Low-Dimensional Input and High-Dimensional Output Modelling Using Gaussian Process

In this paper, a unified low-dimensional input and high-dimensional output modelling method is proposed to deal with complex molecular simulation and design problems. First, a convex optimization framework is constructed to decompose vertically stacked molecular weight distribution (MWD) matrix into low-rank and sparse parts, while the intrinsic structure can be explored, and abnormal points can be eliminated. Then, considering the correlations between independent output channels, an effective coregionalization kernel is adopted in Gaussian Process (GP) to implement the low-dimensional multi-output tasks. The whole procedure consists of data filtering, feature compressing and multi-output GP, which is named by DF-MGP. Case study of an ethylene homo-polymerization with the Ziegler-Natta catalyst system shows the effectiveness of the proposed DF-MGP strategy.