Adaptive MLS-HDMR metamodeling techniques for high dimensional problems

Metamodeling technique is to represent the approximation of input variables and output variables. With the exponential increase of dimension of assigned problems, accurate and robust model is difficult to achieve by popular regression methodologies. High-dimensional model representation (HDMR) is a general set of metamodel assessment and analysis tools to improve the efficiency of deducing high dimensional underlying system behavior. In this paper, a new HDMR, based on moving least square (MLS), termed as MLS-HDMR, is introduced. The MLS-HDMR naturally explores and exploits the linearity/nonlinearity and correlation relationships among variables of the underlying function, which is unknown or computationally expensive. Furthermore, to improve the efficiency of the MLS-HDMR, an intelligent sampling strategy, DIviding RECTangles (DIRECT) method is used to sample points. Multiple mathematical test functions are given to illustrate the modeling principles, procedures, and the efficiency and accuracy of the MLS-HDMR models with problems of a wide scope of dimensionalities.