  We study the applicability of a Deep Neural Network (DNN) approach to
simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid
dynamical calculations are used to generate training data-sets corresponding to
a broad range of profiles to perform supervised learning with DNN. The
performance of the DNN approach is analyzed, with a focus on its interpolation
and extrapolation capabilities. Issues such as inference speed, the networks
capacities to interpolate and extrapolate solutions with limited training
samples from both initial geometries and evolution duration aspects are studied
in detail. The optimal DNN performance is achieved when its objective is set to
learn the mapping between hydro profiles after a fixed value time step, which
can then be applied successively to reach moments in time much beyond the
duration contained in the training. The DNN has an advantage over the
conventional numerical methods by not being restricted by the Courant
criterion, and it shows a speedup over the conventional numerical methods by at
least two orders of magnitude.
