An Improved Emulator for Bi-fidelity Computer Experiments with Ordered Monotonicity Information

Description

This project will develop a Gaussian process (GP) model-based statistical emulator for bi-fidelity simulations (i.e., simulations at two levels of fidelity called the high-fidelity (HF) level and low-fidelity (LF) level) that exploits ordered monotonicity information to improve its prediction quality. The term ordered monotonicity information refers to information that both the HF and LF outputs increase/decrease with an input (i.e., they increase/decrease when the input increases), and the HF output increases/decreases either faster or slower than the LF output as the input increases. In other words, the derivatives of the HF and LF outputs with respect to the input are not only known to be nonnegative/nonpositive but are also known to be ordered.  Due to advances in computing technology and modeling software, simulators (i.e., computer models) are increasingly employed in engineering work. Many simulators numerically solve partial differential equations (PDEs) with boundary and initial conditions, which we call PDE models. Simulators based on PDE models with different fidelity (i.e., accuracy) levels are frequently available. In bi-fidelity simulations, the HF simulator gives more accurate predictions but incurs longer run times than the LF simulator. To reduce simulation time for tasks that require many HF simulator runs, one can predict the HF output with a bi-fidelity emulator, i.e., an emulator of the HF and LF simulators built with data from both simulators. A popular bi-fidelity emulator is the autoregressive GP (AGP) emulator, which combines information in HF and LF simulation data by modeling the correlation between the HF and LF outputs. However, the AGP emulator does not incorporate ordered monotonicity information. Because ordered monotonicity information significantly narrows the set of functions known to contain the true paired input-output relationships of the HF and LF simulators, imposing ordered monotonicity constraints on a bi-fidelity emulator can yield substantially improved prediction accuracy and shortened prediction intervals with good coverage. This project will develop an emulator for deterministic bi-fidelity simulations that simultaneously incorporates ordered monotonicity information and captures the correlation between HF and LF outputs by modifying the AGP emulator. Computationally efficient methods for constructing the proposed bi-fidelity emulator will be developed. Additionally, prediction performance improvements attained by the proposed emulator over the AGP emulator and emulators that incorporate monotonicity information only will be investigated. The proposed emulator is expected to become a valuable tool for bi-fidelity simulations as it will allow practitioners to exploit ordered monotonicity information to obtain high-quality and physically meaningful emulator predictions.