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I. V. Gosea

Publications and source records attributed to I. V. Gosea.

5 recordsLinked to original sources
arXiv2026

Variable decoupling and the Kolmogorov Superposition Theorem for rational functions

This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for decoupling the variables of multivariate rational functions. The key tool for this development is the Loewner Framework for multivariate functions. Applications of this result involve approximating multivariate non-rational functions by low-complexity multivariate rational and polynomial functions.

math.NA↗
arXiv2024

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

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

math.DS↗
arXiv2022

Approximating a flexible beam model in the Loewner framework

The paper develops the Loewner approach for data-based modeling of a linear distributed-parameter system. This approach is applied to a controlled flexible beam model coupled with a spring-mass system. The original dynamical system is described by the Euler-Bernoulli partial differential equation with the interface conditions due to the oscillations of the lumped part. The transfer function of this model is computed analytically, and its sampled values are then used for the data-driven design of a reduced model. A family of approximate realizations of the corresponding input-output map is constructed within the Loewner framework. It is shown that the proposed finite-dimensional approximations are able to capture the key properties of the original dynamics over a given range of observed frequencies. The robustness of the method to noisy data is also investigated.

math.OC↗
arXiv2020

On Bilinear Time Domain Identification and Reduction in the Loewner Framework

The Loewner framework-(LF) in combination with Volterra series-(VS) offers a non-intrusive approximation method that is capable of identifying bilinear models from time-domain measurements. This method uses harmonic inputs which establish a natural way for data acquisition. For the general class of nonlinear problems with VS representation, the growing exponential approach allows the derivation of the generalized kernels, namely symmetric generalized frequency response functions - (GFRFs). In addition, the homogeneity of the Volterra operator determines the accuracy in terms of how many kernels are considered. For the weakly nonlinear setup, only a few kernels are needed to obtain a good approximation. In this direction, the proposed adaptive scheme is able to improve the estimations of the computationally non-zero kernels. The Fourier transform associates these measurements with the derived GFRFs and the LF makes the connection with system theory. In the linear case, the LF associates the so-called S-parameters with the linear transfer function by interpolating in the frequency domain. The goal of the proposed method is to extend identification to the case of bilinear systems from time-domain measurements and to approximate other general nonlinear systems (by means of the Carleman bilinearizarion scheme). By identifying the linear contribution with the LF, a considerable reduction is achieved by means of the SVD. The fitted linear system has the same McMillan degree as the original linear system. Then, the performance of the linear model is improved by augmenting a special nonlinear structure. In a nutshell, we learn reduced-dimension bilinear models directly from a potentially large-scale system that is simulated in the time domain. This is done by fitting first a linear model, and afterwards, by fitting the corresponding bilinear operator.

math.DS↗