  This contribution introduces a model order reduction approach for an
advection-reaction problem with a parametrized reaction function. The
underlying discretization uses an ultraweak formulation with an $L^2$-like
trial space and an 'optimal' test space as introduced by Demkowicz et al. This
ensures the stability of the discretization and in addition allows for a
symmetric reformulation of the problem in terms of a dual solution which can
also be interpreted as the normal equations of an adjoint least-squares
problem. Classic model order reduction techniques can then be applied to the
space of dual solutions which also immediately gives a reduced primal space. We
show that the necessary computations do not require the reconstruction of any
primal solutions and can instead be performed entirely on the space of dual
solutions. We prove exponential convergence of the Kolmogorov $N$-width and
show that a greedy algorithm produces quasi-optimal approximation spaces for
both the primal and the dual solution space. Numerical experiments based on the
benchmark problem of a catalytic filter confirm the applicability of the
proposed method.
