  Online adaptive model reduction efficiently reduces numerical models of
transport-dominated problems by updating reduced spaces over time, which leads
to nonlinear approximations on latent manifolds that can achieve a faster error
decay than classical linear model reduction methods that keep reduced spaces
fixed. Critical for online adaptive model reduction is coupling the full and
reduced model to judiciously gather data from the full model for adapting the
reduced spaces so that accurate approximations of the evolving full-model
solution fields can be maintained. In this work, we introduce lookahead
data-gathering strategies that predict the next state of the full model for
adapting reduced spaces towards dynamics that are likely to be seen in the
immediate future. Numerical experiments demonstrate that the proposed lookahead
strategies lead to accurate reduced models even for problems where previously
introduced data-gathering strategies that look back in time fail to provide
predictive models. The proposed lookahead strategies also improve the
robustness and stability of online adaptive reduced models.
