBO algorithm in high-dimensional hyperparameter optimization to achieve high-precision permeability estimation with strong generalization ability [14]. It was shown that the model is suitable for the task of inverse prediction of inter-well permeability distribution and can be used as an input support model for the reconstruction of seepage fields and the optimization of well network deployment in low-permeability reservoirs. Compared with the traditional methods, the Machine Learning method performs better in the prediction of seepage field lithology parameters (Figure 3) [13]. On the one hand, the Machine Learning method does not need to analyze the mechanism embedded in seepage phenomena or derive formulas for physical processes, but only takes geological and engineering factors as variables, and it can be driven by the data to model the relationship between lithological parameters and influencing factors, which reduces the difficulty of modeling and improves the fitting degree of nonlinear relationships. On the other hand, the Machine Learning method can make predictions from historical data, and the model can be automatically learned and adjusted according to the actual geological and engineering data, which has better flexibility and adaptability [15; 16; 17]. However, the pressure and flow fields are essentially a typical space-time variable controlled by the seepage control equation, and the prediction of these variables not only needs to consider the input characteristics but also needs to take into account the \"physical consistency\", otherwise there will be a non-physical understanding (e.g., negative pressure, infinite gradient) [5], which requires a \"physical embedding mechanism\" such as PINNs, PD-CNN, and so on. P and q are distributed variables (2D or 3D fields), and traditional ML models are \"point prediction\" or \"feature regression\" in nature, and it is difficult to efficiently learn the continuous field structure, while Deep Neural Networks (especially CNN and UNet) are naturally suitable for \"image-to-image\" and \"field-to-field\" mapping; seepage response is highly dependent on the boundary conditions, time series, and source-sink terms, and it is difficult to deal with such complex boundary conditions by traditional ML methods. Models such as PINNs/P-DNN can introduce the boundary information and constrain the physical consistency during the training process through automatic discretization or residual regularization [18; 19; 20]. In addition, with the development of oilfield digitization and informatization, the amount of data has been growing explosively, and in the face of high-dimensional massive data, geologic complexity, big data characteristics, and timeliness, Deep Learning can solve the deficiencies of traditional methods and shallow neural network methods, and it can further enrich the means of seepage field prediction [14; 20; 21; 22].