Symbolic Regression for Derivation of an Accurate Analytical Formulation Using Big Data: An Application Example

Abstract

With emerging of the Big Data era, sample datasets are becoming increasingly large. One of the recently proposed algorithms for Big Data applications is Symbolic Regression (SR). SR is a type of regression analysis that performs a search within mathematical expression domain to generate an analytical expression that fits large size dataset. SR is capable of finding intrinsic relationships within the dataset to obtain an accurate model. Herein, for the first time in literature, SR is applied to derivate a full-wave simulation based analytical expression for the characteristic impedance Z(0) of microstrip lines using Big Data obtained from an 3D-EM simulator, in terms of only its real parameters which are substrate dielectric constant a, height h and strip width w within 1-10 GHz band. The obtained expression is compared with the targeted simulation data together with the other analytical counterpart expressions of Z(0) for different types of error function. It can be concluded that SR is a suitable algorithm for obtaining accurate analytical expressions where the size of the available data is large and the interrelations within the data are highly complex, to be used in Electromagnetic analysis and designs.