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SUMMARY:The future of governing equations - J. Nathan Kutz (University of 
 Washington)
DTSTART:20240125T150000Z
DTEND:20240125T160000Z
UID:TALK210121@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:A major challenge in the study of dynamical systems is that of
  model discovery: turning data into reduced order models that are not just
  predictive\, but provide insight into the nature of the underlying dynami
 cal system that generated the data. We introduce a number of data-driven s
 trategies for discovering nonlinear multiscale dynamical systems and their
  embeddings from data. We consider two canonical cases: (i) systems for wh
 ich we have full measurements of the governing variables\, and (ii) system
 s for which we have incomplete measurements. For systems with full state m
 easurements\, we show that the recent sparse identification of nonlinear d
 ynamical systems (SINDy) method can discover governing equations with rela
 tively little data and introduce a sampling method that allows SINDy to sc
 ale efficiently to problems with multiple time scales\, noise and parametr
 ic dependencies. For systems with incomplete observations\, we show that t
 he Hankel alternative view of Koopman (HAVOK) method\, based on time-delay
  embedding coordinates and the dynamic mode decomposition\, can be used to
  obtain a linear models and Koopman invariant measurement systems that nea
 rly perfectly captures the dynamics of nonlinear quasiperiodic systems. Ne
 ural networks are used in targeted ways to aid in the model reduction proc
 ess. Together\, these approaches provide a suite of mathematical strategie
 s for reducing the data required to discover and model nonlinear multiscal
 e systems.
LOCATION:Centre for Mathematical Sciences\, MR2
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