题目: Identifying Nonlinear Dynamics with High Confidence from Sparse Time Series Data

摘要:

I will introduce a novel 5 step procedure that given time series data generated by a stationary deterministic nonlinear dynamical system provides a lower bound on the probability that the system generates specific local and/or global dynamic behavior.
More precisely,  the time series data is used to define a Gaussian process (GP).
The mean of this GP provides a surrogate model.
The dynamics of the surrogate model is interrogated using combinatorial methods and characterized using algebraic topological invariants (Conley index).
The GP predictive distribution provides a lower bound on the probability that these topological invariants (and hence the characterized dynamics) apply to the unknown dynamical system (a random path of the GP).  
The focus of this talk is on explaining the ideas, thus I restrict our examples to one-dimensional systems and show how to capture the existence of fixed points, periodic orbits, connecting orbits, chaotic dynamics, and bistability.
This is based on joint work with B. Batko, M. Gameiro, Y. Hung, W. Kalies, E. Vieira, and C. Thieme