Analog forecasting with dynamics-adapted kernels

Zhizhen Zhao, Dimitrios Giannakis

Research output: Contribution to journalArticle

Abstract

Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record of observations which most closely resembles the current initial data. Here, we introduce a suite of forecasting methods which improve traditional analog forecasting by combining ideas from kernel methods developed in harmonic analysis and machine learning and state-space reconstruction for dynamical systems. A key ingredient of our approach is to replace single-analog forecasting with weighted ensembles of analogs constructed using local similarity kernels. The kernels used here employ a number of dynamics-dependent features designed to improve forecast skill, including Takens' delay-coordinate maps (to recover information in the initial data lost through partial observations) and a directional dependence on the dynamical vector field generating the data. Mathematically, our approach is closely related to kernel methods for out-of-sample extension of functions, and we discuss alternative strategies based on the Nyström method and the multiscale Laplacian pyramids technique. We illustrate these techniques in applications to forecasting in a low-order deterministic model for atmospheric dynamics with chaotic metastability, and interannual-scale forecasting in the North Pacific sector of a comprehensive climate model. We find that forecasts based on kernel-weighted ensembles have significantly higher skill than the conventional approach following a single analog.

Original languageEnglish (US)
Pages (from-to)2888-2939
Number of pages52
JournalNonlinearity
Volume29
Issue number9
DOIs
StatePublished - Aug 12 2016

Fingerprint

forecasting
Forecasting
analogs
kernel
Analogue
Kernel Methods
Forecast
Dynamical systems
Ensemble
Dynamical system
dynamical systems
Partial Observation
Climate models
Metastability
Climate Models
Harmonic analysis
Harmonic Analysis
Pyramid
Deterministic Model
harmonic analysis

Keywords

  • analog forecasting
  • delay-coordinate maps
  • kernel methods
  • out-of-sample extension

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Analog forecasting with dynamics-adapted kernels. / Zhao, Zhizhen; Giannakis, Dimitrios.

In: Nonlinearity, Vol. 29, No. 9, 12.08.2016, p. 2888-2939.

Research output: Contribution to journalArticle

Zhao, Zhizhen ; Giannakis, Dimitrios. / Analog forecasting with dynamics-adapted kernels. In: Nonlinearity. 2016 ; Vol. 29, No. 9. pp. 2888-2939.
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