Bayesian deep learning for probabilistic aquifer vulnerability and uncertainty prediction.

Groundwater is the planet’s largest distributed store of freshwater and a critical buffer against drought. Yet aquifers are still managed largely with static, deterministic vulnerability indices that neither capture nonlinear hydrogeological interactions nor convey predictive uncertainty. Accurate and interpretable aquifer vulnerability assessments (AVA) are essential for sustaining groundwater resources under increasing hydro-environmental pressures. This study presents a Bayesian Convolutional Neural Network (Bayesian CNN) framework for probabilistic AVA, integrating prior hydrogeological knowledge through regularization. The model inputs multi-layered hydro-environmental data, learns spatial patterns in contamination occurrence, and outputs full predictive distributions rather than single vulnerability scores. The Bayesian CNN achieved stable convergence, outperformed deterministic deep learning baselines, and produced well-calibrated probabilistic predictions of aquifer vulnerability. Predictive entropy was decomposed into epistemic and aleatoric components, enabling clear attribution of uncertainty to model limitations versus inherent environmental variability. Explainable Artificial Intelligence (XAI) analyses based on SHapley Additive exPlanations (SHAP) identified the dominant vulnerability predictors, reinforcing physical consistency and improving interpretability. By combining Bayesian inference, uncertainty prediction, and XAI, this framework advances adaptive, transparent, and risk-aware sustainable groundwater management. It supports targeted monitoring, resource allocation, and decision-making under uncertainty, providing a scalable pathway toward climate-resilient and evidence-based groundwater governance in data-scarce regions.