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This work introduces an empirical quadrature-based hyperreduction procedureand greedy training algorithm to effectively reduce the computational cost ofsolving convection-dominated problems with limited training. The proposedapproach circumvents the slowly decaying $n$-width limitation of linear modelreduction techniques applied to convection-dominated problems by using anonlinear approximation manifold systematically defined by composing alow-dimensional affine space with bijections of the underlying domain. Thereduced-order model is defined as the solution of a residual minimizationproblem over the nonlinear manifold. An online-efficient method is obtained byusing empirical quadrature to approximate the optimality system such that itcan be solved with mesh-independent operations. The proposed reduced-ordermodel is trained using a greedy procedure to systematically sample theparameter domain. The effectiveness of the proposed approach is demonstrated ontwo shock-dominated computational fluid dynamics benchmarks.

Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature