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We consider machine-learning of time-dependent quantities of interest derivedfrom solution trajectories of parabolic partial differential equations. Forlarge-scale or long-time integration scenarios, where using a full order model(FOM) to generate sufficient training data is computationally prohibitive, wepropose an adaptive hierarchy of intermediate Reduced Basis reduced ordermodels (ROM) to augment the FOM training data by certified ROM training datarequired to fit a kernel model.

An adaptive model hierarchy for data-augmented training of kernel models for reactive flow