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Simulation of complex dynamical systems arising in many applications iscomputationally challenging due to their size and complexity. Model orderreduction, machine learning, and other types of surrogate modeling techniquesoffer cheaper and simpler ways to describe the dynamics of these systems butare inexact and introduce additional approximation errors. In order to overcomethe computational difficulties of the full complex models, on one hand, and thelimitations of surrogate models, on the other, this work proposes a newaccelerated time-stepping strategy that combines information from both. Thisapproach is based on the multirate infinitesimal general-structure additiveRunge-Kutta (MRI-GARK) framework. The inexpensive surrogate model is integratedwith a small timestep to guide the solution trajectory, and the full model istreated with a large timestep to occasionally correct for the surrogate modelerror and ensure convergence. We provide a theoretical error analysis, andseveral numerical experiments, to show that this approach can be significantlymore efficient than using only the full or only the surrogate model for theintegration.

A fast time-stepping strategy for dynamical systems equipped with a surrogate model