Physics-inspired integrated space-time artificial neural networks for regional groundwater flow modeling

An integrated space-time artificial neural network (ANN) model inspired by the governing groundwater flow equation was developed to test whether a single ANN is capable of modeling regional groundwater flow systems. Model independent entropy measures and random forest (RF)-based feature selection procedures were used to identify suitable inputs for ANNs. L2 regularization, five-fold cross-validation, and an adaptive stochastic gradient descent (ADAM) algorithm led to a parsimonious ANN model for a 30 691 km(2) agriculturally intensive area in the Ogallala Aquifer of Texas. The model testing at 38 independent wells during the 1956-2008 calibration period showed no overfitting issues and highlighted the model's ability to capture both the observed spatial dependence and temporal variability. The forecasting period (2009-2015) was marked by extreme climate variability in the region and served to evaluate the extrapolation capabilities of the model. While ANN models are universal interpolators, the model was able to capture the general trends and provide groundwater level estimates that were better than using historical means. Model sensitivity analysis indicated that pumping was the most sensitive process. Incorporation of spatial variability was more critical than capturing temporal persistence. The use of the standardized precipitation- evapotranspiration index (SPEI) as a surrogate for pumping was generally adequate but was unable to capture the heterogeneous groundwater extraction preferences of farmers under extreme climate conditions.