Reconstruction of normal forms by learning informed observation geometries from data

Or Yair, Ronen Talmon, Ronald R. Coifman, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an “intrinsic” prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant “normal forms”: a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.

Original languageEnglish (US)
Pages (from-to)E7865-E7874
JournalProceedings of the National Academy of Sciences of the United States of America
Volume114
Issue number38
DOIs
StatePublished - Sep 19 2017

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Data analysis
  • Dynamical systems
  • Empirical models
  • Geometry
  • Graph theory

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