  We propose a new hyper-reduction method for a recently introduced nonlinear
model reduction framework based on dynamically transformed basis functions and
especially well-suited for advection-dominated systems. Furthermore, we discuss
applying this new method to a wildland fire model whose dynamics feature
traveling combustion waves and local ignition and is thus challenging for
classical model reduction schemes based on linear subspaces. The new
hyper-reduction framework allows us to construct parameter-dependent
reduced-order models (ROMs) with efficient offline/online decomposition. The
numerical experiments demonstrate that the ROMs obtained by the novel method
outperform those obtained by a classical approach using the proper orthogonal
decomposition and the discrete empirical interpolation method in terms of run
time and accuracy.
