  In this paper we develop a non-diffusive neural network (NDNN) algorithm for
accurately solving weak solutions to hyperbolic conservation laws. The
principle is to construct these weak solutions by computing smooth local
solutions in subdomains bounded by discontinuity lines (DLs), the latter
defined from the Rankine-Hugoniot jump conditions. The proposed approach allows
to efficiently consider an arbitrary number of entropic shock waves, shock wave
generation, as well as wave interactions. Some numerical experiments are
presented to illustrate the strengths and properties of the algorithms.
