  We propose a model reduction procedure for rapid and reliable solution of
parameterized hyperbolic partial differential equations. Due to the presence of
parameter-dependent shock waves and contact discontinuities, these problems are
extremely challenging for traditional model reduction approaches based on
linear approximation spaces. The main ingredients of the proposed approach are
(i) an adaptive space-time registration-based data compression procedure to
align local features in a fixed reference domain, (ii) a space-time
Petrov-Galerkin (minimum residual) formulation for the computation of the
mapped solution, and (iii) a hyper-reduction procedure to speed up online
computations. We present numerical results for a Burgers model problem and a
shallow water model problem, to empirically demonstrate the potential of the
method.
