Enhancing hydraulic conductivity field characterization through integration of hydraulic head and tracer data using multi-modal neural network models

•For hydraulic conductivity field estimation, the convolutional neural network that uses only hydraulic head data requires the denser monitoring well pattern for better estimation accuracy.•Multi-modal neural network architectures have been constructed to integrate spatial hydraulic head data and temporal tracer data, and subsequently transform them into estimations of hydraulic conductivity fields.•The proposed HC-Net2 model is better at integrating hydraulic head and tracer data, and provides more accurate characterization by effectively combining the spatial and temporal information. Characterizing heterogeneous conductivity field is essential for effective groundwater management and controlling contaminant events. The characterization method is currently advancing towards two promising directions: (1) integration of various types of data, such as hydraulic head (H) and tracer concentration (C) data; (2) usage of machine learning methods of AI area. However, no machine learning model has been proposed to integrate H and C data for aquifer characterization effectively. The two data types have different forms: H data being spatial and C data being temporal. This discrepancy creates challenges for effective integration. We developed three machine learning models—HydroCNN, HC-Net1, and HC-Net2. The HydroCNN model could effectively predict hydraulic conductivity (K) fields from H data alone and thus is used as the baseline for evaluating the following models. HC-Net1 and HC-Net2 models are multi-modal neural network models with different architectures. These multi-modal architectures incorporate both convolutional neural network and fully connected neural network modules, designed to integrate H and C data to enhance characterization accuracy. Results indicate that HC-Net2 significantly outperforms the other models, highlighting its capability to leverage the strengths of both data types effectively. Notably, the HC-Net2 model’s improvement is most significant in scenarios where models relying solely on H data perform poorly.