  Simulation of complex dynamical systems arising in many applications is
computationally challenging due to their size and complexity. Model order
reduction, machine learning, and other types of surrogate modeling techniques
offer cheaper and simpler ways to describe the dynamics of these systems but
are inexact and introduce additional approximation errors. In order to overcome
the computational difficulties of the full complex models, on one hand, and the
limitations of surrogate models, on the other, this work proposes a new
accelerated time-stepping strategy that combines information from both. This
approach is based on the multirate infinitesimal general-structure additive
Runge-Kutta (MRI-GARK) framework. The inexpensive surrogate model is integrated
with a small timestep to guide the solution trajectory, and the full model is
treated with a large timestep to occasionally correct for the surrogate model
error and ensure convergence. We provide a theoretical error analysis, and
several numerical experiments, to show that this approach can be significantly
more efficient than using only the full or only the surrogate model for the
integration.
