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Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs).
Spectral and finite difference solutions of the burgers equation
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Ladislav Kocis and William J Whiten · 1997
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Carl Edward Rasmussen and Christopher KI Williams · 2006
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Youngmin Cho and Lawrence K Saul · 2009
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Gaussian processes for machine learning (gpml) toolbox
Carl Edward Rasmussen and Hannes Nickisch · 2010
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Eric Brochu, Vlad M Cora, and Nando De Freitas · 2010
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Bayesian learning for neural networks
Radford M Neal · 2012
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Multi-fidelity Gaussian process regression for computer experiments
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Gaussian processes for big data
James Hensman, Nicolo Fusi, and Neil D Lawrence · 2013
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Deep neural networks as gaussian processes
Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington, and Jascha Sohl-Dickstein · 2017
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Inferring solutions of differential equations using noisy multi-fidelity data
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Numerical gaussian processes for time-dependent and non-linear partial differential equations
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity bayesian optimization
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Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov · 2014
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Exponential expressivity in deep neural networks through transient chaos
Ben Poole, Subhaneil Lahiri, Maithra Raghu, Jascha Sohl-Dickstein, and Surya Ganguli · 2016
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Fast direct methods for gaussian processes
Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W Hogg, and Michael O’Neil · 2016
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Guofei Pang, Paris Perdikaris, Wei Cai, and George Em Karniadakis · 2017
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Machine learning of linear differential equations using gaussian processes
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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On the complexity of learning neural networks
Le Song, Santosh Vempala, John Wilmes, and Bo Xie · 2017
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Likelihood approximation with hierarchical matrices for large spatial datasets
Alexander Litvinenko, Ying Sun, Marc G Genton, and David Keyes · 2017
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