Abstract
Accurate characterization of hydrogeological structures serves as the foundation for robust hydrogeological process modeling and advances Earth’s scientific understanding. The deep learning technique advances the conventional workflows of hydrogeological characterization. However, the black-box deep neural networks limits interpretability of the characterization process. In this work, we propose a novel approach termed the multiple conditional self-representation network (MCSR-Net). The self-representation learning strategy is presented to improve the interpretation of deep-learning-based characterization approaches and reduce the artifacts in generated realizations. The self-representation learning strategy includes a self-representation network for providing latent representations of hydrogeological structures and a loss function for optimizing the consistency of implicit features. Additionally, to achieve integration of multiple observations, a conditioning data encoder is embedded in MCSR-Net to enhance the efficiency of extracting spatial features. A joint loss function is employed to optimize the training process and improve the performance of conditional simulations. This study systematically evaluates the performance of MCSR-Net using three synthetic data sets of fluvial deposits. A comparative experiment is conducted to demonstrate the advantages of MCSR-Net in characterizing spatial heterogeneity. Results show performance with an average the root mean square error (RMSE), the structural similarity (SSIM), the peak signal-to-noise ratio (PSNR), and F1 Score of 0.013, 0.975, 23.556, and 0.924 overall datasets for our best model. These experimental findings show that although our proposal introduces more hidden parameters, it can improve the interpretability of neural networks. These results underscore the reliability and superiority of MCSR-Net in applications of hydrogeological modeling, and inversion.