Adaptive SVR-HDMR Metamodeling Technique for High Dimensional Problems

Modeling or approximating high dimensional, computationally-expensive problems faces an exponentially increasing difficulty, the “curse of dimensionality”. This paper proposes a new form of high dimensional model representation (HDMR) by utilizing the support vector regression (SVR), termed as adaptive SVR-HMDR, to conquer this dilemma. The proposed model could reveal explicit correlations among different input variables of the underlying function which is unknown or expensive for computation. Taking advantage of HDMR's hierarchical structure, it could alleviate the exponential increasing difficulty, and gain satisfying accuracy with small set of samples by SVR. Numerical examples of different dimensionality are given to illustrate the principle, procedure and performance of SVR-HDMR.