Active Bayesian Inference via Gaussian Process Surrogates for Parameter and Error Estimation

Uncertainties in the parameters of an engineering model often lead to differences between its predictions and experimental data that was observed on the physical structure. To deal with these uncertainties, updating the parameters given the data is a possible approach. Bayesian inference provides a framework for this purpose, which also incorporates the prior information about the parameters. One drawback of this method is the high computational cost of the evaluations of the model responses, which are necessary for the inference process. This work proposes a solution to this high computational cost that includes Gaussian Process (GP) regression to approximate the model responses. This GP surrogate is trained with a limited number of model simulations and emulates the system responses. Additionally, to select these ‘training’ points, an evidence-based active learning procedure is incorporated to adaptively refine the posterior distribution of the parameters. The proposed approach allows the estimation of the posterior distribution of both the parameters of interest of the model, and the standard deviation of the observational noise, allowing a complete characterization of the model and the observational uncertainty. The proposed methodology is applied to an illustrative example, demonstrating its efficiency in estimating the posterior distribution with a low computational cost. This framework is general, applicable to a variety of problems involving complex or computationally expensive models.