  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 truly 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, building upon the
works of Kennedy and O'Hagan (2001) and Higdon et al. (2008), while
incorporating the local approximate Gaussian Process framework proposed by
Gramacy and Apley (2015). 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 the methods outlined in Higdon et al. (2008)
for functional response, while drastically reducing computational costs. The
proposed emulator is applied to quickly calibrate the multiphysics continuum
hydrodynamics simulator FLAG with a large ensemble of 20000 runs. The methods
presented are implemented in the R package FlaGP.
