Data-driven non-Markovian Reduced-Order Modeling
Abstract
This presentation will provide an overview of Multilayered Stochastic Modeling (MSM) [Kondrashov, Chekroun and Ghil, 2015] and its applications in hierarchy of models for oceanic and atmospheric turbulent flows. MSM is a data-driven reduced-order framework that aims to obtain a low-order nonlinear system of prognostic equations driven by stochastic forcing, and estimates both the dynamical operator and the properties of the driving noise from multivariate time series of observations or a high-end model's simulation. MSM leads to a system of stochastic differential equations (SDEs) involving hidden (auxiliary) variables of fast-small scales ranked by layers, which interact with the macroscopic (observed) variables of large-slow scales to model the dynamics of the latter. MSM dynamics of observed variables is governed by three types of interactions: (a) nonlinear deterministic Markovian part; (b) non-Markovian part conveying memory effects of interactions with hidden variables; and (c) spatio-temporal noise. New MSM applications focus on development of computationally efficient reduced-order models by using data-adaptive decomposition methods that convey memory effects by time-embedding techniques, such as Multichannel Singular Spectrum Analysis (M-SSA) [Ghil et al. 2002]. Recently developed Data-Adaptive Harmonic (DAH) decomposition method [Chekroun and Kondrashov, 2016] is another multivariate technique that adopts time-embedding information, but that is distinctly different from M-SSA by its frequency-based, rather than variance-based content, to decompose time-evolving signals. DAH decomposition allows in a data-adaptive way, for the extraction of mode pairs that come in exact phase quadrature, and are narrow-band time series in the frequency domain that can be very efficiently modeled as a system of coupled oscillators. New results by DAH modeling for geophysical flows will be presented.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMNG11A..02K
- Keywords:
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- 3315 Data assimilation;
- ATMOSPHERIC PROCESSES