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Mathematical Physics Seminar

Konstantin Mischaikow - Identifying Nonlinear Dynamics from Sparse Data

Location:  Hill 705
Date & time: Thursday, 09 November 2023 at 12:00PM - 1:00PM

Konstantin Mischaikow – Rutgers University

Date/Time/Location
Thursday,
November 9th, 12:00pm; Hill Center 705

  Identifying Nonlinear Dynamics from Sparse Data

There are a variety of statistical techniques that given sufficient 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 dynamics 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 it 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 of the dynamics is co

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