Physics-inspired machine learning methods for modeling regional groundwater flow systems
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The availability of suitable models and software is essential for forecasting groundwater levels, predicting the impacts of climate change and anthropogenic stresses on groundwater availability. Data-driven modeling formulations are becoming increasingly common for capturing nonlinear aquifer response dynamics since they can address practical limitations of physics-based frameworks such as ill-posed calibration processes, costly computation time, and large data requirements. In this dissertation, two novel machine learning modeling algorithms were formulated to expand the capability of machine learning approaches for simulating regional-scale groundwater flow systems. In the first study, an integrated spatio-temporal Artificial Neural Networks (ANN) model was constructed, inspired by the groundwater flow equation, to evaluate the hypothesis that a single ANN model is sufficient for the concurrent characterization of the spatio-temporal aquifer responses. In this model, explanatory features involved location parameters, delayed water levels at the well, water levels at the four closest surrounding wells, and a drought index (SPEI) – which was utilized as a surrogate for pumping. Advanced settings in ANN model calibration such as L2 regularization, rectified linear unit function, adaptive moment stochastic gradient method (ADAM), and cross-validation were used to avoid overfitting. The results indicated that the proposed space-time single neural networks showed promising potential for mapping the water table at regional scales and served as a valuable tool for water resources managers especially in areas with limited hydrogeological data. The second paper demonstrates the use of the bootstrap aggregation approach to construct a novel space-time neural networks ensemble model for regional groundwater flow modeling. Several different neural networks models operate together in this modeling paradigm to describe groundwater level fluctuations. Using the ensemble approach increases the model's capacity for prediction in terms of stability and generalization, as well as the ability to calculate uncertainty limits and confidence intervals. The developed model showed excellent performance in the training stage including data from 220 wells between the years 1980 and 2013 where at the least 80% correlation between the observed and simulated water table and maximum 0.60 m of mean absolute error were achieved as error metrics. Assessing the ability of the model during the forecasting stage (2014-2019) also demonstrated the potential of the developed model to predict groundwater level dynamics one-year ahead in both time and space where maximum 0.5 m absolute error and less than 5% bias were obtained in the majority (90 %) of wells.
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