Sparse identification of posynomial models

Abstract

Posynomials are nonnegative combinations of monomials with possibly fractional and both positive and negative exponents. Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP). However, while quite a vast literature exists on GP-based design, very few contributions can yet be found on the problem of identifying posynomial models from experimental data. Posynomial identification amounts to determining not only the coefficients of the combination, but also the exponents in the monomials, which renders the identification problem numerically hard. In this draft, we propose an approach to the identification of multivariate posynomial models, based on the expansion on a given large-scale basis of monomials. The model is then identified by seeking coefficients of the combination that minimize a mixed objective, composed by a term representing the fitting error and a term inducing sparsity in the representation, which results in a problem formulation of the "squareroot LASSO" type, with nonnegativity constraints on the variables. We propose to solve the problem via a sequential coordinate-descent scheme, which is suitable for large-scale implementations.

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

“…Recent work based on compressed sensing has been used to handle noise and outliers [ 35 ] for linear system identification and large libraries of candidate functions [ 36 ]. Sparse regularization, which has been demonstrated for parameter and structure identification [ 2 , 34 , 37 , 38 ], is a particularly promising direction as this can promote robustness and generalizability in models. We refer the reader to an extensive review on nonlinear system identification methods [ 39 ] and a recent review in the context of machine learning [ 40 ].…”

A time-varying SIRD model for the COVID-19 contagion in Italy

“…The idea is then to let the identification algorithm single out which of the many basis functions is useful for the identification purposes, by seeking a solution with a sparse coefficient vector. A similar approach has been employed for instance in Calafiore, Ghaoui, and Novara (2015) in the context of posynomial identification problems. The described goal can be achieved by considering a modified cost function of the Lasso type: where is a tradeoff parameter that weights the accuracy of the solution and its sparsity level.…”

Seyrek Tanılama Yöntemi ile Doğrusal Olmayan Dinamik Sistemlerin Model İncelenmesi

“…To calculate the subset of candidate terms of the system, sparse regression method like "least absolute shrinkage and selection operator (LASSO)", ElasticNet, "least-square method (LSM)" and "sequential thresholded least-squares (STLSQ)" can be used. Unlike other methods, LASSO and STLSQ have noise elimination and improved robustness performance , (Brunton et al, 2017), (Rudy et al, 2017), (Kukreja et al, 2006), (Calafiore et al, 2015).…”

“…LASSO, which is a widely used regression method for data-driven modelling, learns the linear relationship between a dependent variable and explanatory variables (Misra et al, 2020), (J. . Besides, LASSO is used extensively for the model or feature selection and system identification in statistics, machine learning, and control theory , (Kukreja et al, 2006), (Calafiore et al, 2015), (J. . LASSO implements an 1 regularization term that can produce sparse coefficients.…”