Emulation of multivariate simulators using thin-plate splines with application to atmospheric dispersion

TL;DR

This paper introduces a novel thin-plate spline based method for emulating multivariate computer simulators with structured spatial output, demonstrating improved accuracy and computational efficiency over existing techniques in hazard prediction models.

Contribution

It develops and compares thin-plate spline based emulators for multivariate outputs, showing they outperform principal component methods and offer better uncertainty quantification and computational speed.

Findings

Thin-plate spline emulators outperform principal component emulators.

Separable thin-plate spline emulator provides realistic uncertainty quantification.

Proposed methods are computationally efficient for high-resolution data.

Abstract

It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer simulator taking into account output structure in the responses. The utility of this approach is demonstrated by applying it to a chemical and biological hazard prediction model. Predicting the hazard area that results from an accidental or deliberate chemical or biological release is imperative in civil and military planning and also in emergency response. The hazard area resulting from such a release is highly structured in space and we therefore propose the use of a thin-plate spline to capture the spatial structure and fit a Gaussian process emulator to the coefficients of the resultant basis functions. We compare and contrast four different techniques for emulating multivariate output: dimension-reduction using (i) a fully Bayesian approach with a principal component basis, (ii) a fully Bayesian approach with a thin-plate spline basis, assuming that the basis coefficients are independent, and (iii) a "plug-in" Bayesian approach with a thin-plate spline basis and a separable covariance structure; and (iv) a functional data modeling approach using a tensor-product (separable) Gaussian process. We develop methodology for the two thin-plate spline emulators and demonstrate that these emulators significantly outperform the principal component emulator. Further, the separable thin-plate spline emulator, which accounts for the dependence between basis coefficients, provides substantially more realistic quantification of uncertainty, and is also computationally more tractable, allowing fast emulation. For high resolution output data, it also offers substantial predictive and computational advantages over the tensor-product Gaussian process emulator.