When studying observations of chem. reaction dynamics, closed form equations based on a putative mechanism may not be available. Yet when sufficient data from exptl. observations can be obtained, even without knowing what exactly the phys. 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 phys. understanding, by building intrinsic "information geometries" of the observed data, and thus enabling prediction without phys./chem. 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" phys. quantities. We discuss current limitations and possible extensions of the procedure.