Integration of Physics‐Constrained Learning With Adversarial Autoencoders for Simultaneous Inference of Hydraulic Conductivity and Contaminant Sources

Determining heterogeneous conductivity fields and reconstructing contaminant release histories in subsurface remediation often lead to a high‐dimensional inverse problem. To tackle this issue, researchers typically integrate model outputs with sparse and noisy measurements of hydraulic head and concentration. However, this approach remains highly challenging due to the high‐dimensional non‐Gaussian property of the conductivity field and the significant computational cost of repeated forward model evaluations. In this study, we use a convolutional adversarial autoencoder (CAAE) with a low‐dimensional latent representation to parameterize heterogeneous conductivity fields, reducing the inverse problem's dimensionality and incorporating prior knowledge. The CAAE is incorporated into a physics‐constrained learning strategy (PCL) to estimate the unknown parameters, forming an efficient deterministic CAAE‐PCL inverse framework. The CAAE‐PCL can infer the unknown parameters by computing the gradients of deep neural networks and partial differential equation solvers using automatic differentiation. The effectiveness of CAAE‐PCL is tested on a synthetic three‐dimensional contaminant source and conductivity field identification problem. The results indicate that the CAAE is a robust method for parameterizing a highly heterogeneous non‐Gaussian conductivity field. The CAAE‐PCL achieves accurate inversion results with measurements from candidate observation wells. Additionally, to eliminate redundant wells, we propose an observation well optimization strategy based on the maximum information minimum redundancy (MIMR) criterion to identify the optimal subset of wells from the candidates. Using measurements from these optimally selected sparse wells, the CAAE‐PCL achieves inversion accuracy comparable to that obtained with all candidate wells.