Sparse Identification of Posynomial Models

TL;DR

This paper introduces a method for identifying multivariate posynomial models from data by formulating a sparse optimization problem that combines fitting accuracy with model simplicity, suitable for large-scale problems.

Contribution

It proposes a novel approach to posynomial model identification using a sparse optimization framework based on square-root LASSO with a sequential coordinate-descent algorithm.

Findings

Effective identification of posynomial models from experimental data.

Sparsity-inducing formulation improves model interpretability.

Suitable for large-scale applications.

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 ``square-root 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.