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Development of generalized potential-energy surfaces using many-body expansions, neural networks, and moiety energy approximations
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10.1063/1.3124802
/content/aip/journal/jcp/130/18/10.1063/1.3124802
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/18/10.1063/1.3124802

Figures

Image of FIG. 1.
FIG. 1.

Flow chart for the general many-body expansion/NN fitting algorithm.

Image of FIG. 2.
FIG. 2.

Flow chart for the many-body expansion/NN fitting algorithm for the specific case of clusters with the expansion truncated after the three-body terms.

Image of FIG. 3.
FIG. 3.

Distribution of fitting errors for , , and clusters with four-body terms included in the many-body expansion. The mean absolute testing set error is 0.0056 eV. With the database covering an energy range of about 6 eV, the error corresponds to a fitting accuracy of about 0.093%.

Image of FIG. 4.
FIG. 4.

Comparison of the fitted energies obtained using Eq. (1) with the NNs specified under calculation 1 in Table II with the ab initio DFT energies for clusters. If the fitting were perfect, all points would fall on the 45° line in the figure. The mean absolute testing set error is 0.0353 eV, which corresponds to a mean percent testing set error of 0.21%.

Image of FIG. 5.
FIG. 5.

Distribution of fitting errors for clusters when the many-body expansion is truncated after the four-body term and the NNs are those described under calculation 1 in Table II. The mean absolute testing set error is 0.0353 eV, which corresponds to a mean percent error of 0.21%.

Image of FIG. 6.
FIG. 6.

Comparison of the fitted energies obtained using Eq. (1) with the NNs specified under fit 1 in Table III with the ab initio UMP4(SDQ) energies for the vinyl bromide database. If the fitting were perfect, all points would fall on the 45° line in the figure. The mean absolute testing set error is 0.0808 eV, which corresponds to a mean percent error of 1.01%.

Image of FIG. 7.
FIG. 7.

Distribution of testing set errors for the vinyl bromide database when the many-body expansion is truncated after the four-body term and the NNs are those described under fit 1 in Table III. The mean absolute testing set error is 0.0808 eV, which corresponds to a mean percent error of 1.01%.

Tables

Generic image for table
Table I.

Number of configurations of each of the clusters in the training set.

Generic image for table
Table II.

NN specifications for the many-body expansions for clusters. Errors are given in eV. denotes the mean absolute testing set error. The entry labeled % error is , where range is the total energy range spanned by the database employed in the fitting of the potential. The entry labeled No. of parameters gives the total number of weight and bias parameters contained in the three NNs.

Generic image for table
Table III.

Many-body expansion/NN/ME results for two different network architectures for fitting the vinyl bromide database. Testing set errors are given in eV.

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/content/aip/journal/jcp/130/18/10.1063/1.3124802
2009-05-11
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Development of generalized potential-energy surfaces using many-body expansions, neural networks, and moiety energy approximations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/18/10.1063/1.3124802
10.1063/1.3124802
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