Diagnostics for Gaussian Process Emulators

Bastos, Leonardo Soares; O'Hagan, Anthony

doi:10.1198/tech.2009.08019

Cited by 350 publications

(360 citation statements)

References 20 publications

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“…(iii) The GPE uses these points to produce the whole surface energy with relative 90% confidence bands [56] (iv) We compare the resulting GPE energies with the ones obtained using the whole HFB grid.…”

Section: B Gaussian Process Emulatormentioning

confidence: 99%

“…The GPE is a statistical model of interpolation [56] that can be used for a function, in the current case the energy surface E tot (Z, ρ b ), whose values are the output of a complex non-random calculation, here an HFB calculation. Each single calculation normally has several input parameters and the output is expected to vary smoothly with the input, although in an unknown way.…”

Section: B Gaussian Process Emulatormentioning

confidence: 99%

See 1 more Smart Citation

A new statistical method for the structure of the inner crust of neutron stars

Pastore¹,

Shelley²,

Baroni³

et al. 2017

J. Phys. G: Nucl. Part. Phys.

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We investigated the structure of the low density regions of the inner crust of neutron stars using the Hartree-Fock-Bogoliubov (HFB) model to predict the proton content Z of the nuclear clusters and, together with the lattice spacing, the proton content of the crust as a function of the total baryonic density ρ b . The exploration of the energy surface in the (Z, ρ b ) configuration space and the search for the local minima require thousands of calculations. Each of them implies an HFB calculation in a box with a large number of particles, thus making the whole process very demanding. In this work, we apply a statistical model based on a Gaussian Process Emulator that makes the exploration of the energy surface ten times faster. We also present a novel treatment of the HFB equations that leads to an uncertainty on the total energy of ≈ 4 keV per particle. Such a high precision is necessary to distinguish neighbour configurations around the energy minima.

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Section: B Gaussian Process Emulatormentioning

confidence: 99%

Section: B Gaussian Process Emulatormentioning

confidence: 99%

A new statistical method for the structure of the inner crust of neutron stars

Pastore¹,

Shelley²,

Baroni³

et al. 2017

J. Phys. G: Nucl. Part. Phys.

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show abstract

“…Latin hypercube sampling (LHS) [29]). The GPE can be validated to check if there are any large discrepancies between the emulator and simulator as in [30]. This is done to ensure that the initial approximation is of a reasonable overall quality.…”

Section: Initialization and Samplingmentioning

confidence: 99%

“…The error bars reflect the 95% credible interval for each prediction. In the centre column the individual prediction errors (IPE) are plotted as suggested in [30]. The IPE should have a student-t distributions and should therefore lie in the interval [ 2,2], 95% of the time.…”

Section: D Wing Weight Modelmentioning

confidence: 99%

Adaptive Emulation-Based Reliability Analysis

Hristov¹,

DiazDelaO²,

Kubiak³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. This paper presents an approximation method for performing reliability analysis with high fidelity computer codes at a reasonable computational cost. Complex models are common in science and engineering due to their ability to substitute costly and some times infeasible practical experiments. These models, however, suffer from high computational cost. This causes problems when performing sampling -based reliability analysis, since the failure modes of the system typically occupy a small region of the input space and thus relatively large sample sizes are required for the accurate estimation of their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and Subset Simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset Simulation is used to efficiently populate those regions of the initial approximation which are likely to lead to the performance function exceeding a predefined critical threshold. Among all samples, the ones that are likely to contribute most to increasing the quality of the surrogate in the vicinity of the failure regions are selected, using Bayesian optimisation methods. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region in performance space is developed at a reasonable computational cost. The presented method is applied to a number of benchmark problems.

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“…Third order polynomials were used as the set of candidate regression terms for β i j g i j (x A i ) in equation (15), with linear model selection based on AIC criteria used to choose both the list of active inputs x A i , and the final list of polynomial terms used, for each output labelled by i. As we had access to reasonable numbers of runs at each wave we used a vague prior limit for the β i j parameters and corresponding OLS estimates for the total residual variance σ 2 i = σ 2 u i + σ 2 v i , with σ 2 v i = ασ 2 i where α was chosen so the nugget term represented a small proportion of the total variance, checked using emulator diagnostics (Bastos & O'Hagan 2008). The correlation lengths were specified to be θ i = 0.35, following the argument for the residual of a third order polynomial fit presented by Vernon et al (2010a).…”

Section: Appendix A: Details Of the History Matching Proceduresmentioning

confidence: 99%

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Rodrigues

Vernon

Bower

2016

Mon. Not. R. Astron. Soc.

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We explore the parameter space of the semi-analytic galaxy formation model GALFORM, studying the constraints imposed by measurements of the galaxy stellar mass function (GSMF) and its evolution. We use the Bayesian Emulator method to quickly eliminate vast implausible volumes of the parameter space and zoom in on the most interesting regions, allowing us to identify a set of models that match the observational data within model uncertainties. We find that the GSMF strongly constrains parameters related to quiescent star formation in discs, stellar and AGN feedback and threshold for disc instabilities, but weakly restricts other parameters. Constraining the model using local data alone does not usually select models that match the evolution of the GSMF well. Nevertheless, we show that a small subset of models provides acceptable match to GSMF data out to redshift 1.5. We explore the physical significance of the parameters of these models, in particular exploring whether the model provides a better description if the mass loading of the galactic winds generated by starbursts (β 0,burst ) and quiescent disks (β 0,disc ) is different. Performing a principal component analysis of the plausible volume of the parameter space, we write a set of relations between parameters obeyed by plausible models with respect to GSMF evolution. We find that while β 0,disc is strongly constrained by GSMF evolution data, constraints on β 0,burst are weak. Although it is possible to find plausible models for which β 0,burst = β 0,disc , most plausible models have β 0,burst > β 0,disc , implying -for these -larger SN feedback efficiency at higher redshifts.

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Diagnostics for Gaussian Process Emulators

Cited by 350 publications

References 20 publications

A new statistical method for the structure of the inner crust of neutron stars

A new statistical method for the structure of the inner crust of neutron stars

Adaptive Emulation-Based Reliability Analysis

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

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