Kernel method for corrections to scaling

TL;DR

This paper introduces a kernel method based on Gaussian process regression to accurately infer scaling exponents and functions in critical phenomena, even with corrections to scaling, improving upon traditional methods.

Contribution

A novel kernel method that effectively handles corrections to scaling in scaling analysis, enabling more reliable inference of critical properties from data.

Findings

Inference results converge with increasing data precision.

The method works effectively with corrections to scaling.

Applicable to real data in critical phenomena.

Abstract

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.