Variational autoencoder-least squares generative adversarial Network (VA-LSGAN): a latent-space parameterization framework linking three-dimensional aquifer heterogeneity characterization and perfluorooctanoic acid (PFOA) inverse modeling

Accurate characterization of three-dimensional aquifer heterogeneity is essential for contaminant transport modeling, yet direct inversion of grid-scale hydraulic conductivity fields is often ill-posed and computationally expensive. This study proposes a variational autoencoder-least squares generative adversarial network (VA-LSGAN) for compact latent-space parameterization of three-dimensional heterogeneous hydraulic conductivity fields and applies it to perfluorooctanoic acid (PFOA) inverse modeling at a contaminated field site. The VA-LSGAN combines a three-dimensional convolutional variational autoencoder with a least-squares adversarial loss, retaining the encoder-decoder structure required for inversion while improving the preservation of spatial contrasts and continuity. A principal component analysis-based empirical latent covariance sampling strategy is further introduced to preserve the covariance structure of the learned latent space. Compared with a conventional variational autoencoder, the VA-LSGAN produced sharper reconstructions and more closely reproduced reference spatial autocorrelation patterns, although its pixel-wise reconstruction error was slightly higher. The learned latent representation was coupled with groundwater flow and solute transport models and an ensemble smoother with multiple data assimilation for field-scale PFOA inverse modeling. Data assimilation reduced the ensemble concentration-envelope width at the monitoring well by 67.5%, while retaining posterior uncertainty in decoded conductivity fields and source-related parameters. These results demonstrate the potential of VA-LSGAN as a flexible, uncertainty-aware parameterization linking three-dimensional aquifer heterogeneity characterization with process-based contaminant inverse modeling.