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SUMMARY:Residual Dynamic Mode Decomposition: Robust and verified Koopmanis
 m for nonlinear dynamical systems - Matthew Colbrook (University of Cambri
 dge)
DTSTART:20230309T160000Z
DTEND:20230309T170000Z
UID:TALK198010@talks.cam.ac.uk
DESCRIPTION:Dynamic Mode Decomposition (DMD) describes complex dynamic pro
 cesses through a data-driven hierarchy of simpler coherent features. DMD i
 s regularly used to understand the fundamental characteristics of turbulen
 ce and is closely related to Koopman operators (infinite-dimensional opera
 tors that globally linearize nonlinear dynamical systems). However\, verif
 ying the decomposition\, equivalently the computed spectral features of Ko
 opman operators\, remains a significant challenge due to the infinite-dime
 nsional nature of Koopman operators. Challenges include spurious (unphysic
 al) modes and dealing with continuous spectra\, which occur regularly in t
 urbulent flows. Residual Dynamic Mode Decomposition (ResDMD) overcomes the
 se challenges through the data-driven computation of residuals associated 
 with the full infinite-dimensional Koopman operator\, allowing practitione
 rs to gain confidence in the computed results. We apply ResDMD to several 
 problems in fluid dynamics. For example\, we compare ResDMD and DMD for pa
 rticle image velocimetry data from turbulent wall-jet flow\, prediction of
  the acoustic signature of laser-induced plasma\, and the turbulent flow p
 ast a cascade of aerofoils. We also discuss the theory of ResDMD. ResDMD r
 igorously computes spectra of general Koopman operators with error control
  and spectral measures (including continuous spectra) with explicit high-o
 rder convergence theorems. Moreover\, the error control provided by ResDMD
  allows a posteriori verification of learned basis functions.\n[1] Colbroo
 k\, Matthew J.\, and Alex Townsend. "Rigorous data-driven computation of s
 pectral properties of Koopman operators for dynamical systems."&nbsp\;arXi
 v preprint arXiv:2111.14889&nbsp\;(2021).\n[2] Colbrook\, Matthew J.\, Lor
 na J. Ayton\, and M&aacute\;t&eacute\; Szőke. "Residual dynamic mode deco
 mposition: robust and verified Koopmanism."&nbsp\;Journal of Fluid Mechani
 cs 955 (2023).\n[3] Colbrook\, Matthew J. "The mpEDMD algorithm for data-d
 riven computations of measure-preserving dynamical systems."&nbsp\;arXiv p
 reprint arXiv:2209.02244&nbsp\;(2022).
LOCATION:Seminar Room 2\, Newton Institute
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