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Identifying Nonlinear Dynamics with High Confidence from Sparse Data.
- Source :
- SIAM Journal on Applied Dynamical Systems; 2024, Vol. 23 Issue 1, p383-409, 27p
- Publication Year :
- 2024
-
Abstract
- We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More precisely, the sparse data is used to construct a statistical surrogate model based on a Gaussian process (GP). 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 confidence that these topological invariants, and hence the characterized dynamics, apply to the unknown dynamical system (assumed to be a sample path of the GP). The focus of this paper is on explaining the ideas, thus we restrict our examples to one-dimensional systems and show how to capture the existence of fixed points, periodic orbits, connecting orbits, bistability, and chaotic dynamics. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15360040
- Volume :
- 23
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Applied Dynamical Systems
- Publication Type :
- Academic Journal
- Accession number :
- 175180915
- Full Text :
- https://doi.org/10.1137/23M1560252