Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology

TL;DR

This paper introduces a computationally efficient emulator model for large-scale computer experiments using compactly supported correlation functions, demonstrated on a cosmology application with 20,000 evaluations.

Contribution

The paper presents a novel emulator approach combining low-order regression and compactly supported correlations, reducing computational cost while maintaining accuracy.

Findings

Achieved significant computational savings with large datasets.

Maintained high predictive accuracy using the new correlation structure.

Demonstrated effectiveness on a cosmological simulator with 20,000 evaluations.

Abstract

Statistical emulators of computer simulators have proven to be useful in a variety of applications. The widely adopted model for emulator building, using a Gaussian process model with strictly positive correlation function, is computationally intractable when the number of simulator evaluations is large. We propose a new model that uses a combination of low-order regression terms and compactly supported correlation functions to recreate the desired predictive behavior of the emulator at a fraction of the computational cost. Following the usual approach of taking the correlation to be a product of correlations in each input dimension, we show how to impose restrictions on the ranges of the correlations, giving sparsity, while also allowing the ranges to trade off against one another, thereby giving good predictive performance. We illustrate the method using data from a computer simulator of photometric redshift with 20,000 simulator evaluations and 80,000 predictions.