Surrogate-assisted Bayesian inference with ERT data for contaminant transport modelling in the subsurface

Understanding and predicting groundwater contaminant transport is inherently challenging due to uncertainties in both field-specific properties and contaminant-related parameters. These uncertainties pose challenges for effective environmental management, including project planning, non-invasive long-term monitoring, and remediation efforts. To address this, we propose a framework that combines geophysical monitoring, surrogate-assisted Bayesian inference, and dimensionality reduction techniques to quantify and reduce these uncertainties and aid in decision making processes. For the implementation of Bayesian inference, our work focuses on electrical resistivity tomography, a geophysical method that is particularly well-suited for the abovementioned purpose due to its sensitivity to variations in fluid content and temperature.

The proposed approach addresses two major computational challenges. First, Bayesian inference requires extensive model runs, which can become computationally prohibitive for large domains with fine grids, multiple processes, and multiple time steps. To mitigate this, we use surrogate models that approximate the full physics-based model using input-output data pairs, significantly reducing computational costs. Second, the high-dimensional nature of ERT data complicates both surrogate training and Bayesian inference. High output dimensions lead to increased training times, larger data requirements, and difficulties in likelihood estimation due to the "curse of dimensionality." To overcome this, we incorporate dimension reduction techniques into the framework.

Our main focus is to evaluate how surrogate modeling approximations and dimension reduction strategies influence the accuracy and efficiency of Bayesian inference when using ERT measurements for contaminant transport applications. We apply our framework on a 2D synthetic non-reactive contaminant transport scenario, integrating ERT measurements while accounting for uncertainties in both field-specific and contaminant-related parameters. This methodology provides a practical tool for subsurface engineering, offering improvements in planning, parameter estimation, and long-term monitoring to enhance contaminant transport predictions and remediation strategies.