Integration of Deep Learning and Information Theory for Designing Monitoring Networks in Heterogeneous Aquifer Systems

Groundwater monitoring networks are direct sources of information for revealing subsurface system dynamic processes. However, designing such networks is difficult due to uncertainties in the spatial heterogeneity of aquifer parameters such as permeability (k). This study combines deep learning and information theory with an optimization framework to address network design problems in heterogeneous aquifer systems. The framework first employs a generative adversarial network to parameterize heterogeneous k distribution using a low‐dimensional latent representation. Then, surrogate models are developed based on the deep neural networks to perform uncertainty quantification of pressure heads and solute concentrations at locations of pre‐designed candidate monitoring stations. The monitoring stations are then ranked using the greedy search algorithm based on the maximum information minimum redundancy (MIMR) criterion. In order to depict the importance of each candidate monitoring location, the hotspot maps of the selection probability (Ps) are derived from MIMR repetition results. Comprehensive monitoring networks derived from the hotspot maps are then conducted as the final monitoring stations to improve monitoring information compared to MIMR results. Additionally, nine entropy quantization strategies are compared to evaluate their effects on monitoring network optimization results. Results indicate that caution should be taken when selecting entropy quantization strategies to achieve the accuracy required for model calibration and to improve the efficiency of monitoring optimization. Considering high‐dimensional uncertainties associated with aquifer parameters, the developed framework can provide important insights for monitoring network designs in various earth observational projects. Plain Language Summary Groundwater is widely distributed throughout the crust and lithosphere playing a critical role in geological evolution processes and environmental problems. This study presents an integrated framework for designing groundwater monitoring networks in heterogeneous aquifer systems. The proposed model takes advantage of the strength of deep‐learning algorithms and deals with high‐dimensional and highly non‐linear problems of entropy‐based methods for designing the monitoring networks. The framework can efficiently provide monitor locations for complex aquifers. The monitoring data collected by the designed network can significantly reduce uncertainties ass