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

TL;DR

This paper introduces a scalable, fast emulator for functional data using local Gaussian process regression, enabling efficient calibration of large-scale simulators with dense outputs, significantly reducing computational costs.

Contribution

It presents a novel, scalable emulator for functional responses that leverages local GP regression and global lengthscale estimates, improving speed and efficiency over traditional Bayesian methods.

Findings

Achieves substantial speedup in emulation of functional data.

Successfully calibrates a complex hydrodynamics simulator with 20,000 runs.

Implemented in the R package FlaGP for practical use.

Abstract

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.