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Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources.
Predicting the mechanical response of oligocrystals with deep learning
Ari L Frankel, Reese E Jones, Coleman Alleman, and Jeremy A Templeton · 1901
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Ari Frankel, Kousuke Tachida, and Reese Jones · 1910
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Tensor basis gaussian process models of hyperelastic materials
Ari Frankel, Reese Jones, and Laura Swiler · 1912
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The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process
Michael F Driscoll · 1973
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Design and analysis of computer experiments
Jerome Sacks, William J Welch, Toby J Mitchell, and Henry P Wynn · 1989
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Monotone smoothing with application to dose-response curves and the assessment of synergism
Colleen Kelly and John Rice · 1990
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Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
Francis J Narcowich and Joseph D Ward · 1994
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Fitting Gaussian Markov random fields to Gaussian fields
Hååvard Rue and Hååkon Tjelmeland · 2002
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Solving noisy linear operator equations by gaussian processes: Application to ordinary and partial differential equations
Thore Graepel · 2003
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The design and analysis of computer experiments
Thomas J Santner, Brian J Williams, and William I Notz · 2003
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Derivative observations in Gaussian process models of dynamic systems
Ercan Solak, Roderick Murray-Smith, William E Leithead, Douglas J Leith, and Carl E Rasmussen · 2003
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Gaussian processes for machine learning
Matthias Seeger · 2004
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Warped Gaussian processes
Edward Snelson, Zoubin Ghahramani, and Carl E Rasmussen · 2004
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A unifying view of sparse approximate Gaussian process regression
Joaquin Quiñonero-Candela and Carl Edward Rasmussen · 2005
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Analysis of some methods for reduced rank Gaussian process regression
Joaquin Quinonero-Candela and Carl Edward Rasmussen · 2005
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Gaussian Processes for Machine Learning
Carl Edward Rasmussen and Christopher KI Williams · 2006
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Refined error estimates for matrix-valued radial basis functions
Edward J Fuselier Jr · 2007
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Monotonic regression based on Bayesian P – splines: An application to estimating price response functions from store-level scanner data
Andreas Brezger and Winfried J Steiner · 2008
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Covariance tapering for likelihood-based estimation in large spatial data sets
Cari G Kaufman, Mark J Schervish, and Douglas W Nychka · 2008
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Learning divergence-free and curl-free vector fields with matrix-valued kernels
Ives Macêdo and Rener Castro · 2008
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Computation of multivariate normal and t t probabilities , volume 195
Alan Genz and Frank Bretz · 2009
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Vector field learning via spectral filtering
Luca Baldassarre, Lorenzo Rosasco, Annalisa Barla, and Alessandro Verri · 2010
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Gaussian processes with monotonicity information
Jaakko Riihimäki and Aki Vehtari · 2010
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Implicitly constrained Gaussian process regression for monocular non-rigid pose estimation
Mathieu Salzmann and Raquel Urtasun · 2010
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Reproducing kernel Hilbert spaces in probability and statistics
Alain Berlinet and Christine Thomas-Agnan · 2011
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A constrained ℓ 1 \ell_{1} minimization approach to sparse precision matrix estimation
Tony Cai, Weidong Liu, and Xi Luo · 2011
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Linear operators and stochastic partial differential equations in gaussian process regression
Simo Särkkä · 2011
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Gaussian process modeling with inequality constraints
Sébastien Da Veiga and Amandine Marrel · 2012
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Large scale distributed deep networks
Jeffrey Dean, Greg Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Mark Mao, Marc’aurelio Ranzato, Andrew Senior, Paul Tucker, Ke Yang, et al · 2012
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Machine learning: a probabilistic perspective
Kevin P Murphy · 2012
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Tapered covariance: Bayesian estimation and asymptotics
Benjamin Shaby and David Ruppert · 2012
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Bounded Gaussian process regression
Bjørn Sand Jensen, Jens Brehm Nielsen, and Jan Larsen · 2013
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GPstuff: Bayesian modeling with Gaussian processes
Jarno Vanhatalo, Jaakko Riihimäki, Jouni Hartikainen, Pasi Jylänki, Ville Tolvanen, and Aki Vehtari · 2013
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Modeling magnetic fields using Gaussian processes
Niklas Wahlström, Manon Kok, Thomas B Schön, and Fredrik Gustafsson · 2013
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Sparse precision matrix estimation with calibration
Tuo Zhao and Han Liu · 2013
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Local Gaussian process approximation for large computer experiments
Robert B. Gramacy and Daniel W. Apley · 2014
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Scaling intrinsic Gaussian Markov random field priors in spatial modelling
Sigrunn Holbek Sørbye and Håvard Rue · 2014
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Fast Kronecker inference in Gaussian processes with non-Gaussian likelihoods
Seth Flaxman, Andrew Wilson, Daniel Neill, Hannes Nickisch, and Alex Smola · 2015
Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
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Hidden physics models: Machine learning of nonlinear partial differential equations
Maziar Raissi and George Em Karniadakis · 2018
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Numerical Gaussian processes for time-dependent and nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2018
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Chemical Mixtures and Combined Chemical and Non-Chemical Stressors, Ch. 15
Cynthia Rider and Jane Ellen Simmons, editors · 2018
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Modeling and interpolation of the ambient magnetic field by Gaussian processes
Arno Solin, Manon Kok, Niklas Wahlström, Thomas B Schön, and Simo Särkkä · 2018
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Bayesian Numerical Homogenization
Houman Owhadi · 2015
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Modeling of magnetic fields and extended objects for localization applications
Niklas Wahlström · 2015
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Kernel interpolation for scalable structured Gaussian processes (KISS-GP)
Andrew Wilson and Hannes Nickisch · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
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lagp: Large-scale spatial modeling via local approximate Gaussian processes in R
Robert Gramacy · 2016
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The Elements of Statistical Learning: Data Mining, Inference and Prediction
Trevor Hastie, Robert Tibshirani, and Jerome Friedman · 2016
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Xiu Yang, Guzel Tartakovsky, and Alexandre Tartakovsky · 2018
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Gaussian processes with linear operator inequality constraints
Christian Agrell · 2019
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Maximum likelihood estimation for Gaussian processes under inequality constraints
François Bachoc, Agnes Lagnoux, Andrés F López-Lopera, et al · 2019
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Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence
Nathan Baker, Frank Alexander, Timo Bremer, Aric Hagberg, Yannis Kevrekidis, Habib Najm, Manish Parashar, Abani Patra, James Sethian, Stefan Wild, et al · 2019
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Data-driven science and engineering: Machine learning, dynamical systems, and control
Steven L Brunton and J Nathan Kutz · 2019
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Robust training and initialization of deep neural networks: An adaptive basis viewpoint
Eric C Cyr, Mamikon A Gulian, Ravi G Patel, Mauro Perego, and Nathaniel A Trask · 2019
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Scalable Gaussian process computations using hierarchical matrices
Christopher J Geoga, Mihai Anitescu, and Michael L Stein · 2019
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Machine learning of space-fractional differential equations
Mamikon Gulian, Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2019
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Constraint-aware neural networks for Riemann problems
Jim Magiera, Deep Ray, Jan S Hesthaven, and Christian Rohde · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors
Pallavi Ray, Debdeep Pati, and Anirban Bhattacharya · 2019
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Know your boundaries: Constraining Gaussian processes by variational harmonic features
Arno Solin and Manon Kok · 2019
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Hilbert space methods for reduced-rank Gaussian process regression
Arno Solin and Simo Särkkä · 2019
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Physics-informed CoKriging: A Gaussian-process-regression-based multifidelity method for data-model convergence
Xiu Yang, David Barajas-Solano, Guzel Tartakovsky, and Alexandre M Tartakovsky · 2019
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Gaussian process regression for data fulfilling linear differential equations with localized sources
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