Supervised learning from noisy observations

  • Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data -driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles forData-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data -driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems. (C) 2021 Elsevier B.V. All rights reserved.show moreshow less

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Metadaten
Author details:Georg A. GottwaldORCiDGND, Sebastian ReichORCiDGND
DOI:https://doi.org/10.1016/j.physd.2021.132911
ISSN:0167-2789
ISSN:1872-8022
Title of parent work (English):Physica : D, Nonlinear phenomena
Subtitle (English):Combining machine-learning techniques with data assimilation
Publisher:Elsevier
Place of publishing:Amsterdam
Publication type:Article
Language:English
Date of first publication:2021/09/01
Publication year:2021
Release date:2023/09/06
Tag:Data assimilation; Data-driven modelling; Random feature maps
Volume:423
Article number:132911
Number of pages:15
Funding institution:Deutsche Forschungsgemeinschaft (DFG, German Science Foundation)German Research Foundation (DFG) [SFB 1294/1 - 318763901]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
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