Fast inverse estimation of hydraulic conductivity field based on a deep convolutional-cycle generative adversarial neural network

Abstract

This study proposes a novel deep convolutional-cycle generative adversarial neural network (DC-CGAN) for estimating the hydraulic conductivity field K from the observed head field H. The estimation of the heterogeneous hydraulic conductivity is apparently a high-dimensional inverse problem. Although the indirect approach is popularly utilized to solve the inverse problem, when compared with the indirect approach, the direct approach can conduct the inversion task faster without any iteration process. The key of the direct approach is to establish the inverse operator which maps the observed head to hydraulic conductivity. However, the complex inverse mapping relationship and high-dimensional estimation have always challenged the direct approach. Owing to the potential ability to handle high-dimensional images, six residual blocks with convolutional kernels have been designed as the generators of DC-CGAN to capture the potential distribution for enhancing the generation of estimation images similar to the real hydraulic conductivity. However, the traditional adversarial pattern of one-way generator and discriminator might suffer from the equifinality from different parameters. Therefore, to alleviate the equifinality, a cycle adversarial training pattern involving two generators and discriminators has been employed to supervise the map. Particularly, this pattern performs a forward map from H to K and then the reconstructed K back to H. The reconstruction process has been a supervision to the forward map process. A hypothetical case with 40×30 unknown K values has been designed to evaluate the performance of DC-CGAN, and the results indicate that DC-CGAN has achieved a desired generalization accuracy of MRE of 9.25 % and SSIM of 0.85 with the swift running speed of 0.2 s, which outperforms indirect approach. The application of the proposed DC-CGAN shows that it can provide a reliable and fast high-dimensional estimation task for the heterogenous hydraulic conductivity.