  We propose a supervised deep learning (DL) approach to perform adaptive
zoning on time dependent partial differential equations that model the
propagation of 1D shock waves in a compressible medium. We train a neural
network on a dataset composed of different static shock profiles associated
with the corresponding adapted meshes computed with standard adaptive zoning
techniques. We show that the trained DL model learns how to capture the
presence of shocks in the domain and generates at each time step an adapted
non-uniform mesh that relocates the grid nodes to improve the accuracy of
Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space
discretization schemes. We also show that the surrogate DL model reduces the
computational time to perform adaptive zoning by at least a 2x factor with
respect to standard techniques without compromising the accuracy of the
reconstruction of the physical quantities of interest.
