Premium
Data‐driven Evolution Equation Reconstruction for Parameter‐Dependent Nonlinear Dynamical Systems
Author(s) -
Sroczynski David W.,
Yair Or,
Talmon Ronen,
Kevrekidis Ioannis G.
Publication year - 2018
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.201700147
Subject(s) - observable , singularity , invertible matrix , nonlinear system , transformation (genetics) , physical law , cusp (singularity) , statistical physics , realization (probability) , physical system , dynamical systems theory , chemistry , mathematics , mathematical analysis , physics , quantum mechanics , geometry , statistics , biochemistry , gene
When studying observations of chemical reaction dynamics, closed form equations based on a putative mechanism may not be available. Yet when sufficient data from experimental observations can be obtained, even without knowing what exactly the physical meaning of the parameter settings or recorded variables are, data‐driven methods can be used to construct minimal (and in a sense, robust) realizations of the system. The approach attempts, in a sense, to circumvent physical understanding, by building intrinsic “information geometries” of the observed data, and thus enabling prediction without physical/chemical knowledge. Here we use such an approach to obtain evolution equations for a data‐driven realization of the original system – in effect, allowing prediction based on the informed interrogation of the agnostically organized observation database. We illustrate the approach on observations of (a) the normal form for the cusp singularity, (b) a cusp singularity for the nonisothermal CSTR, and (c) a random invertible transformation of the nonisothermal CSTR, showing that one can predict even when the observables are not “simply explainable” physical quantities. We discuss current limitations and possible extensions of the procedure.