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In this study, we present a purely data-driven method that uses the Loewnerframework (LF) along with nonlinear optimization techniques to infer quadraticwith affine control dynamical systems that admit Volterra series (VS)representations from input-output (i/o) time-domain measurements. The proposedmethod extensively employs optimization tools for interpolating the symmetricgeneralized frequency response functions (GFRFs) derived in the VS framework.The GFRF estimations are obtained from the Fourier spectrum (phase andamplitude) of the quasi-steady state system response under harmonic excitation.Appropriate treatment of these measurements under the developed frameworkallows the identification of low-order quadratic state-space models withnon-trivial stable equilibria, such as in the Lorenz '63 forced system. We thuscan achieve low-order global model identification for systems that canbifurcate to multiple equilibria after solely collecting measurements from alocal stable operational regime. The developed framework is tested for severalexamples of increasing dimension and complexity, up to a test case of theviscous Burgers' equation with Robin boundary conditions. In the latter case,this study enforces new directions of employing data-driven reduced modelinference that successfully can provide low-order accurate surrogate predictivemodels suitable for control. Future directions and open challenges concludethis work.

Data-driven quadratic modeling in the Loewner framework from input-output time-domain measurements