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Efficiently reducing models of chemically reacting flows is often challengingbecause their characteristic features such as sharp gradients in the flowfields and couplings over various time and length scales lead to dynamics thatevolve in high-dimensional spaces. In this work, we show that online adaptivereduced models that construct nonlinear approximations by adaptinglow-dimensional subspaces over time can predict well latent dynamics withproperties similar to those found in chemically reacting flows. The adaptationof the subspaces is driven by the online adaptive empirical interpolationmethod, which takes sparse residual evaluations of the full model to computelow-rank basis updates of the subspaces. Numerical experiments with a premixedflame model problem show that reduced models based on online adaptive empiricalinterpolation accurately predict flame dynamics far outside of the trainingregime and in regimes where traditional static reduced models, which keepreduced spaces fixed over time and so provide only linear approximations oflatent dynamics, fail to make meaningful predictions.

Reduced models with nonlinear approximations of latent dynamics for model premixed flame problems