| Abstract [eng] |
Data science uses methods, processes, algorithms to extract knowledge and insights from structured and unstructured data. It involves various fields of mathematics, statistics, and computer science. Data science seeks an actionable and logically based model for prediction, extrapolation or interpolation uses. That makes data science different from traditional analytics and close to data mining. Therefore, data science allows generating effective analytical methods in areas such as medicine and social sciences that do not have specific data models in those areas. A surrogate model is an engineering method used when an outcome of interest cannot be easily directly measured. Thus, a model of the outcome is used instead. Quite frequently, computer simulation of real systems can take many minutes, hours or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and what-if analysis become impossible since they require thousands or even millions of simulation evaluations. One way to solve this problem is constructing approximation models, known as surrogate models, response surface models, metamodels or emulators that simulate a modelling object in a simplified way, creating and applying. However, deterministic data analysis by traditional methods of interpolation or extrapolation requires various additional assumptions and does not take into account the uncertainty associated with data reconstruction (Shepard, 1968; Shumaker, 1976). Therefore, it is relevant to study the application of Gaussian random field (GRF) models to the analysis of experimental data. The properties of GRF depend on the covariances describing the dependencies between the points where computer or physical experiments were performed. The statistical models of GRF, when covariances are described by Euclidean distances between objects in fractional degrees have not yet been well studied, therefore their investigation and application to the analysis of experimental data for solving extrapolation, optimization or experiment design problems is a relevant problem. |
