Clustered active-subspace based local Gaussian process emulator for high-dimensional and complex computer models

Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the computation in such problems, and in this regard the Gaussian Process (GP) emulator is a popular choice for its ability to quantify the approximation error in the emulator itself. However, a major limitation of the GP emulator is that it can not handle problems of very high dimensions, which is often addressed with dimension reduction techniques. In this work we hope to address an issue that the models of interest are so complex that they admit different low dimensional structures in different parameter regimes. Building upon the active subspace method for dimension reduction, we propose a clustered active subspace method which identifies the local low-dimensional structures as well as the parameter regimes they are in (represented as clusters), and then construct low dimensional and local GP emulators within the clusters. Specifically we design a clustering method based on the gradient information to identify these clusters, and a local GP construction procedure to construct the GP emulator within a local cluster. With numerical examples, we demonstrate that the proposed method is effective when the underlying models are of complex low-dimensional structures.