Bayesian Active Learning with Polynomial Chaos Expanded Gaussian Process

The development of accurate surrogate models for complex physical systems and computer simulations often requires extensive and resource-intensive experimental efforts. In addition, the modeled physical dependencies exhibit complex behaviors characterized by non-linearities and non-stationary behaviors. To address these challenges, machine learning (ML) methods used to construct surrogate models should strategically minimize the number of queries and capture both non-linear and non-stationary behaviors. In this context, Polynomial Chaos Expanded Gaussian Process (PCEGP) is used as a method to model non-linearity and non-stationarity with limited data points. The Polynomial Chaos Expansion (PCE) is utilized in this approach to compute the hyperparameters of the Gaussian process (GP), enhancing the model's ability to capture complex dependencies between inputs and outputs. A key advantage of PCEGP is its simple model structure, which enables the flexible generation of nonstationary lengthscale parameters in the GP. Unlike established non-stationary GP approaches such as deep GP (DGP) or GP models with input partitioning, the introduced PCEGP method retains its interpretability while modeling complex non-stationary behavior. The PCEGP model is introduced as a fully Bayesian surrogate for active learning (AL), demonstrating low prediction errors across various non-stationary benchmarks. Its performance competes with or surpasses stationary GPs, DGPs, and inputpartitioned GP models.