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UID:1187170725f986e93aa5a330cea1942e
CATEGORIES:Mathematical Physics Seminar
CREATED:20231101T102134
SUMMARY:Konstantin Mischaikow - Identifying Nonlinear Dynamics from Sparse Data
LOCATION:Hill 705
DESCRIPTION:Konstantin Mischaikow – Rutgers University\nDate/Time/Location\n Thursday, 
 November 9th, 12:00pm; Hill Center 705\n  Identifying Nonlinear Dynamics fr
 om Sparse Data\nThere are a variety of statistical techniques that given su
 fficient time series  identify explicit models, e.g. differential equations
  or maps, that are then evaluated to predict dynamics. However, it is well 
 established that bifurcations can take place on all scales and hence dynami
 cs is sensitive  to the choice of model and hence to small errors in data. 
 This suggests a potential inherent instability in going directly from data 
 to models. We propose a novel method, combining Conley theory and Gaussian 
 Process surrogate modeling with uncertainty quantification, through which i
 t is possible to characterize local and global dynamics, e.g., existence of
  fixed points, periodic orbits, connecting orbits, bistability, and chaotic
  dynamics, with lower bounds on the confidence that this characterization o
 f the dynamics is co\n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin-bottom: 6px; text-align: center; background: #f7f7f7;"><st
 rong>Konstantin Mischaikow&nbsp;– Rutgers University</strong></p><p style="
 margin-bottom: 6px; text-align: center; background: #f7f7f7;"><strong>Date/
 Time/Location<br> Thursday, </strong><strong>November 9th</strong><strong>,
  12:00pm; Hill Center 705</strong></p><p style="text-align: center; backgro
 und: #f7f7f7;">&nbsp;<strong>&nbsp;</strong><strong>Identifying Nonlinear D
 ynamics from Sparse Data</strong></p><p><strong>There are a variety of stat
 istical techniques that given sufficient time series&nbsp; identify explici
 t models, e.g. differential equations or maps, that are then evaluated to p
 redict dynamics. However, it is well established that bifurcations can take
  place on all scales and hence dynamics is sensitive&nbsp; to the choice of
  model and hence to small errors in data. This suggests a potential inheren
 t instability in going directly from data to models. We propose a novel met
 hod, combining Conley theory and Gaussian Process surrogate modeling with u
 ncertainty quantification, through which it is possible to characterize loc
 al and global dynamics, e.g., existence of fixed points, periodic orbits, c
 onnecting orbits, bistability, and chaotic dynamics, with lower bounds on t
 he confidence that this characterization of the dynamics is co</strong></p>
DTSTAMP:20260830T125609
DTSTART;TZID=America/New_York:20231109T120000
DTEND;TZID=America/New_York:20231109T130000
SEQUENCE:0
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