Bayesian Neural Networks for Quantifying Uncertainty in Solute Transport Through Saturated Porous Media

Uncertainty quantification (UQ) is critical for predicting solute transport in heterogeneous porous media, with applications in groundwater management and contaminant remediation. Traditional UQ methods, such as Monte Carlo (MC) simulations, are computationally expensive and impractical for real-time decision-making. This study introduces a novel machine learning framework to address these limitations. We developed a surrogate model for a 2D advection-dispersion solute transport model using a Bayesian Neural Network (BNN). The BNN was trained on a synthetic dataset generated by simulating solute transport across various stochastic permeability and dispersivity fields. Uncertainty was quantified through variational inference, capturing both data-related (aleatoric) and model-related (epistemic) uncertainties. We evaluated the framework’s performance against traditional MC simulations. Our BNN model accurately predicts solute concentration distributions with a mean squared error (MSE) of 9.8 × 10−5, significantly outperforming other machine learning surrogates. The framework successfully quantifies uncertainty, providing calibrated confidence intervals that align closely with the spread of the MC results. The proposed approach achieved a 98.5% reduction in computational time compared to a standard Monte Carlo simulation with 1000 realizations, representing a 65-fold speed-up. A sensitivity analysis revealed that permeability field heterogeneity is the dominant source of uncertainty in plume migration. The developed machine learning framework offers a computationally efficient and robust alternative for quantifying uncertainty in solute transport models. By accurately predicting solute concentrations and their associated uncertainties, our approach can inform risk-based decision-making in environmental and hydrogeological applications. The method shows promise for scaling to more complex, three-dimensional systems.