ML MRB1: Difference between revisions

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{{TAGDEF|ML_FF_MRB1_MB|[integer]|{{TAG|ML_FF_MRB2_MB}}/2}}
{{TAGDEF|ML_MRB1|[integer]|8}}


Description: This tag sets the number of radial basis sets used to expand the atomic distribution for the radial descriptor within the machine learning force field method.
Description: This tag sets the number <math>N_\text{R}^0</math> of radial basis functions used to expand the radial descriptor <math>\rho^{(2)}_i(r)</math> within the machine learning force field method.
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The radial descriptor is constructed from


The value of {{TAG|ML_FF_MRB1_MB}} depends on the choice of the cut-off radius ({{TAG|ML_FF_RCUT1_MB}} and the width of the Gaussian functions used in the broadening of the atomic distributions {{TAG|ML_FF_SION1_MB}}. The error of the basis calculated on a predetermined grid is calculated on the beginning of the calculations (for details see reference {{cite|jinnouchi2:arx:2019}}).
<math>
\rho_{i}^{(2)}\left(r\right) = \frac{1}{4\pi} \int \rho_{i}\left(r\hat{\mathbf{r}}\right) d\hat{\mathbf{r}}, \quad \text{where} \quad
\rho_{i}\left(\mathbf{r}\right) = \sum\limits_{j=1}^{N_{\mathrm{a}}} f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right)
</math>


== References ==
and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions <math>\chi_{n0}(r)</math> (see [[Machine learning force field: Theory#Basis set expansion|this section]] for more details):
<references/>


<noinclude>
<math>
\rho_{i}^{(2)}\left(r\right) = \frac{1}{\sqrt{4\pi}} \sum\limits_{n=1}^{N^{0}_{\mathrm{R}}} c_{n00}^{i} \chi_{n0}\left(r\right).
</math>
 
The tag {{TAG|ML_MRB1}} sets the number <math>N_\text{R}^0</math> of radial basis functions to use in this expansion. The value of {{TAG|ML_MRB1}} is the default value for {{TAG|ML_MRB2}}.
   
   
== Related Tags and Sections ==
== Related Tags and Sections ==
{{TAG|ML_FF_LMLFF}}, {{TAG|ML_FF_MRB2_MB}}, {{TAG|ML_FF_W1_MB}}, {{TAG|ML_FF_W2_MB}}
{{TAG|ML_LMLFF}}, {{TAG|ML_MRB2}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_SION1}}


{{sc|ML_FF_MRB1_MB|Examples|Examples that use this tag}}
{{sc|ML_MRB1|Examples|Examples that use this tag}}
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[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]
[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]

Revision as of 12:55, 13 October 2021

ML_MRB1 = [integer]
Default: ML_MRB1 = 8 

Description: This tag sets the number of radial basis functions used to expand the radial descriptor within the machine learning force field method.


The radial descriptor is constructed from

and is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions (see this section for more details):

The tag ML_MRB1 sets the number of radial basis functions to use in this expansion. The value of ML_MRB1 is the default value for ML_MRB2.

Related Tags and Sections

ML_LMLFF, ML_MRB2, ML_W1, ML_RCUT1, ML_SION1

Examples that use this tag