## 5 Conclusions and Discussion  
Reservoir stochastic modeling can effectively capture the spatial distribution characteristics of reservoir parameters, and its characterization results provide reliable theoretical support for oil and gas exploration and development. Traditional numerical simulation methods, however, struggle to characterize heterogeneous and nonstationary reservoir geological bodies, particularly with limited observation data. While the modeling method based on GANs can address some limitations of traditional simulations and extract geological patterns effectively, traditional GANs may suffer from unstable training, limited feature extraction capabilities, and poor conditioning constraints, which lead to the difficulty of fine characterization of reservoir geological bodies. Based on this, a CSNGAN-ASPP framework for stochastic modeling is proposed in this paper, which can achieve efficient reconstruction performances of reservoir structural models with limited data constraints. By refining the network structure, the generator can extract local information across multiple scales to improve simulation performance. Additionally, the network parameters are further optimized through a joint loss function to ensure accurate simulation under conditioning data constraints. The details are discussed as follows:  
(1) The encoder-decoder architecture is introduced by the G of CSNGAN-ASPP to improve its reconstruction performance for reservoir geological models. Specifically, the  
Figure 25: Reconstruction results generated by CSNGAN-ASPP and DCGAN for three TIs with the conditioning data, and the comparisons of variogram function curves. (**a**) 2D nonstationary delta facies reconstruction; (**b**) 3D lithofacies-fold structure model reconstruction; (**c**) 3D heterogeneous aquifer model reconstruction. encoder directly transfers extracted shallow features into the corresponding positions in the decoder, avoiding the loss of feature information typically caused by the deep convolution process. Simultaneously, by coupling the ASPP structure with multiple parallel dilated convolutions, the network effectively captures and fuses multi-scale local features and their corresponding deep statistical properties of the geological model. The decoder then combines these deep and shallow features, up-sampling them progressively to reconstruct the model while balancing global and local features. This multi-scale feature fusion boots the capture capability of the generator for nonstationary geological patterns and improves the extraction of multi-scale local features. (2) The discriminator of CSNGAN-ASPP mainly refers to the PatchGAN framework, leveraging fully convolutional networks to extract deep features from the input data and assess the correlation between neighboring patches within the image through the output scalar field matrix. At the same time, spectral normalization is applied on each convolutional layer to moderate parameter variations, which ensures that the discriminator function complies with the 1-Lipschitz constraint. (3) To address the issue of poor performance in conditional simulation under sparse data conditions, a preprocessing operation of pixel expansion is adopted for 2D conditioning constraints, enhancing the influence of conditioning data on the generated results. Additionally, a joint loss function combining the adversarial loss and conditioning loss terms is designed, ensuring the spatial distribution of the simulation results is similar to the original TI while satisfying the specified conditioning data constraints. By incorporating an attention mechanism, the network is better able to focus on critical features within the feature map, leading to advanced simulation performance and training efficiency. In the experiment, three types of TIs, namely, delta facies, lithofacies folded structure model, and heterogeneous aquifer model, are used to evaluate the simulation results of CSNGAN-ASPP.