Development of explainable hybrid quantum-inspired recurrent neural networks for predicting groundwater quality: A case study at West Azerbaijan, Iran

Abstract

Effective groundwater quality monitoring is essential for ensuring sustainable water resource management. Total dissolved solids (TDS) is a key indicator of groundwater quality. This study presents advanced hybrid deep learning frameworks for forecasting TDS levels at West Azerbaijan, Iran. Six diverse input combinations of pH, Mg, total alkalinity, HCO 3 , Ca, and total hardness were defined. A quantum-inspired recurrent neural network (QRNN) was first developed as baseline model. Two hybrid models, QRNN-CNN and GBO-QRNN-CNN, were then introduced to enhance predictive performance by integrating convolutional neural network (CNN) and gradient- based optimizer (GBO). Comparative evaluations demonstrated that both hybrid models outperformed the standalone QRNN, with GBO-QRNN-CNN achieving the highest accuracy. Root mean square error of TDS prediction via the best model (GBO-QRNN-CNN-6) was reduced by 48.36 % compared with baseline QRNN-6. Moreover, long short-term memory (LSTM) was implemented, denoting its lower accuracy than QRNN-based models. Additionally, SHapley Additive exPlanation (SHAP) was employed to assess the influence of input variables, revealing that total hardness and calcium had the highest impacts on TDS predictions. The QRNN frameworks proposed in this study taking into account the outcomes of SHAP, offer powerful TDS predictive tools for data-driven groundwater quality assessment, supporting more informed decision-making in water resource management.