  Multi-physics simulation often involve multiple different scales. The ARKODE
ODE solver package in the SUNDIALS library addresses multi-scale problems with
a multi-rate time-integrator that can work with a right-hand side that has fast
scale and slow scale components. In this report, we use dynamic mode
decomposition and time delay embedding to extract the fast and and slow
components of the right-hand sides of a simple ODE from data. We then use the
extracted components to solve the ODE with ARKODE. Finally, to move towards a
real-world use case, we attempt to extract fast and slow scale dynamics from
synthetic seismic modeling data.
