An integrated framework of deep learning and entropy theory for enhanced high-dimensional permeability field identification in heterogeneous aquifers

Accurately estimating high-dimensional permeability (k) fields through data assimilation is critical for minimizing uncertainties in groundwater flow and solute transport simulations. However, designing an effective monitoring network to obtain diverse system responses in heterogeneous aquifers for data assimilation presents significant challenges. To investigate the influence of different measurement types (hydraulic heads, solute concentrations, and permeability) and monitoring strategies on the accuracy of permeability characterization, this study integrates a deep learning-based surrogate modeling approach and the entropy-based maximum information minimum redundancy (MIMR) monitoring design criterion into a data assimilation framework. An ensemble MIMR-optimized method is developed to provide more comprehensive monitoring information and avoid missing key information due to the randomness of stochastic response datasets in entropy analysis. A numerical case of solute transport with log-Gaussian permeability fields is presented, with twelve scenarios designed by combining different measurement types and monitoring strategies. The results demonstrated that the proposed ensemble MIMR-optimized method significantly improved the k-field estimates compared to the conventional MIMR method. Additionally, high prediction accuracy in forward modeling is essential for ensuring reliable inversion results, especially for observation data with strong nonlinearity. The findings of this study enhance our understanding and management of k-field estimation in heterogeneous aquifers, contributing to the development of more robust inversion frameworks for general data assimilation tasks.