Year: 2024
Type: article
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.
DOI: 10.1137/23m1560252
Authors: Bogdan Batko, Marcio Gameiro, Ying Hung, William Kalies, Konstantin Mischaikow, Ewerton Vieira
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Simons Foundation, Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Narodowe Centrum Nauki, National Institutes of Health, Defense Advanced Research Projects Agency, National Institute of General Medical Sciences, Division of Mathematical Sciences, Division of Computing and Communication Foundations, Air Force Office of Scientific Research, Army Research Office
Awards: G173048481, Applications of Computational and Topological Methods to Dynamical Systems, G2405702604, G2515541506, G2593738098, G295657101, G3064008058, G3749599873, Tripods+X:Res: Collaborative Research: Identification of Gene Regulatory Network Function from Data, G5270150132, G593423661, Collaborative Research: Efficient Bayesian Global Optimization with Applications to Deep Learning and Computer Experiments, G6517621824, HDR TRIPODS: Data Science Principles of the Human-Machine Convergence, Needle in a haystack: effective search for dynamics across the space of networks, G8596430976
OpenAlex ID: W4391170336