An Adaptive Data-Driven Reduced Order Model Based on Higher Order Dynamic Mode Decomposition

A new data-driven reduced order model is developed to efficiently simulate transient dynamics, with the aim at computing the final attractor. The method combines a standard numerical solver and time extrapolation based on a recent data processing tool, called higher order dynamic mode decomposition. Such combination is made using interspersed time intervals, called snapshots computation (obtained from the numerical solver) and extrapolation intervals (computed by the model). The process continues, alternating snapshots computation and extrapolation intervals, until that moment at which the final attractor is reached. Thus, the method adapts the extrapolated approximations to the varying dynamics along the transient simulation. The performance of the new method is tested considering representative transient solutions of the one-dimensional complex Ginzburg-Landau equation. In this application, the speed-up factor of the reduced order model, comparing its computational cost with that of the standard numerical solver, is always much larger than one in the computation of representative periodic and quasi-periodic attractors.