Abstract
Complex multiscale systems are ubiquitous in many areas. This research expository article discusses the development and applications of a recent information-theoretic framework as well as novel reduced-order nonlinear modeling strategies for understanding and predicting complex multiscale systems. The topics include the basic mathematical properties and qualitative features of complex multiscale systems, statistical prediction and uncertainty quantification, state estimation or data assimilation, and coping with the inevitable model errors in approximating such complex systems. Here, the information-theoretic framework is applied to rigorously quantify the model fidelity, model sensitivity and information barriers arising from different approximation strategies. It also succeeds in assessing the skill of filtering and predicting complex dynamical systems and overcomes the shortcomings in traditional path-wise measurements such as the failure in measuring extreme events. In addition, information theory is incorporated into a systematic data-driven nonlinear stochastic modeling framework that allows effective predictions of nonlinear intermittent time series. Finally, new efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems. The contents here include the general mathematical theories, effective numerical procedures, instructive qualitative models, and concrete models from climate, atmosphere and ocean science.
| Original language | English (US) |
|---|---|
| Article number | 644 |
| Journal | Entropy |
| Volume | 20 |
| Issue number | 9 |
| DOIs | |
| State | Published - Aug 28 2018 |
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Keywords
- Information barrier
- Information-theoretic framework
- Intermittent extreme events
- Model error
- Model sensitivity
- Multiscale slow-fast systems
- Physics-constrained nonlinear stochastic model
- Reduced-order models
- State estimation and prediction
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Model error, information barriers, state estimation and prediction in complex multiscale systems. / Majda, Andrew; Chen, Nan.
In: Entropy, Vol. 20, No. 9, 644, 28.08.2018.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Model error, information barriers, state estimation and prediction in complex multiscale systems
AU - Majda, Andrew
AU - Chen, Nan
PY - 2018/8/28
Y1 - 2018/8/28
N2 - Complex multiscale systems are ubiquitous in many areas. This research expository article discusses the development and applications of a recent information-theoretic framework as well as novel reduced-order nonlinear modeling strategies for understanding and predicting complex multiscale systems. The topics include the basic mathematical properties and qualitative features of complex multiscale systems, statistical prediction and uncertainty quantification, state estimation or data assimilation, and coping with the inevitable model errors in approximating such complex systems. Here, the information-theoretic framework is applied to rigorously quantify the model fidelity, model sensitivity and information barriers arising from different approximation strategies. It also succeeds in assessing the skill of filtering and predicting complex dynamical systems and overcomes the shortcomings in traditional path-wise measurements such as the failure in measuring extreme events. In addition, information theory is incorporated into a systematic data-driven nonlinear stochastic modeling framework that allows effective predictions of nonlinear intermittent time series. Finally, new efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems. The contents here include the general mathematical theories, effective numerical procedures, instructive qualitative models, and concrete models from climate, atmosphere and ocean science.
AB - Complex multiscale systems are ubiquitous in many areas. This research expository article discusses the development and applications of a recent information-theoretic framework as well as novel reduced-order nonlinear modeling strategies for understanding and predicting complex multiscale systems. The topics include the basic mathematical properties and qualitative features of complex multiscale systems, statistical prediction and uncertainty quantification, state estimation or data assimilation, and coping with the inevitable model errors in approximating such complex systems. Here, the information-theoretic framework is applied to rigorously quantify the model fidelity, model sensitivity and information barriers arising from different approximation strategies. It also succeeds in assessing the skill of filtering and predicting complex dynamical systems and overcomes the shortcomings in traditional path-wise measurements such as the failure in measuring extreme events. In addition, information theory is incorporated into a systematic data-driven nonlinear stochastic modeling framework that allows effective predictions of nonlinear intermittent time series. Finally, new efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems. The contents here include the general mathematical theories, effective numerical procedures, instructive qualitative models, and concrete models from climate, atmosphere and ocean science.
KW - Information barrier
KW - Information-theoretic framework
KW - Intermittent extreme events
KW - Model error
KW - Model sensitivity
KW - Multiscale slow-fast systems
KW - Physics-constrained nonlinear stochastic model
KW - Reduced-order models
KW - State estimation and prediction
UR - http://www.scopus.com/inward/record.url?scp=85053665307&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85053665307&partnerID=8YFLogxK
U2 - 10.3390/e20090644
DO - 10.3390/e20090644
M3 - Article
VL - 20
JO - Entropy
JF - Entropy
SN - 1099-4300
IS - 9
M1 - 644
ER -