But how can I optimise my high-dimensional problem with only very little data? A composite manufacturing application

In this research, a Gaussian process (GP) surrogate modelling framework for the forming process of dry carbon-fibre textile was investigated. A particular focus of the work is the development of dimension reduction algorithms, allowing to solve high-dimensional sparse optimisation problems. The concept of active subspace is adopted to find the principal space of the problem. Then, a low-dimensional (i.e., active) subspace can be obtained by selecting the directions with highest explained variance. A kernel-combined GP format is developed. This takes advantage of the active subspace to build a robust, high-dimensional emulator that can be regarded as a special case of multi-fidelity GP. A two-step adaptive sequential design approach is adopted, which further improves the efficiency of data design. Different sequential design strategies are compared. A case study with eight input parameters demonstrates the capability of the proposed approach, where an accurate and robust optimum condition is obtained from only tens of simulations.