Multilevel on-the-fly sparse grids for coupling coarse-grained and high fidelity models in heterogeneous catalysis

Abstract

Coupling microscopic high-fidelity models, such as microkinetic models, into continuum scale simulations can easily become intractable in practice due to the costs of the high-fidelity model evaluation. To lift this burden, we present a novel multilevel self-consistent on-the-fly sparse grid approach, which integrates the construction of surrogates of the high-fidelity model in a multilevel fashion into the continuum solution process. Besides its efficiency, an appealing feature of the approach is its simplicity and robustness. A single hyperparameter controls the whole workflow, from training set design to the accuracy of the reactor model. We demonstrate the methodology on a recent microkinetic model for catalytic combustion in a fixed-bed reactor model as a representative example. Already with modest numbers of data, the approach achieves sufficient accuracy, reducing the effort by orders of magnitude compared to a direct coupling.