Deep Gaussian Process Emulation using Stochastic Imputation

Ming, Deyu; Williamson, Daniel; Guillas, Serge

doi:10.48550/arxiv.2107.01590

Cited by 2 publications

(2 citation statements)

References 29 publications

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“…The most common emulator is the Gaussian process emulator (Kennedy & O'Hagan, 2001), where the map between the input parameters and the numerical model outputs is modeled via a Gaussian process. Several developments on the vanilla Gaussian process have been proposed for the purpose of emulation, such as the treed Gaussian process (Gramacy & Lee, 2008) and the deep Gaussian process of Damianou & Lawrence (2013) or variants thereof (Monterrubio-Gómez et al, 2020, Ming et al, 2021, Marmin & Filippone, 2022, Sauer et al, 2022.…”

Section: Deep Emulationmentioning

confidence: 99%

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

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Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

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Section: Deep Emulationmentioning

confidence: 99%

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

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“…e.g. when too little training data are available or when the assumption of a smooth functional mapping which be violated (for which we suggest the use of deep GPs [46,47].…”

mentioning

confidence: 99%

An Adaptive Strategy for Sequential Designs of Multilevel Computer Experiments

Ehara

Guillas

2023

Int. J. UncertaintyQuantification

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Investigating uncertainties in computer simulations can be prohibitive in terms of computational costs, since the simulator needs to be run over a large number of input values. Building an emulator, i.e., a statistical surrogate model of the simulator constructed using a design of experiments made of a comparatively small number of evaluations of the forward solver, greatly alleviates the computational burden to carry out such investigations. Nevertheless, this can still be above the computational budget for many studies. Two major approaches have been used to reduce the budget needed to build the emulator: efficient design of experiments, such as sequential designs, and combining training data of different degrees of sophistication in a so-called multifidelity method, or multilevel in case these fidelities are ordered typically for increasing resolutions. We present here a novel method that combines both approaches, the multilevel adaptive sequential design of computer experiments in the framework of Gaussian process (GP) emulators. We make use of reproducing kernel Hilbert spaces as a tool for our GP approximations of the differences between two consecutive levels. This dual strategy allows us to allocate efficiently limited computational resources over simulations of different levels of fidelity and build the GP emulator. The allocation of computational resources is shown to be the solution of a simple optimization problem in a special case where we theoretically prove the validity of our approach. Our proposed method is compared to other existing models of multifidelity Gaussian process emulation. Gains in orders of magnitudes in accuracy or computing budgets are demonstrated in some numerical examples for some settings.

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Deep Gaussian Process Emulation using Stochastic Imputation

Cited by 2 publications

References 29 publications

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Statistical Deep Learning for Spatial and Spatio-Temporal Data

An Adaptive Strategy for Sequential Designs of Multilevel Computer Experiments

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