ML MRB1: Difference between revisions

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{{TAGDEF|ML_MRB1|[integer]|8}}
{{DISPLAYTITLE:ML_MRB1}}
{{TAGDEF|ML_MRB1|[integer]|12}}


Description: This tag sets the number <math>N_\text{R}^0</math> of radial basis functions used to expand the atomic distribution for the radial descriptor within the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors|this section]].
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 value of {{TAG|ML_MRB1}} is the default value for {{TAG|ML_MRB2}}.
The radial descriptor is constructed from
 
<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>
 
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):
 
<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.
   
   
 
== Related tags and articles ==
== Related Tags and Sections ==
{{TAG|ML_LMLFF}}, {{TAG|ML_MRB2}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_SION1}}
{{TAG|ML_LMLFF}}, {{TAG|ML_MRB2}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_SION1}}


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[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]
[[Category:INCAR tag]][[Category:Machine-learned force fields]]

Latest revision as of 08:06, 9 May 2023

ML_MRB1 = [integer]
Default: ML_MRB1 = 12 

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.

Related tags and articles

ML_LMLFF, ML_MRB2, ML_W1, ML_RCUT1, ML_SION1

Examples that use this tag