Dynamically Optimal Projection onto Slow Spectral Manifolds for Linear Systems

Abstract

We derive the dynamically optimal projection onto the linear slow manifold from a temporal variational principle. We demonstrate that the projection captures transient dynamics of the overall dissipative system and leads to a considerably improved fit of reduced trajectories compared to full trajectories. We illustrate these optimal model reduction properties on explicit examples, including the linear three-component Grad's moment system.