Lightweight Depthwise Autoregressive Convolutional Surrogate for Efficient Joint Inversion of Hydraulic Conductivity and Time-Varying Contaminant Sources

Accurate joint estimation of heterogeneous hydraulic conductivity fields and time-varying contaminant source parameters in groundwater systems constitutes a challenging high-dimensional inverse problem, particularly under sparse observational conditions and high computational demands. To alleviate this limitation, this study proposes an autoregressive depthwise convolutional neural network (AR-DWCNN) as a lightweight surrogate model for coupled groundwater flow and contaminant transport simulations. The proposed model employs depthwise separable convolutions and dense connectivity within an encoder–decoder framework to capture nonlinear flow and spatiotemporal transport dynamics while reducing model complexity and computational demand relative to conventional convolutional architectures. The AR-DWCNN is further integrated with an enhanced Iterative Local Updating Ensemble Smoother incorporating Levenberg–Marquardt regularization, enabling efficient joint inversion of high-dimensional hydraulic conductivity fields and multi-period contaminant source strengths. Numerical experiments conducted on a synthetic two-dimensional heterogeneous aquifer demonstrate that the surrogate-assisted inversion framework achieves posterior estimates that closely match those obtained using the numerical forward model, while significantly improving computational efficiency. These results indicate that the AR-DWCNN-based inversion method provides an effective and scalable solution for high-dimensional groundwater contaminant transport inverse problems, offering practical potential for uncertainty quantification and remediation design in complex subsurface systems.