Proper Orthogonal Decomposition

A modal decomposition technique that extracts orthogonal basis functions (modes) from data or solution snapshots via eigen-decomposition of the covariance operator or singular value decomposition, representing dominant energetic structures in a low-dimensional linear subspace.

A data‑driven model‑reduction technique that computes an orthogonal basis (modes) from snapshots by solving the eigenproblem of the snapshot covariance or correlation operator (equivalently the Karhunen–Loève expansion) so that the leading modes capture the largest portion of variance (energy); truncated projection onto these modes yields a low‑dimensional approximation minimizing mean‑square reco