Multivariate Gaussian process emulation for multifidelity computer models with high-dimensional spatial outputs

Risk assessment of hurricane-driven storm surge relies on deterministic computer models that produce outputs over a large spatial domain. The surge models can often be run at a range of fidelity levels, with greater precision yielding more accurate simulations. Improved accuracy comes with a significant increase in computational expense, necessitating the development of an emulator which leverages information from the more plentiful low-fidelity outputs to provide fast and accurate predictions of high-fidelity simulations. To properly assess the risk of storm surge over a geographic region at aggregated spatial resolution, an emulator must account for spatial dependence between outputs yet remain computationally feasible for high-dimensional simulations. To address this challenge, we exploit the autoregressive cokriging framework to develop two cross-covariance structures to account for spatial dependence. One approach uses a separable covariance structure with a sparse Cholesky prior for the inverse of the cross-covariance matrix; the other involves a low-rank approximation via basis representations. We demonstrate their predictive performance in the storm surge application and a testbed example.