  Physics-informed neural networks (PINN) have recently become attractive for
solving partial differential equations (PDEs) that describe physics laws. By
including PDE-based loss functions, physics laws such as mass balance are
enforced softly in PINN. This paper investigates how mass balance constraints
are satisfied when PINN is used to solve the resulting PDEs. We investigate
PINN's ability to solve the 1D saturated groundwater flow equations for
homogeneous and heterogeneous media and evaluate the local and global mass
balance errors. We compare the obtained PINN's solution and associated mass
balance errors against a two-point finite volume numerical method and the
corresponding analytical solution. We also evaluate the accuracy of PINN in
solving the 1D saturated groundwater flow equation with and without
incorporating hydraulic heads as training data. We demonstrate that PINN's
local and global mass balance errors are significant compared to the finite
volume approach. Tuning the PINN's hyperparameters, such as the number of
collocation points, training data, hidden layers, nodes, epochs, and learning
rate, did not improve the solution accuracy or the mass balance errors compared
to the finite volume solution. Mass balance errors could considerably challenge
the utility of PINN in applications where ensuring compliance with physical and
mathematical properties is crucial.
