%ASroczynski, David [Department of Chemical and Biological Engineering Princeton University Princeton NJ 08540]%AYair, Or [Department of Electrical Engineering Technion – Israel Institute of Technology Haifa 32000 Israel]%ATalmon, Ronen [Department of Electrical Engineering Technion – Israel Institute of Technology Haifa 32000 Israel]%AKevrekidis, Ioannis [Department of Chemical and Biomolecular Engineering, Applied Mathematics and Statistics, and Urology (JHMS) Johns Hopkins University Baltimore MD 21218]%BJournal Name: Israel Journal of Chemistry; Journal Volume: 58; Journal Issue: 6-7; Related Information: CHORUS Timestamp: 2023-09-11 12:09:12 %D2018%IWiley Blackwell (John Wiley & Sons) %JJournal Name: Israel Journal of Chemistry; Journal Volume: 58; Journal Issue: 6-7; Related Information: CHORUS Timestamp: 2023-09-11 12:09:12 %K %MOSTI ID: 10056125 %PMedium: X %TData‐driven Evolution Equation Reconstruction for Parameter‐Dependent Nonlinear Dynamical Systems %XAbstract

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 equationsfor 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.

%0Journal Article