On the role of nonlinear correlations in reduced-order modeling

Understand

A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure.

• Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but converges slowly for advection-dominated flows and tends to overestimate the number of dynamically relevant variables.
• We show that nonlinear correlations in the temporal POD coefficients can be exploited to identify the underlying attractor, characterized by a minimal set of driving modes and a manifold equation for the remaining modes.
• By viewing these nonlinear correlations as an invariant manifold reduction, this least-order representation can be used to stabilize POD-Galerkin models or as a state space for data-driven model identification.