Moving Least Squares Metamodels—Hyperparameter, Variable Reduction and Model Selection

The objective of metamodel applications is to obtain a large amount of system information from a small data set. Areas of application within the Computer-aided engineering are e.g. optimization problems, robust design engineering or sensitivity analysis. This paper deals with the metamodel techniques Least Squares (LS) regression and Moving Least Squares (MLS) as well as with their application in case of multivariate and nonlinear system behavior. In this context, LS regression represents a widely used method, which is limited in application due to the fixed polynomial order and the resulting relationship between existing support points and necessary polynomial coefficients. A more flexible metamodel technique regarding the description of nonlinearities is the MLS approach. In this procedure, the support points are weighted to build a local polynomial. The multivariate MLS-application is implemented by an anisotropic distance measure and a variable reduction. The selection of the most appropriate metamodel is tested for a deterministic model framework of mathematical test functions regarding the polynomial order, variable reduction and metamodel technique.