Turning Black-Box Into White Functions

Abstract

Modeling of high dimensional expensive black-box (HEB) functions is challenging. A recently developed method, radial basis function-based high dimensional model representation (RBF-HDMR), has been found promising. This work extends RBF-HDMR to enhance its modeling capability beyond the current second order form and “uncover” black-box functions so that not only a more accurate metamodel is obtained, but also key information of the function can be gained and thus the black-box function can be turned “white.” The key information that can be gained includes 1) functional form, 2) (non)linearity with respect to each variable, 3) variable correlations. The resultant model can be used for applications such as sensitivity analysis, visualization, and optimization. The RBF-HDMR exploration is based on identifying the existence of certain variable correlations through derived theorems. The adaptive process of exploration and modeling reveals the black-box functions till all significant variable correlations are found. The black-box functional form is then represented by a structure matrix that can manifest all orders of correlated behavior of variables. The proposed approach is tested with theoretical and practical examples. The test result demonstrates the effectiveness and efficiency of the proposed approach.