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

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