## 2 Development of Seepage Field Prediction Methods
### Deep Learning-Based Method for Seepage Field Prediction  
Unlike traditional Machine Learning methods, Deep Learning methods can more accurately predict and optimize an extraction plan for complex lithological parameters during the high WCP in the late stage of an oil field, as well as seepage response variables considering the physical equations, spatial structure, and dynamic boundaries. (1) Deep Learning methods can extract richer and finer features from complex field data to better capture the complex correlation between seepage field response variables; (2) The response variables of a seepage field in high-water-containing reservoirs are affected by the nonlinearities of various factors, such as geology and engineering, etc., and a Deep Neural Network structure can flexibly model nonlinear relationships to better capture the complex correlation between the response variables of the seepage field and the factors affecting them; (3) The Recurrent Neural Network (RNN), Long Short-Term Memory Network (LSTM), and Short Short-Term Memory Network (SSTRM) of Deep Learning can be used for the optimization of extraction schemes. RNN, LSTM, and other structures in Deep Learning can effectively handle time-series field data, which are suitable for capturing the cyclic evolution characteristics and dynamic trends of seepage fields in high-water-containment-period reservoirs, and they help to identify temporal response mechanisms such as advancement of the driving front edge and movement of residual oil; (4) Prediction of seepage fields in high-water-containment period reservoirs usually involves a large amount of well network operation data, geological parameters, and development history. The Deep Learning model has strong fusion-modeling capability under multi-source big data conditions, which can realize the joint prediction of seepage response variables under complex conditions [11] and improve its scenario-generalization and real-time prediction capability. [PERSON] et al. [5] proposed a representative Hidden Fluid Mechanics (HFM) framework based on the idea of PINNs (Physics-Informed Neural Networks) to invert the full-field pressure and velocity distributions of a flow field system from velocity field images. The method has good physical consistency and generalization ability without the need of direct observation of pressure data and only reconstructs the hidden physical variables by visualizing the flow field samples. Although the study was initially applied to hydrodynamic visualization experiments, the method has a strong capacity for migration, and it is suitable  
Figure 3: Flow chart of Machine Learning-based seepage field prediction compared to traditional methods. for pressure-velocity inversion modeling in visualization and monitoring of reservoirs during high WCPs [5]. In order to solve the problem that traditional data-driven models are prone to deviate from physical laws, [PERSON] et al. (2022) proposed a physics-regularized Deep Neural Network (physics-regularized DNN) framework for predicting pressure field evolution in non-homogeneous reservoirs, which is particularly suitable for modeling seepage dynamics in high-water-bearing periods [2]. The method uses physical consistency as a network training constraint term by embedding single-phase unsteady seepage control equations, initial conditions, and boundary conditions in the neural network loss function. The experimental results show that the model still has good robustness and accuracy under scenarios with noisy data and fewer samples, especially in the prediction of pressure distribution in high WC areas with significant advantages. In their subsequent study, [PERSON] et al. [2] further proposed the Physical Difference Convolutional Neural Network (PD-CNN), which integrates the finite difference idea with the structure of a Convolutional Neural Network to realize high-accuracy prediction of the pressure and saturation fields in multiphase seepage flows.