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Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks
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10.1063/1.3095491
/content/aip/journal/jcp/130/13/10.1063/1.3095491
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/13/10.1063/1.3095491

Figures

Image of FIG. 1.
FIG. 1.

Schematic of a two-layer NN.

Image of FIG. 2.
FIG. 2.

coordinate labels.

Image of FIG. 3.
FIG. 3.

Histogram of number of configurations stored and corresponding maximum acceleration when the configurations are stored at equally spaced time intervals. Acceleration is given in units of , where one atomic time unit (atu) is .

Image of FIG. 4.
FIG. 4.

Histogram of a number of configurations stored and corresponding maximum acceleration when the time interval for sampling is obtained from Eqs. (24) and (25). Acceleration is given in units of , where one atomic time unit (atu) is .

Image of FIG. 5.
FIG. 5.

Data sampling and location of the discontinuity in the Sudhakaran–Raff analytic potential denoted as surface I in Ref. 33. The curve in the figure shows the location of the discontinuity.

Image of FIG. 6.
FIG. 6.

Comparison of Sudhakaran–Raff energies with the predictions of the median NN for a test set of configurations.

Image of FIG. 7.
FIG. 7.

Distribution of interpolation errors in the potential for the median NN.

Image of FIG. 8.
FIG. 8.

Comparison of Sudhakaran–Raff forces with the predictions of the median NN for a test set of configurations.

Image of FIG. 9.
FIG. 9.

Distribution of interpolation errors in the force for the median NN.

Image of FIG. 10.
FIG. 10.

Difference between bond distances computed using the analytical potential and the NN during the MD simulation vs time integration steps of 0.1 fs.

Image of FIG. 11.
FIG. 11.

Difference between energies computed using the analytical potential and the NN during the MD simulation vs time integration steps of 0.1 fs.

Tables

Generic image for table
Table I.

rms test set errors for Bayesian regularization and CFDA for ten different NNs.

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Table II.

Median rms test set errors for Bayesian regularization and CFDA. Training set contains 3000 data points. Test set contains data points. The potential errors are expressed in eV and the force errors are expressed in eV/Å.

Generic image for table
Table III.

Median rms test set errors for Bayesian regularization and CFDA. Training set contains 1500 data points. Test set contains data points. The potential errors are expressed in eV and the force errors are expressed in eV/Å.

Generic image for table
Table IV.

Median rms test set errors for Bayesian regularization and CFDA. Training set contains 750 data points. Test set contains data points. The potential errors are expressed in eV and the force errors are expressed in eV/Å.

Generic image for table
Table V.

Reaction yields out of 1000 trajectories at 1.2 eV.

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/content/aip/journal/jcp/130/13/10.1063/1.3095491
2009-04-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/13/10.1063/1.3095491
10.1063/1.3095491
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