A common feature in computations of chemical and physical properties is the investigation of phenomena at different levels of computational accuracy. Less accurate computations are used to provide a relatively quick understanding of the behavior of a system and allow a researcher to focus on regions of initial conditions and parameter space where interesting phenomena are likely to occur. These inexpensive calculations are often discarded when more accurate calculations are performed. This paper demonstrates how computations at different levels of accuracy can be simultaneously incorporated to study chemical and physical phenomena with less overall computational effort than the most expensive level of computation. A smaller set of computationally expensive calculations is needed because the set of expensive calculations is correlated with the larger set of less expensive calculations. We present two applications. First, we demonstrate how potential energy surfaces can be fit by simultaneously using results from two different levels of accuracy in electronic structure calculations. In the second application, we study the optical response of metallic nanostructures. The optical response is generated with calculations at two different grid resolutions, and we demonstrate how using these two levels of computation in a correlated fashion can more efficiently optimize the response.

1.
T.
Yan
,
W. L.
Hase
, and
C.
Doubleday
,
J. Chem. Phys.
120
,
9253
(
2004
).
2.
R. L.
Miller
,
Z.
Xie
,
S.
Leyffer
,
M. J.
Davis
, and
S. K.
Gray
,
J. Phys. Chem. C
114
,
20741
(
2010
).
3.
J. M.
Montgomery
,
T. W.
Lee
, and
S. K.
Gray
,
J. Phys.: Condens. Matter
20
,
323201
(
2008
).
4.
A. I. J.
Forrester
,
A.
Sobester
, and
A. J.
Keane
,
Engineering Design via Surrogate Modeling: A Practical Guide
(
Wiley
,
Hoboken
,
2008
).
5.
A. I. J.
Forrester
,
A.
Sobester
, and
A. J.
Keane
,
Proc. Roy. Soc. A
463
,
3251
(
2007
).
6.
S.
Kirkpatrick
,
C. D.
Gelatt
, and
M. P.
Vecchi
,
Science
220
,
671
(
1983
).
7.
D. G.
Krige
,
J. Chem. Metall. Min. Soc. South Africa
52
,
119
(
1951
).
8.
C. M.
Handley
,
G. I.
Hawe
,
D. B.
Kell
, and
P. L. A.
Popelier
,
Phys. Chem. Chem. Phys
11
,
6365
(
2009
).
9.
A. P.
Bartok
,
M. C.
Payne
,
R.
Kondor
, and
G.
Csanyi
,
Phys. Rev. Lett.
104
,
136403
(
2010
).
10.
M. C.
Kennedy
and
A.
O’Hagan
,
Biometrika
87
,
1
(
2000
).
11.
S. R.
Yates
and
A. W.
Warrick
,
Soil Sci. Soc. Am. J.
51
,
23
(
1987
).
12.
Z. H.
Han
,
R.
Zimmermann
, and
S.
Gortz
, AIAA Paper No. 2010-1225,
2010
.
13.
J.
Sacks
,
W. J.
Welch
,
T. J.
Mitchell
, and
H. P.
Wynn
,
Stat. Sci.
4
,
409
(
1989
).
14.
C. E.
Rassmussen
and
C. K. I.
Williams
,
Gaussian Processes for Machine Learning
(
MIT
,
Cambridge
,
2006
).
15.
D. R.
Jones
,
J. Global Optim.
21
,
345
(
2001
).
16.
M. D.
Mackay
,
R. J.
Beckman
, and
W. J.
Conover
,
Technometrics
21
,
239
(
1979
).
17.
M.
Johnson
,
L.
Moore
, and
D.
Ylvisaker
,
J. Stat. Plan. Infer.
26
,
131
(
1990
).
18.
E.
van Dam
,
D.
den Hertog
,
B.
Husslage
, and
G.
Rennen
, Department of Econometrics and Operations Research, Tilburg University, Netherlands; see http://www.spacefillingdesigns.nl.
19.
W. J.
Welch
,
R. J.
Buck
,
J.
Sacks
,
H. P.
Wynn
,
T. J
Mitchell
, and
M. D.
Morris
,
Technometrics
34
,
15
(
1992
).
20.
M.
Abramowitz
and
I. A.
Stegun
,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
(
Dover
,
New York
,
1972
).
21.
S. N.
Lophaven
,
H. B.
Nielsen
, and
J.
Sondergaard
, DACE – A Matlab Kriging Toolbox, Version 2.0; Report IMM-REP-2002-12, Technical University of Denmark,
2002
.
22.
D.
Townsend
,
S. A.
Lahankar
,
S. K.
Lee
,
S. D.
Chambreau
,
A. G.
Suits
,
X.
Zhang
,
J.
Rheinecker
,
L. B.
Harding
, and
J. M.
Bowman
,
Science
306
,
1158
(
2004
).
23.
L. B.
Harding
,
S. J.
Klippenstein
, and
A. W.
Jasper
,
Phys. Chem. Chem. Phys.
9
,
4055
(
2007
).
24.
R. A.
Kendall
,
T. H.
Dunning
 Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
25.
P.
Celani
and
H.-J
Werner
,
J. Chem. Phys.
112
,
5546
(
2000
).
26.
H.-J.
Werner
,
P. J.
Knowles
,
R.
Lindh
,
F. R.
Manby
,
M.
Schütz
 et al, MOLPRO version 2006.1, a package of ab initio programs, 2006, see http://www.molpro.net.
27.
R.
Dawes
,
D. L.
Thompson
,
Y.
Guo
,
A. F.
Wagner
, and
M.
Minkoff
,
J. Chem. Phys.
126
,
184108
(
2007
).
28.
K. S.
Yee
,
IEEE Trans. Antennas Propag.
14
,
302
(
1966
).
29.
J. P.
Berenger
,
J. Comput. Phys.
114
,
185
(
1994
).
30.
Reference Guide for FDTD Solutions™ Release 6.5, 2009; see http://www.lumerical.com/fdtd.
31.
P. B.
Johnson
and
R. W.
Christy
,
Phys. Rev. B
6
,
4370
(
1972
).
32.
S. H.
Chang
,
S. K.
Gray
, and
G. C.
Schatz
,
Opt. Express
13
,
3150
(
2005
).
33.
M.
Schmeits
,
Solid State Commun.
67
,
169
(
1988
).
34.
J.
Prikulis
,
P.
Hanarp
,
L.
Olofsson
,
D.
Sutherland
, and
M.
Kall
,
Nano Lett.
4
,
1003
(
2004
).
35.
T.
Park
,
N.
Mirin
,
J.
Lassiter
,
C.
Nehl
,
N.
Halas
, and
P.
Nordlander
,
ACS Nano
2
,
25
(
2008
).
36.
W. J.
Welch
,
R. J.
Buck
,
J.
Sacks
,
H. P.
Wynn
,
T. J.
Mitchell
, and
M. D.
Morris
,
Technometrics
34
,
15
(
1992
).
37.
M.
Schonlau
and
W. J.
Welch
, in
Screening Methods for Experimentation in Industry, Drug Discovery, and Genetics
, edited by
A.
Dean
and
S.
Lewis
(
Springer
,
New York
,
2006
), pp.
308
327
.
38.
C. J.
Paciorek
and
M. J.
Schervish
, in
Advances in Neural Information Processing Systems 16
, edited by
S.
Thrun
,
K.
Saul
, and
B.
Scholkopf
(
MIT Press
,
Cambridge, MA
,
2004
), pp.
273–280
.
39.
C. J.
Paciorek
and
M. J.
Schervish
,
Environmetrics
17
,
483
(
2006
).
40.
R. B.
Gramacy
,
J. Stat. Software
19
(
9
),
1
(
2007
).
41.
C. M.
Bishop
,
Neural Networks for Pattern Recognition
(
Oxford University Press
,
Oxford
,
1995
), Chaps. 5 and 9.
42.
R.
Jin
,
W.
Chen
, and
T. W.
Simpson
,
Struct. Multidiscip. Optim.
23
,
1
(
2001
).
43.
J.
Behler
and
M.
Parrinello
,
Phys. Rev. Lett.
98
,
146401
(
2007
).
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