Definitions of distance function in radial basis function approach

TL;DR

This paper explores redefining the distance function in radial basis functions (RBFs) to incorporate problem-specific features, aiming to improve the construction of more efficient, problem-dependent RBFs for various applications.

Contribution

It introduces a new approach to redefine RBF distance functions based on problem features, enhancing the adaptability and effectiveness of RBFs.

Findings

Redefining distance functions improves RBF performance.

Incorporating problem features leads to more efficient RBFs.

The approach allows for problem-dependent and time-space distance functions.

Abstract

Very few studies involve how to construct the efficient RBFs by means of problem features. Recently the present author presented general solution RBF (GS-RBF) methodology to create operator-dependent RBFs successfully [1]. On the other hand, the normal radial basis function (RBF) is defined via Euclidean space distance function or the geodesic distance [2]. This purpose of this note is to redefine distance function in conjunction with problem features, which include problem-dependent and time-space distance function.