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 correct. Furthermore, numerical experiments indicate that it is possible to identify nontrivial dynamics with high confidence with surprisingly small data sets.