Research on high-dimensional model representation with various metamodels

Constructing approximation models with surrogate modelling is often carried out in engineering design to save computational cost. However, the problem of the ‘curse of dimensionality’ still exists, and high-dimensional model representation (HDMR) has been proven to be very efficient in solving high-dimensional, computationally expensive black-box problems. This article proposes a new HDMR by combining separate stand-alone metamodels to form an ensemble based on cut-HDMR. It can improve prediction accuracy and alleviate prediction uncertainty for different problems compared with previous HDMRs. In this article, 10 representative mathematical examples and two engineering examples are used to illustrate the proposed technique and previous HDMRs. Furthermore, a comprehensive comparison of four metrics between the ensemble HDMR and other single HDMRs is presented, with a wide scope of dimensionalities. The results show that the single HDMRs perform well on specified examples but the ensemble HDMR provides more accurate predictions for all the test problems.