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We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian processes.
I. Palasti and A. Renyi
1956
Earlier work this paper cites.
J. Quinonero-Candela and C. E. Rasmussen
1959
Earlier work this paper cites.
A. V. Sul’din
1959
Earlier work this paper cites.
G. S. Kimeldorf and G. Wahba
1970
Earlier work this paper cites.
G. Kimeldorf and G. Wahba
1971
Earlier work this paper cites.
F. M. Larkin
1972
Earlier work this paper cites.
W. Anderson, Jr and G. Trapp
1975
Earlier work this paper cites.
C. A. Micchelli and T. J. Rivlin
1977
Earlier work this paper cites.
J. F. Traub, G. W. Wasilkowski, and H. Woźniakowski
1984
Earlier work this paper cites.
P. Diaconis
1988
Earlier work this paper cites.
A. V. Vecchia
1988
Earlier work this paper cites.
G. Wahba
1990
Earlier work this paper cites.
P. D. Sampson and P. Guttorp
1992
Earlier work this paper cites.
J. Skilling
1992
Earlier work this paper cites.
A. Cochocki and R. Unbehauen
1993
Earlier work this paper cites.
K. Krischer, R. Rico-Martínez, I. Kevrekidis, H. Rotermund, G. Ertl, and J. Hudson
1993
Earlier work this paper cites.
R. Rico-Martinez and I. G. Kevrekidis
1993
Earlier work this paper cites.
T. Uchiyama and N. Sonehara
1993
Earlier work this paper cites.
J. F. Traub, G. Wasilkowski, H. Wozniakowski, and E. Novak
1994
Earlier work this paper cites.
H. W. Engl, M. Hanke, and A. Neubauer
1996
Earlier work this paper cites.
V. I. Bogachev
1998
Earlier work this paper cites.
I. E. Lagaris, A. C. Likas, and D. I. Fotiadis
1998
Earlier work this paper cites.
O. Perrin and P. Monestiez
1999
Earlier work this paper cites.
I. Babuška and J. Osborn
2000
Earlier work this paper cites.
I. E. Lagaris, A. C. Likas, and D. G. Papageorgiou
2000
Earlier work this paper cites.
X. Zhang, K. Z. Song, M. W. Lu, and X. Liu
2000
Earlier work this paper cites.
J. Friedman, T. Hastie, and R. Tibshirani
2001
Earlier work this paper cites.
M. L. Stein
2002
Earlier work this paper cites.
R. A. Adams and J. J. Fournier
2003
Earlier work this paper cites.
H. Wendland
2004
Earlier work this paper cites.
B. Djeridane and J. Lygeros
2006
Cited alongside, same era.
J. Kaipio and E. Somersalo
2006
Cited alongside, same era.
J. Nocedal and S. Wright
2006
Cited alongside, same era.
R. Schaback and H. Wendland
2006
Cited alongside, same era.
C. K. I. Williams and C. E. Rasmussen
2006
Cited alongside, same era.
J. O. Ramsay, G. Hooker, D. Campbell, and J. Cao
2007
Cited alongside, same era.
M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich
2008
Cited alongside, same era.
Z. Long, Y. Lu, X. Ma, and B. Dong
2018
Later among the works it cites.
H. Owhadi and C. Scovel
2018
Later among the works it cites.
M. Raissi, P. Perdikaris, and G. E. Karniadakis
2018
Later among the works it cites.
B. Scholkopf and A. J. Smola
2018
Later among the works it cites.
J. Sirignano and K. Spiliopoulos
2018
Later among the works it cites.
E. Weinan and B. Yu
2018
Later among the works it cites.
Y. Zhu and N. Zabaras
2018
Later among the works it cites.
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2008
Cited alongside, same era.
V. D. Rădulescu
2008
Cited alongside, same era.
A. W. van der Vaart and J. H. van Zanten
2008
Cited alongside, same era.
B. Calderhead, M. Girolami, and N. D. Lawrence
2009
Cited alongside, same era.
H. Brezis
2010
Cited alongside, same era.
2019
Later among the works it cites.
J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami
2019
Later among the works it cites.
H. Owhadi and C. Scovel
2019
Later among the works it cites.
H. Owhadi, C. Scovel, and F. Schäfer
2019
Later among the works it cites.
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Later among the works it cites.
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2019
Later among the works it cites.
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2019
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2020
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Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, A. Stuart, K. Bhattacharya, and A. Anandkumar
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M. Raissi, A. Yazdani, and G. E. Karniadakis
2020
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arXiv preprint arXiv:2004.01806, 2020
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Later among the works it cites.
L. P. Swiler, M. Gulian, A. L. Frankel, C. Safta, and J. D. Jakeman
2020
Later among the works it cites.
arXiv preprint arXiv:2002.06269, 2020
R. van der Meer, C. Oosterlee, and A. Borovykh · 2020
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arXiv preprint arXiv:2007.14527, 2020
S. Wang, X. Yu, and P. Perdikaris · 2020
Later among the works it cites.
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