Computer model calibration via Bayesian optimization based on a bi-fidelity Gaussian process model for transformed sum of squared errors

Bi-fidelity simulations involve a high-fidelity (HF) (high-accuracy) simulator and a low-fidelity (LF) simulator. Calibration of the HF simulator’s parameter vector via minimizing a function, called the HF SSE, that computes the sum of squared errors (SSE) between the HF simulator output and field data is a common engineering problem. To overcome computational challenges in calibrating time-consuming HF simulators with high-dimensional outputs, which are prevalent in practice, this paper proposes an efficient method to calibrate such simulators that uses a novel bi-fidelity Gaussian process (GP) emulator to minimize the HF SSE. The proposed bi-fidelity GP emulator fuses data from both the HF simulator and the faster LF simulator to reduce its need for costly HF simulation data via a GP prior that jointly models identical Box-Cox transformations of the HF SSE and a modified version of the LF SSE, where the LF SSE is a function that computes the SSE between the LF simulator output and field data. The LF SSE is modified so that it approximates the HF SSE better, and the Box-Cox transformation is applied to find a transformed HF SSE and a transformed modified LF SSE that are jointly well modeled by the assumed GP prior. Our proposed emulator is used to estimate calibration parameters via a Bayesian optimization (BO) method for minimizing the HF SSE that we prove has some desirable properties. This proposed method outperforms several alternative methods in an example on calibrating an office thermal environment simulator and two other examples. © 2025 “IISE”