Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification

By Ilias Bilionis, Nicholas Zabaras, Bledar A. Konomi, Guang Lin. 2013

181 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

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Citations in the corpus

Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems (2019, methodology): “As discussed in section 1, these methods have been successful in a wide spectrum of applications including design optimization [1, 2, 3, 4, 5], model calibration [7, 8, 9], and uncertainty quantification [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].”
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks (2018, background): “However, despite the fact that much progress has been made over the last two decades, the most popular methods for scientific computing under uncertainty, such as polynomial chaos expansions [17, 18, 19], sparse grid quadratures [20, 21], multi-level/multi-fidelity Monte Carlo sampling [22, 23], pro”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, background): “include, Gaussian processes [11, 12, 13, 14, 15], polynomial chaos expansions [16, 17, 18, 19], radial basis functions [20] and relevance vector machines [21].”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “Traditional choices for surrogate models include Gaussian process regression (GPR) (or Kriging) [15, 16, 17, 18, 19], polynomial chaos expansion [20, 21, 22, 23], and radial basis functions [24, 25].”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, methodology): “Gaussian processes have recently also become a popular tool in the machine learning literature as surrogates of expensive regression surfaces, such as log-likelihoods [17]; optimization surfaces [8, 24]; simulations of physical systems [6]; emulation of computer codes [10]; and for accelerating ABC ”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, background): “However, in practice, multi-output functions arise widely in geostatistics [16], robotics [17], sensor networks [18], chemometrics [19], traffic flow forecasting [20] and computational physics [21], [22], just to name a few.”
Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, methodology): “More recent eﬀorts have employed Gaussian Processes (GPs, [6, 8]) or multivariate regression schemes [7].”
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification (2018, methodology): “In [2], KLE was used for dimensionality reduction of the permeability field and then GP was performed as independent task for Bayesian regression.”
Remarks on multi-output Gaussian process regression (2018, background): “, discontinuous problems [52, 100]; (4) sampling strategies for sequential updating of the MOGPs by considering the output correlations and, particularly, the computing ratios between different fidelity levels in asymmetric scenarios [75, 101]; and (5) MOGP-assisted optimization [102, 103] and uncer”