Open AccessUsing waveform information in nonlinear data assimilation
Author(s) -
Daniel Rey,
Michael Eldridge,
Uriel Morone,
Henry D. I. Abarbanel,
Ulrich Parlitz,
Jan Schumann-Bischoff
Publication year - 2014
Publication title -
physical review. e, statistical, nonlinear and soft matter physics
Language(s) - English
Resource type - Journals
eISSN - 1550-2376
pISSN - 1539-3755
DOI - 10.1103/physreve.90.062916
Subject(s) - nonlinear system , waveform , data assimilation , chaotic , computer science , dynamical systems theory , stability (learning theory) , control theory (sociology) , colpitts oscillator , nonlinear dynamical systems , instability , statistical physics , physics , artificial intelligence , machine learning , telecommunications , radar , control (management) , local oscillator , quantum mechanics , radio frequency , meteorology , mechanics , vackář oscillator
Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators