Dynamically learning the parameters of a chaotic system using partial observations

2021/08/18 by Elizabeth Carlson, Joshua Hudson, Carlson, Elizabeth +9 · 5 citations
Computer Science · Physics and Astronomy · #34A55 #34D06 #34H10 #35B30 #37C50 #60H10 #Chaos control and synchronization #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2108.08354

openalex publication_date 2021/08/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this algorithm to the correct parameters when the system in question is the classic three-dimensional Lorenz system. Computationally, we demonstrate the efficacy of this algorithm on the Lorenz system by recovering any proper subset of the three non-dimensional parameters of the system, so long as a corresponding subset of the state is observable. We also provide computational evidence that this algorithm works well beyond the hypotheses required in the rigorous analysis, including in the presence of noisy observations, stochastic forcing, and the case where the observations are discrete and sparse in time.

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