  We propose a new data-driven method to learn the dynamics of an unknown
hyperbolic system of conservation laws using deep neural networks. Inspired by
classical methods in numerical conservation laws, we develop a new conservative
form network (CFN) in which the network learns the flux function of the unknown
system. Our numerical examples demonstrate that the CFN yields significantly
better prediction accuracy than what is obtained using a standard
non-conservative form network, even when it is enhanced with constraints to
promote conservation. In particular, solutions obtained using the CFN
consistently capture the correct shock propagation speed without introducing
non-physical oscillations into the solution. They are furthermore robust to
noisy and sparse observation environments.
