Comparative Analysis of Surrogate Modeling Methods in the Presence of Multi-Precision Samples

Abstract

In the process of technological development and increasing computing power, the quality of mathematical and simulation models has increased, and it has become possible to implement complex multiparametric systems. However, despite the high accuracy of the results obtained, the amount of time required for calculations is important. For example, when solving optimization problems, it is necessary to perform many calculations of function values, and in the case when calculating one value may take several hours, it is not possible to search for the optimal set of parameters (in an acceptable time less than weeks and months). In such situations, they resort to using approximation (surrogate) models, which speed up the process of obtaining the value of the function.
The purpose of this article is to provide an overview of existing methods for constructing approximation models for one and two multi-point samples, and also a new method for approximation for multi-point samples using gradient refinement or its estimation for MF models of the kriging family is proposed. A theorem on the form of an approximating function is formulated and proved in the presence of multi-precision samples and knowledge about the gradient based on the kriging model, and application to test functions is demonstrated. To build an approximation for a single sample, the models PRS (Polynomial Response Surface), IDW (Inverse Distance Weighing), RBF (Radial Basis Function), Kriging are considered. For the case of two different-precision samples, MMS (Multi-Fidelity Multiplicative Surrogate), MFA (Multi-Fidelity Additive Surrogate), MFHS (Multi-Fidelity Hybrid Surrogate), Co-kriging models, MFG (Multi-Fidelity Gradient) model.