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Model Error, Information Barriers, State Estimation and Prediction in Complex Multiscale Systems.

Andrew J Majda1,2, Nan Chen1

  • 1Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study introduces an information-theoretic framework and nonlinear modeling for complex multiscale systems. It improves predictions and quantifies uncertainty, especially for extreme events in climate and ocean science.

Keywords:
information barrierinformation-theoretic frameworkintermittent extreme eventsmodel errormodel sensitivitymultiscale slow-fast systemsphysics-constrained nonlinear stochastic modelreduced-order modelsstate estimation and prediction

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Area of Science:

  • Complex systems science
  • Information theory
  • Nonlinear dynamics
  • Climate science
  • Atmosphere and ocean science

Background:

  • Complex multiscale systems are prevalent across scientific disciplines.
  • Understanding and predicting these systems presents significant challenges due to their intricate nature.
  • Existing methods often struggle with uncertainty quantification and capturing extreme events.

Purpose of the Study:

  • To develop and apply an information-theoretic framework for analyzing complex multiscale systems.
  • To introduce novel reduced-order nonlinear modeling strategies for enhanced prediction capabilities.
  • To address limitations in current approaches for state estimation, data assimilation, and model error quantification.

Main Methods:

  • Application of an information-theoretic framework to quantify model fidelity, sensitivity, and information barriers.
  • Integration of information theory into data-driven nonlinear stochastic modeling.
  • Development of efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration.

Main Results:

  • The information-theoretic framework successfully assesses prediction skills and overcomes shortcomings of traditional path-wise measurements, particularly for extreme events.
  • A systematic data-driven nonlinear stochastic modeling framework enables effective predictions of nonlinear intermittent time series.
  • New modeling strategies provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems.

Conclusions:

  • The developed framework and modeling strategies offer a rigorous approach to understanding and predicting complex multiscale systems.
  • This research enhances the ability to handle model errors, quantify uncertainty, and predict extreme events.
  • The findings have direct applications in climate, atmosphere, and ocean science, improving forecasting and analysis.