Numerical groundwater models help us understand the dynamics of the sub- surface water reservoirs and are essential in our management strategies. The decision support offered by these models helps decision-makers protect and optimize the use of the precious fresh drinking water resource. Climate change introduces a previously unseen stress on these reservoirs making optimal groundwater management even more vital in the future. Extensive numerical investigations become necessary for decision-makers to explore all possible outcomes of an event before making any decisions. Here, an issue presents itself as the complex numerical models can be computationally heavy to run making decision support time-consuming and expensive for most purposes. In this PhD dissertation, we present a method for training a neural network to replace the numerical model engine in different groundwater management problems. Initially, we train a neural network to predict drawdown from groundwater abstraction in two different groundwater models. Later, we turn to the computationally heavy problem of predicting well recharge areas of wells. For all problems, results show that the neural networks predict responses with high accuracy and much faster than the numerical simulation period. We further contribute with a way of including stochastic model variability in the neural network predictions using an ensemble of numerical models with parameter variability. The neural network predicts probabilistic recharge areas in less than a second. This potentially allows decision-makers to perform extensive investigations previously deemed infeasible in everyday management tasks. Furthermore, decisions can now be based on probabilities or risks instead of deterministic model responses. We anticipate that the project findings will influence both academia and the industry, where our research has the potential to benefit future administrative groundwater management professionals.