Integration of DDPM and ILUES for Simultaneous Identification of Contaminant Source Parameters and Non-Gaussian Channelized Hydraulic Conductivity Field

Identifying highly channelized hydraulic conductivity fields and contaminant source parameters remains a challenging task, primarily due to the non-Gaussian nature and high dimensionality of the parameter space, as well as the computational burden caused by repeatedly running forward numerical models. This study proposes a novel deep learning parameterization method called AEdiffusion, which combines Diffusion Denoising Probabilistic Model (DDPM) with Variational Autoencoder (VAE) for dimensionality reduction. The method employs a generator-refiner strategy to generate high-dimensional aquifer properties from low-dimensional latent representations. The inversion modeling was performed on a synthetic non-Gaussian hydraulic conductivity field with line-source contamination using the Iterative Local Updating Ensemble Smoother (ILUES) algorithm. The results demonstrate that the AEdiffusion-ILUES framework can accurately identify model parameters. To reduce the computational burden, an AR-Net-WL (ARNW) surrogate model was introduced, resulting in an efficient inversion framework (AEdiffusion-ILUES-ARNW) with similar prediction accuracy and predictive uncertainty estimation as the AEdiffusion-ILUES but at a lower computational cost.