Bayesian analysis of multi-fidelity modeling in the stochastic simulations

Abstract

Multi-fidelity surrogate modeling has received intensive attention owing to its strong applicability to engineering design problems. Generally, unknown parameters in a surrogate model are estimated using simulation data, introducing parameter estimation uncertainty into the model prediction. This uncertainty can be further aggravated by the presence of random noise in stochastic simulations. To tackle this issue, this paper develops a novel Bayesian meta-modeling method for multi-fidelity simulations in stochastic situations. Utilizing prior information about the parameters and Bayesian posterior inference, a new closed-form predictive distribution is derived within the autoregressive cokriging framework. This formula explicitly accounts for both parameter estimation uncertainty and measurement error in response without requiring time-consuming Markov chain Monte Carlo methods. Numerical experiments conducted on the classic Borehole function and a stochastic customer order scheduling problem illustrate the performance of the proposed method. Results demonstrate that the proposed method surpasses existing methods and maintains robust predictive performance under heterogeneous stochastic circumstances with varying noise levels.