  This work introduces an empirical quadrature-based hyperreduction procedure
and greedy training algorithm to effectively reduce the computational cost of
solving convection-dominated problems with limited training. The proposed
approach circumvents the slowly decaying $n$-width limitation of linear model
reduction techniques applied to convection-dominated problems by using a
nonlinear approximation manifold systematically defined by composing a
low-dimensional affine space with bijections of the underlying domain. The
reduced-order model is defined as the solution of a residual minimization
problem over the nonlinear manifold. An online-efficient method is obtained by
using empirical quadrature to approximate the optimality system such that it
can be solved with mesh-independent operations. The proposed reduced-order
model is trained using a greedy procedure to systematically sample the
parameter domain. The effectiveness of the proposed approach is demonstrated on
two shock-dominated computational fluid dynamics benchmarks.
