Konstantin Mischaikow (Rutgers) will be presenting to the group.
Title: Identifying Nonlinear Dynamics with High Confidence from Sparse Data
Abstract: 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, chaotic dynamics and bifurcation theory implies sensitivity with respect to small errors in data and parameters, respectively.
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.