Dynamically Optimal Projection onto Slow Spectral Manifolds for Linear Systems

2025/03/23 by Kogelbauer, Florian, Karlin, Ilya
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.18021

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.

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