关键词: 近似模型, 最小二乘支持向量机（LS-SVM）, 切割高维模型表示（Cut-HDMR）, 自适应采样

Abstract: In order to construct approximation model for high dimensional problems, Least Squares Support Vector Machine（LS-SVM） is introduced into High Dimensional Model Representation（HDMR）, and a modified approximation model construction method called SVM-HDMR for high dimensional nonlinear problems and corresponding adaptive sampling and model construction algorithm are proposed. This method transforms high dimensional problem into a series of low dimensional problems using Cut-HDMR, and then these low dimensional problems are solved using LS-SVM. The results of numerical examples show that the new method has good approximation quality and reduces computational expense dramatically, so it is more suitable for high dimensional problems.

Key words: approximation model, Least Squares Support Vector Machine（LS-SVM）, Cut-High Dimensional Model Representation（HDMR）, adaptive sampling