Bayesian analysis of multifidelity computer models with local features and non-nested experimental designs: Application to the WRF model

TL;DR

This paper introduces a novel Bayesian emulator for multifidelity models with non-nested designs, specifically applied to climate modeling with the WRF model, addressing non-stationarity and discontinuities.

Contribution

It extends co-kriging with a treed partition and an efficient imputation mechanism, enabling analysis of non-hierarchical experimental designs in multifidelity settings.

Findings

Demonstrates improved performance on benchmark examples.

Successfully applied to large-scale climate modeling with WRF.

Provides a computationally feasible Monte Carlo emulator.

Abstract

We propose a multi-fidelity Bayesian emulator for the analysis of the Weather Research and Forecasting (WRF) model when the available simulations are not generated based on hierarchically nested experimental design. The proposed procedure, called Augmented Bayesian Treed Co-Kriging, extends the scope of co-kriging in two major ways. We introduce a binary treed partition latent process in the multifidelity setting to account for non-stationary and potential discontinuities in the model outputs at different fidelity levels. Moreover, we introduce an efficient imputation mechanism which allows the practical implementation of co-kriging when the experimental design is non-hierarchically nested by enabling the specification of semi-conjugate priors. Our imputation strategy allows the design of an efficient RJ-MCMC implementation that involves collapsed blocks and direct simulation from conditional distributions. We develop the Monte Carlo recursive emulator which provides a Monte Carlo proxy for the full predictive distribution of the model output at each fidelity level, in a computationally feasible manner. The performance of our method is demonstrated on a benchmark example, and compared against existing methods. The proposed method is used for the analysis of a large-scale climate modeling application which involves the WRF model.