### Abstract

The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change projections. Although information transfer between dynamical system components is an established concept for nonlinear multivariate time series, the specific nature of the nonlinear dynamics generating the observed flow of information is ignored in such statistical analysis. Here, a general mathematical theory for information flow between subspaces in ensemble predictions of a dynamical system is developed, which accounts for the specific underlying dynamics. The results below also include potentially useful approximation strategies for practical implementation in dynamical systems with many degrees of freedom. Specific elementary examples are developed here with both stable and unstable dynamics to both illustrate facets of the theory and to test Monte Carlo solution strategies.

Original language | English (US) |
---|---|

Pages (from-to) | 9558-9563 |

Number of pages | 6 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 104 |

Issue number | 23 |

DOIs | |

State | Published - Jun 5 2007 |

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### Keywords

- Ensemble predictions
- Information transfer

### ASJC Scopus subject areas

- Genetics
- General

### Cite this

**Information flow between subspaces of complex dynamical systems.** / Majda, Andrew J.; Harlim, John.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 104, no. 23, pp. 9558-9563. https://doi.org/10.1073/pnas.0703499104

}

TY - JOUR

T1 - Information flow between subspaces of complex dynamical systems

AU - Majda, Andrew J.

AU - Harlim, John

PY - 2007/6/5

Y1 - 2007/6/5

N2 - The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change projections. Although information transfer between dynamical system components is an established concept for nonlinear multivariate time series, the specific nature of the nonlinear dynamics generating the observed flow of information is ignored in such statistical analysis. Here, a general mathematical theory for information flow between subspaces in ensemble predictions of a dynamical system is developed, which accounts for the specific underlying dynamics. The results below also include potentially useful approximation strategies for practical implementation in dynamical systems with many degrees of freedom. Specific elementary examples are developed here with both stable and unstable dynamics to both illustrate facets of the theory and to test Monte Carlo solution strategies.

AB - The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change projections. Although information transfer between dynamical system components is an established concept for nonlinear multivariate time series, the specific nature of the nonlinear dynamics generating the observed flow of information is ignored in such statistical analysis. Here, a general mathematical theory for information flow between subspaces in ensemble predictions of a dynamical system is developed, which accounts for the specific underlying dynamics. The results below also include potentially useful approximation strategies for practical implementation in dynamical systems with many degrees of freedom. Specific elementary examples are developed here with both stable and unstable dynamics to both illustrate facets of the theory and to test Monte Carlo solution strategies.

KW - Ensemble predictions

KW - Information transfer

UR - http://www.scopus.com/inward/record.url?scp=34547466031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547466031&partnerID=8YFLogxK

U2 - 10.1073/pnas.0703499104

DO - 10.1073/pnas.0703499104

M3 - Article

VL - 104

SP - 9558

EP - 9563

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 23

ER -