Fast Emulation, Modular Calibration, and Active Learning for Simulators with Functional Response

Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian process (GP) models are commonly employed for emulation, they face limitations in scaling to large datasets. Furthermore, when dealing with dense functional output, such as spatial or time-series data, additional complexities arise, requiring careful handling to ensure fast emulation. This work presents a highly scalable emulator for functional data incorporating local Gaussian process regression. The emulator utilizes global GP lengthscale parameter estimates to scale the input space, leading to a substantial improvement in prediction speed. We demonstrate that our fast approximation-based emulator can serve as a viable alternative to a fully Bayesian approach for functional response, while drastically reducing computational costs. The proposed emulator is applied to quickly calibrate a multiphysics continuum hydrodynamics simulator with a large ensemble of 20000 runs. The methods presented are implemented in the R package FlaGP.