Core Concepts
Multivariate Gaussian Process Regression offers a novel approach to modal analysis for spatiotemporal data, overcoming limitations of traditional methods.
Abstract
This content delves into the application of Multivariate Gaussian Process Regression (MVGPR) in modal analysis for spatiotemporal data. It discusses the challenges faced by traditional modal analysis techniques and introduces MVGPR as a promising alternative. The paper establishes connections between MVGPR, Koopman operator theory, and existing modal analysis methods like Dynamic Mode Decomposition (DMD) and Spectral Proper Orthogonal Decomposition (SPOD). It also benchmarks MVGPR against DMD and SPOD on various examples to showcase its effectiveness in handling temporally irregular data. The content further explores the identification of stationary flow systems using MVGPR with Linear Model of Coregionalization (LMC) kernel structure. Additionally, it draws parallels between SPOD and MVGPR methodologies, highlighting their differences and similarities in capturing system dynamics.
Stats
C(𝜏) = E{𝑥 𝑗 (0)2 cos2( 𝑗𝜔0𝑡) + 𝑦 𝑗 (0)2 sin2( 𝑗𝜔0𝑡)} cos( 𝑗𝜔0𝜏)
E[|⟨q(𝑡, 𝝃), 𝝋(𝑡, 𝝃)⟩|2]
E[|⟨q(𝑡, 𝝃), 𝝋(𝑡, 𝝃)⟩|2]
E[|⟨ˆq( 𝑓 , 𝝃), u𝑗 ( 𝑓 , 𝝃)⟩|]
∫ ∞ −∞ ∫ Ω pH(t, η)q(t, η)dηdt = max {E[|⟨q(t, η), υ(t, η)⟩|^2]}
Quotes
"Modal analysis has become an essential tool to understand the coherent structure of complex flows."
"MVGPR is shown to produce a low-order linear dynamical system for spatiotemporal datasets."
"MVGPR offers a promising alternative to classical modal analysis methods for handling sparse and irregular data."