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Interpolating moving least-squares methods for fitting potential-energy surfaces: Further improvement of efficiency via cutoff strategies
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10.1063/1.2162171
/content/aip/journal/jcp/124/5/10.1063/1.2162171
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/5/10.1063/1.2162171

Figures

Image of FIG. 1.
FIG. 1.

The behavior of [Eq. (27)] for , 5, and 10.

Image of FIG. 2.
FIG. 2.

A demonstration of the continuity of gradients obtained by the method (solid curve) and the DAC method (dashed curve). Panels (a) and (b) show, respectively, the gradient element and the cutoff radius as functions of the distance .

Image of FIG. 3.
FIG. 3.

The rms errors as functions of for the Kuhn et al. (Ref. 18) potential and its gradient fitted by IMLS with a plain weight function (dashed line) and with cutoff weight functions using the FRC [panels (a) and (b)] and DAC [panels (c) and (d)] methods with selected (FRC) and (DAC) parameters, respectively. The default values were used for other parameters ( and ).

Image of FIG. 4.
FIG. 4.

The rms errors as functions of for the Kuhn et al. (Ref. 18) potential and its gradient fitted by IMLS with a plain weight function (dashed line) and with cutoff weight functions using the FRC [panels (a) and (b)] and DAC [panels (c) and (d)] methods with selected (FRC) and (DAC) parameters, respectively. The default values were used for other parameters ( and ).

Image of FIG. 5.
FIG. 5.

The rms errors as functions of for the Kuhn et al. (Ref. 18) potential and its gradient fitted by IMLS with a plain weight function (dashed line) and with cutoff weight functions using the FRC [panels (a) and (b)] and DAC [panels (c) and (d)] methods with selected (FRC) and (DAC) parameters, respectively. The default values were used for other parameters (, , and ).

Image of FIG. 6.
FIG. 6.

The [panel (a)] and [panel (b)] errors and the average number of ab initio points included by the cutoff [panel (c)] vs parameter for the IMLS fits of the Kuhn et al. (Ref. 18) potential employing a plain weight function (dashed line) and DAC cutoff weight functions with selected parameters. The default values were used for other parameters , , and ).

Image of FIG. 7.
FIG. 7.

Characteristics of the IMLS fits employing a plain weight function (dashed line) and the FRC [panels (a)–(d)], and DAC [panels (e)–(h)] cutoff procedures tested for the Kuhn et al. (Ref. 18) potential. The default values were used for all parameters (, , and ). Characteristics displayed are in panels (a) and (e), in panels (b) and (f), the average number of ab initio points included by the cutoff in panels (c) and (g), and the ratio of the computational time of the cutoff procedure relative to standard or no-cutoff procedure in panels ((d) and (h)). For the meaning of hollow or filled symbols, see the text.

Image of FIG. 8.
FIG. 8.

The rms errors for the potential energy and its gradient vs the computational time relative to standard or no-cutoff procedure for the FRC and DAC methods.

Tables

Generic image for table
Table I.

Relationship between two parameters with fitting accuracy. (See text for details.)

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/content/aip/journal/jcp/124/5/10.1063/1.2162171
2006-02-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interpolating moving least-squares methods for fitting potential-energy surfaces: Further improvement of efficiency via cutoff strategies
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/5/10.1063/1.2162171
10.1063/1.2162171
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