An integrated surrogate model constructing method: Annealing combinable Gaussian process

Abstract

Surrogate models are widely used to mimic complex systems to reduce the high experimental cost. As the system becomes high-dimensional and complex, there is an increasing demand for building relatively simplified surrogate models that capture key variables and represent complex interactions. This study proposes the annealing combinable Gaussian process, an integrated solution for identifying key variables and constructing the high-precision surrogate model. Firstly, to identify redundant variables, this study optimises variables selection with a modified simulated annealing algorithm over the complete model space. This process is called the outer loop. Secondly, to improve the model accuracy and structure, this study constructs a non-parametric Gaussian process model with additive or multiplicative kernel, effectively extracting high-order interactions. Simultaneously, a Markov chain is proposed to sample the model space. The conditional entropy is used as the scoring rule for the simulated annealing algorithm of the outer loop. It is named the inner loop. This study also discusses the rationality of conditional entropy as a criterion. The annealing combinable Gaussian process performs well in various application scenarios, including regression and classification problems. Finally, our method is implemented with the particle-in-cell simulation to find out the key physics parameters.