Nonparametric forecasting of low-dimensional dynamical systems

Tyrus Berry, Dimitrios Giannakis, John Harlim

Research output: Contribution to journalArticle

Abstract

This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Niño-3.4 data set which is used as a proxy of the El Niño Southern Oscillation.

Original languageEnglish (US)
Article number032915
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number3
DOIs
StatePublished - Mar 19 2015

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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