Comparison of parallel optimization algorithms on computationally expensive groundwater remediation designs

Uncertainty-based saltwater intrusion prediction using integrated Bayesian machine learning modeling (IBMLM) in a deep aquifer

Data-driven machine learning approaches are promising to substitute physically based groundwater numerical models and capture input-output relationships for reducing computational burden. But the performance and reliability are strongly influenced by different sources of uncertainty. Conventional researches generally rely on a stand-alone machine learning surrogate approach and fail to account for errors in model outputs resulting from structural deficiencies. To overcome this issue, this study proposes a flexible integrated Bayesian machine learning modeling (IBMLM) method to explicitly quantify uncertainties originating from structures and parameters of machine learning surrogate models. An Expectation-Maximization (EM) algorithm is combined with Bayesian model averaging (BMA) to find out maximum likelihood and construct posterior predictive distribution. Three machine learning approaches representing different model complexity are incorporated in the framework, including artificial neural network (ANN), support vector machine (SVM) and random forest (RF). The proposed IBMLM method is demonstrated in a field-scale real-world "1500-foot" sand aquifer, Baton Rouge, USA, where overexploitation caused serious saltwater intrusion (SWI) issues. This study adds to the understanding of how chloride concentration transport responds to multi-dimensional extraction-injection remediation strategies in a sophisticated saltwater intrusion model. Results show that most IBMLM exhibit r values above 0.98 and NSE values above 0.93, both slightly higher than individual machine learning, confirming that the IBMLM is well established to provide better model predictions than individual machine learning models, while maintaining the advantage of high computing efficiency. The IBMLM is found useful to predict saltwater intrusion without running the physically based numerical simulation model. We conclude that an explicit consideration of machine learning model structure uncertainty along with parameters improves accuracy and reliability of predictions, and also corrects uncertainty bounds. The applicability of the IBMLM framework can be extended in regions where a physical hydrogeologic model is difficult to build due to lack of subsurface information.

Two-step approach based multi-objective groundwater remediation using enhanced random vector functional link integrated with evolutionary marine predator algorithm

We here propose a two-step approach-based simulation-optimization model for multi-objective groundwater remediation using enhanced random vector functional link (ERVFL) and evolutionary marine predator algorithm (EMPA). In this study, groundwater flow and solute transport models are developed using MODFLOW and MT3DMS. The ERVFL network is used to approximate the flow and transport models, enhancing the computational performance. This study also improves the robustness of the ERVFL network using a kernel density estimator (KDE) based weighted least square approach. We further develop the EMPA by modifying the marine predator algorithm (MPA) using elite opposition-based learning, biological evolution operators, and elimination mechanisms. In the multi-objective version of EMPA, the non-dominated/Pareto-optimal solutions are stored in an external repository using an archive controller and adaptive grid mechanism to promote better convergence and diversity of the Pareto front. The proposed methodologies are applied for multi-objective groundwater remediation of a hypothetical unconfined aquifer based on the two-step method. The first step directly integrates flow and transport models with EMPA and finds the optimal locations of pumping wells by minimizing the percent of contaminant mass remaining in the aquifer. In the second step, the ERVL-based proxy model is integrated with EMPA and used for multi-objective optimization while explicitly using the pumping well locations obtained in the first step. The multi-objective optimization generates a Pareto-optimal solution representing the relationship between the rate of pumping and the amount of contaminant mass in the aquifer. Further analyses show a significant advantage of the two-step approach over a traditional method for multi-objective groundwater remediation.

A data-driven approach to exploring the causal relationships between distributed pumping activities and aquifer drawdown

Groundwater depletion, typically caused by the distributed pumping activities of multiple stakeholders (i.e., water users) that share a hydrologically connected aquifer, has led to severe environmental and ecological problems in many river basins worldwide. Conventionally, the effects of pumping on aquifer depletion are quantified using well hydraulics or physically based hydrological models in groundwater management. However, the derivation of well hydraulics-based analytical solutions requires numerous simplifying assumptions, while the construction and calibration of a physically based groundwater flow model require detailed information about the subsurface properties, which are subject to large uncertainties. In this study, we develop a novel modeling framework that does not rely on well hydraulics or groundwater flow models. The proposed framework integrates (1) a deep learning model that captures the spatiotemporal variations in the aquifer in response to distributed pumping activities in multiple well fields and (2) a statistical causal inference model that identifies the causal networks among stakeholders to quantify the causal effects of individual pumping activities on aquifer depletion. The proposed framework is tested on a synthetic case study site with well fields that have various spatial distributions and pumping rates. The modeling results show that the deep learning method can effectively capture the water table dynamics influenced by distributed pumping activities with R² >90 % for all observation data. More importantly, our model is capable of assessing the causal networks between the drawdown of water table and the pumping activities of multiple well fields and quantifying their causal strengths. These results suggest that our modeling framework can be used to explicitly assess the extent to which each individual stakeholder's pumping activities contribute to aquifer depletion at the system level. The concepts and techniques developed in this study can be used to resolve classic externality problems in the context of common-pool groundwater management.