  Numerical simulations of groundwater flow are used to analyze and predict the
response of an aquifer system to its change in state by approximating the
solution of the fundamental groundwater physical equations. The most used and
classical methodologies, such as Finite Difference (FD) and Finite Element (FE)
Methods, use iterative solvers which are associated with high computational
cost. This study proposes a physics-based convolutional encoder-decoder neural
network as a surrogate model to quickly calculate the response of the
groundwater system. Holding strong promise in cross-domain mappings,
encoder-decoder networks are applicable for learning complex input-output
mappings of physical systems. This manuscript presents an Attention U-Net model
that attempts to capture the fundamental input-output relations of the
groundwater system and generates solutions of hydraulic head in the whole
domain given a set of physical parameters and boundary conditions. The model
accurately predicts the steady state response of a highly heterogeneous
groundwater system given the locations and piezometric head of up to 3 wells as
input. The network learns to pay attention only in the relevant parts of the
domain and the generated hydraulic head field corresponds to the target samples
in great detail. Even relative to coarse finite difference approximations the
proposed model is shown to be significantly faster than a comparative
state-of-the-art numerical solver, thus providing a base for further
development of the presented networks as surrogate models for groundwater
prediction.
