Regularization of Kriging interpolation on irregularly spaced data

TL;DR

This paper presents a regularization method for Kriging interpolation on irregularly spaced data by controlling the kernel function through the condition number of the self-correlation matrix, enhancing reliability in sparse data scenarios.

Contribution

The paper introduces a novel regularization approach for Kriging interpolation that manages the kernel function via the condition number, improving performance on irregularly spaced data.

Findings

Enhanced interpolation reliability in sparse data regions

Effective control of kernel function via condition number

Improved robustness against noise and data sparsity

Abstract

Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the insurgence of spurious noise. Noise sources can be prevented using proper countermeasures when the training set is designed, but the data sparsity is inevitable in some cases. A typical example is represented by the application of an optimization algorithm: the area where the minimum or maximum of the objective function is assumed to be present is where new data is abundantly added, but other areas of design variable space are significantly neglected. In these cases, a regularization of the interpolation model becomes absolutely crucial. In this paper we are presenting an approach for the regularization of an interpolator based on the control of its kernel function via the condition number of the self-correlation matrix.