  Efficiently reducing models of chemically reacting flows is often challenging
because their characteristic features such as sharp gradients in the flow
fields and couplings over various time and length scales lead to dynamics that
evolve in high-dimensional spaces. In this work, we show that online adaptive
reduced models that construct nonlinear approximations by adapting
low-dimensional subspaces over time can predict well latent dynamics with
properties similar to those found in chemically reacting flows. The adaptation
of the subspaces is driven by the online adaptive empirical interpolation
method, which takes sparse residual evaluations of the full model to compute
low-rank basis updates of the subspaces. Numerical experiments with a premixed
flame model problem show that reduced models based on online adaptive empirical
interpolation accurately predict flame dynamics far outside of the training
regime and in regimes where traditional static reduced models, which keep
reduced spaces fixed over time and so provide only linear approximations of
latent dynamics, fail to make meaningful predictions.
