Regularization to orthogonal-polynomials fitting with application to magnetization data

TL;DR

This paper introduces a regularization method with cross validation for two-variable orthogonal-polynomials fitting, effectively addressing overfitting and improving magnetization data modeling accuracy.

Contribution

It proposes a novel regularization and cross validation scheme for orthogonal-polynomials fitting, with practical application to magnetization data analysis.

Findings

Achieved satisfactory fitting precision on magnetization data

Quantitatively assessed overfitting degree in the fitting process

Provided a reliable basis for future magnetic material studies

Abstract

An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and corresponding cross validation scheme is proposed for two-variable polynomials fitting. While the Fortran implementation of above scheme is applied to magnetization data, a satisfactory fitting precision is reached, and overfitting problem can be quantitatively assessed, which therefore offers the quite reliable base for future comprehensive investigations of magnetocaloric and phase-transition properties of magnetic functional materials.