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Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases
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10.1063/1.3431624
/content/aip/journal/jcp/132/20/10.1063/1.3431624
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/20/10.1063/1.3431624

Figures

Image of FIG. 1.
FIG. 1.

Definition of atom numbering, interatomic distances, and three-body angles used in the Z-matrix specification of the configuration for the electronic structure calculations.

Image of FIG. 2.
FIG. 2.

Definition of atom numbering, interatomic distances, and three-body angles used in the Z-matrix specification of the vinyl bromide configuration for the electronic structure calculations.

Tables

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Table I.

NN fitting errors to the 10 202 ab initio energies for the system as a function of the form chosen for the configuration input vector. N(h) and are the number of neurons in the NN hidden layer and the total number of weight and bias parameters, respectively (see text for explanation of the notation of the input specification and the details of the fitting procedure).

Generic image for table
Table II.

Mean absolute NN fitting errors (MAE) to the 68 302 ab initio energies for vinyl bromide as a function of the form chosen for the configuration input vector. N(h) and are the number of neurons in the NN hidden layer and the total number of weight and bias parameters, respectively (see text for explanation of the notation of the input specification and the details of the fitting procedure).

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Table III.

Root mean square NN fitting errors (RMSE) to the 15 472 ab initio energies for as a function of the form chosen for the configuration input vector. N(h) and are the number of neurons in the NN hidden layer and the total number of weight and bias parameters, respectively (see text for explanation of the notation of the input specification and the details of the fitting procedure).

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Table IV.

Root mean square NN fitting errors (RMSE) to the 21 584 ab initio energies for HONO as a function of the form chosen for the configuration input vector. N(h) and are the number of neurons in the NN hidden layer and the total number of weight and bias parameters, respectively (see text for explanation of the notation of the input specification and the details of the fitting procedure).

Generic image for table
Table V.

Percent increases in NN fitting errors observed if the input vector to the NN is comprised of inverse powers of the interparticle distances, , with n being assigned a value of 2.00 rather than being optimized. The value is the midpoint of the range of values obtained for the optimized values of n for the four systems studied. The details of the NNs employed in each case are given in Tables I–IV.

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/content/aip/journal/jcp/132/20/10.1063/1.3431624
2010-05-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/20/10.1063/1.3431624
10.1063/1.3431624
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