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We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations.
Theory of reproducing kernels,
N. Aronszajn, · 1950
Earlier work this paper cites.
A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-posed problems, W.H. Winston, 1977
1977
Earlier work this paper cites.
Diagonally implicit Runge–Kutta methods for stiff ODE’s,
R. Alexander, · 1977
Earlier work this paper cites.
Spectral and finite difference solutions of the Burgers equation,
C. Basdevant, M. Deville, P. Haldenwang, J. Lacroix, J. Ouazzani, R. Peyret, P. Orlandi, A. Patera, · 1986
Earlier work this paper cites.
Bayesian numerical analysis,
P. Diaconis, · 1988
Earlier work this paper cites.
S. Saitoh, Theory of reproducing kernels and its applications, volume 189, Longman, 1988
1988
Earlier work this paper cites.
Networks for approximation and learning,
T. Poggio, F. Girosi, · 1990
Earlier work this paper cites.
Some Bayesian numerical analysis,
A. O’Hagan, · 1992
Earlier work this paper cites.
Long short-term memory,
S. Hochreiter, J. Schmidhuber, · 1997
Earlier work this paper cites.
Sparse Bayesian learning and the relevance vector machine,
M. E. Tipping, · 2001
Earlier work this paper cites.
Occam’s razor,
C. E. Rasmussen, Z. Ghahramani, · 2001
Earlier work this paper cites.
B. Schölkopf, A. J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond, MIT press, 2002
2002
Cited alongside, same era.
Gaussian processes for machine learning,
C. E. Rasmussen, · 2006
Cited alongside, same era.
A. Iserles, A first course in the numerical analysis of differential equations, 44, Cambridge University Press, 2009
2009
Cited alongside, same era.
Kalman filtering and smoothing solutions to temporal Gaussian process regression models,
J. Hartikainen, S. Särkkä, · 2010
Cited alongside, same era.
A. Berlinet, C. Thomas-Agnan, Reproducing kernel Hilbert spaces in probability and statistics, Springer Science & Business Media, 2011
2011
Cited alongside, same era.
K. P. Murphy, Machine learning: a probabilistic perspective, MIT press, 2012
Deep learning,
Y. LeCun, Y. Bengio, G. Hinton, · 2015
Later among the works it cites.
Machine learning: Trends, perspectives, and prospects,
M. Jordan, T. Mitchell, · 2015
Later among the works it cites.
Probabilistic numerics and uncertainty in computations,
P. Hennig, M. A. Osborne, M. Girolami, · 2015
Later among the works it cites.
Brittleness of Bayesian inference under finite information in a continuous world,
H. Owhadi, C. Scovel, T. Sullivan, et al., · 2015
Later among the works it cites.
Statistical analysis of differential equations: introducing probability measures on numerical solutions,
P. R. Conrad, M. Girolami, S. Särkkä, A. Stuart, K. Zygalakis, · 2016
Later among the works it cites.
J. C. Butcher, Numerical methods for ordinary differential equations, John Wiley & Sons, 2016
2016
Later among the works it cites.
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2012
Cited alongside, same era.
R. M. Neal, Bayesian learning for neural networks, volume 118, Springer Science & Business Media, 2012
2012
Cited alongside, same era.
V. Vapnik, The nature of statistical learning theory, Springer Science & Business Media, 2013
2013
Cited alongside, same era.
Gaussian processes for big data,
J. Hensman, N. Fusi, N. D. Lawrence, · 2013
Cited alongside, same era.
Probabilistic machine learning and artificial intelligence,
Z. Ghahramani, · 2015
Cited alongside, same era.
Imagenet classification with deep convolutional neural networks,
A. Krizhevsky, I. Sutskever, G. E. Hinton,
Cited in the paper.
H. Poincaré, Calcul des probabilités, Gauthier-Villars, Paris, 1896
Cited in the paper.
Posterior consistency for Gaussian process approximations of Bayesian posterior distributions,
A. M. Stuart, A. L. Teckentrup, · 2016
Later among the works it cites.
Probabilistic numerics, http://probabilistic-numerics.org/index.html , 2017
2017
Closest in time.
Inferring solutions of differential equations using noisy multi-fidelity data,
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2017
Closest in time.
Machine learning of linear differential equations using Gaussian processes,
M. Raissi, G. E. Karniadakis, · 2017
Closest in time.