Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures

Fricker, Thomas E.; Oakley, Jeremy E.; Urban, Nathan M.

doi:10.1080/00401706.2012.715835

Cited by 144 publications

(84 citation statements)

References 32 publications

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“…Similar expressions occur in the study of nonstationary covariance functions (Paciorek and Schervish 2006;Higdon 2002); a special case (diagonal matrices) is given by Fricker et al (2010). These authors construct the covariance matrix using process convolutions, observing that the convolution theorem for Fourier transforms ensures positive definiteness (Higdon 2002(Higdon , 2008.…”

Section: Considering Functions Of the Form Discussed In Equation 13mentioning

confidence: 99%

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Introducingmultivator: A Multivariate Emulator

Hankin¹

2012

J. Stat. Soft.

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A multivariate generalization of the emulator technique described by Hankin (2005) is presented in which random multivariate functions may be assessed. In the standard univariate case (Oakley 1999), a Gaussian process, a finite number of observations is made; here, observations of different types are considered. The technique has the property that marginal analysis (that is, considering only a single observation type) reduces exactly to the univariate theory. The associated software is used to analyze datasets from the field of climate change.

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Section: Considering Functions Of the Form Discussed In Equation 13mentioning

confidence: 99%

“…Recent unpublished work by Fricker et al (2010) also uses convolution techniques and presents a nonseparable covariance structure of which the present work is shown to be a generalization. Related work might also include Kennedy and O'Hagan (2000) …”

Section: Non-separable Covariance Structuresmentioning

confidence: 99%

Introducingmultivator: A Multivariate Emulator

Hankin¹

2012

J. Stat. Soft.

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“…However, the intermolecular energy is a non-stationary function of distance, as it varies rapidly at small interatomic separations, but more gently at larger separation. Designing non-stationary covariance functions is a challenging task 47 . Instead, to deal with this non-stationarity we use the inverse interatomic distances as co-variates in the GP, to achieve approximate stationarity.…”

Section: Gaussian Processesmentioning

confidence: 99%

Molecular simulation of the thermophysical properties and phase behaviour of impure CO₂ relevant to CCS

2016

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Impurities from the CCS chain can greatly influence the physical properties of CO 2 . This has important design, safety and cost implications for the compression, transport and storage of CO 2 . There is an urgent need to understand and predict the properties of impure CO 2 to assist with CCS implementation. However, CCS presents demanding modelling requirements. A suitable model must both accurately and robustly predict CO 2 phase behaviour over a wide range of temperature and pressure, and maintain that predictive power for CO 2 mixtures with numerous, mutually interacting chemical species. A promising technique to address this task is molecular simulation. It offers a molecular approach, with foundations in firmly established physical principles, along with the potential to predict the wide range of physical properties required for CCS. The quality of predictions from molecular simulation depends on accurate force-fields to describe the interactions between CO 2 and other molecules. Unfortunately, there is currently no universally applicable method to obtain force-fields suitable for molecular simulation.In this paper we present two methods of obtaining force-fields: the first being semi-empirical and the second using ab initio quantum-chemical calculations. In the first approach we optimise the impurity force-field against measurements of the phase and pressure-volume behaviour of CO 2 binary mixtures with N 2 , O 2 , Ar and H 2 . A gradient-free optimiser allows us to use the simulation itself as the underlying model. This leads to accurate and robust predictions under conditions relevant to CCS. In the second approach we use quantum-chemical calculations to produce ab initio evaluations of the interactions between CO 2 and relevant impurities, taking N 2 as an exemplar. We use a modest number of these calculations to train a machine-learning algorithm, known as a Gaussian process, to describe these data. The resulting model is then able to accurately predict a much broader set of ab initio force-field calculations at comparatively low numerical cost. Although our method is not yet ready to be implemented in a molecular simulation, † Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See

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“…univariate GPs. This simplification leads to a potentially efficient emulation strategy but it is clearly restrictive [17]. Rougier [18] made the same assumption, in addition to several assumptions regarding the forms of the regression functions, and took advantage of factorizations of the covariance matrix to improve computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

“…Rougier [18] made the same assumption, in addition to several assumptions regarding the forms of the regression functions, and took advantage of factorizations of the covariance matrix to improve computational efficiency. Conti and O'Hagan's approach has recently been extended to non-stationary GPs [19] and to non-separable covariance structures for categorical outputs [17]. Fricker makes use of the linear model of coregionalization [20], which permits a richer covariance structure but is restricted to low dimensions.…”

Section: Introductionmentioning

confidence: 99%

Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap

2015

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In this paper, Isomap and kernel Isomap are used to dramatically reduce the dimensionality of the output space to efficiently construct a Gaussian process emulator of parametrized partial differential equations. The output space consists of spatial or spatio-temporal fields that are functions of multiple input variables. For such problems, standard multioutput Gaussian process emulation strategies are computationally impractical and/or make restrictive assumptions regarding the correlation structure. The method we develop can be applied without modification to any problem involving vector-valued targets and vector-valued inputs. It also extends a method based on linear dimensionality reduction to response surfaces that cannot be described accurately by a linear subspace of the high dimensional output space. Comparisons to the linear method are made through examples that clearly demonstrate the advantages of nonlinear dimensionality reduction.

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Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures

Cited by 144 publications

References 32 publications

Introducingmultivator: A Multivariate Emulator

Introducingmultivator: A Multivariate Emulator

Molecular simulation of the thermophysical properties and phase behaviour of impure CO₂ relevant to CCS

Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap

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Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures

Cited by 144 publications

References 32 publications

Introducingmultivator: A Multivariate Emulator

Introducingmultivator: A Multivariate Emulator

Molecular simulation of the thermophysical properties and phase behaviour of impure CO2 relevant to CCS

Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap

Contact Info

Product

Resources

About

Molecular simulation of the thermophysical properties and phase behaviour of impure CO₂ relevant to CCS