ML MRB2: Difference between revisions

From VASP Wiki
No edit summary
No edit summary
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{TAGDEF|ML_MRB2|[integer]|{{TAG|ML_MRB1}}}}
{{DISPLAYTITLE:ML_MRB2}}
{{TAGDEF|ML_MRB2|[integer]|8}}


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


== Related Tags and Sections ==
<math>
{{TAG|ML_LMLFF}}, {{TAG|ML_MRB1}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT2}}, {{TAG|ML_SION2}}
\rho_{i}^{(3)}\left(r,s,\theta\right) = \iint d\hat{\mathbf{r}} d\hat{\mathbf{s}}  \delta\left(\hat{\mathbf{r}}\cdot\hat{\mathbf{s}} - \mathrm{cos}\theta\right) \sum\limits_{j=1}^{N_{a}} \sum\limits_{k \ne j}^{N_{a}} \rho_{ik} \left(r\hat{\mathbf{r}}\right) \rho_{ij} \left(s\hat{\mathbf{s}}\right), \quad \text{where} \quad
\rho_{ij}\left(\mathbf{r}\right) = 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 <math>p_{n\nu l}^{i}</math> by expanding it into a set of radial basis functions <math>\chi_{nl}(r)</math> and Legendre polynomials <math>P_{l}\left(\mathrm{cos}\theta\right)</math> (see [[Machine learning force field: Theory#Basis set expansion|this section]] for more details):
 
<math>
\rho_{i}^{(3)}\left(r,s,\theta\right) = \sum\limits_{l=1}^{L_{\mathrm{max}}} \sum\limits_{n=1}^{N^{l}_{\mathrm{R}}}\sum\limits_{\nu=1}^{N^{l}_{\mathrm{R}}} \sqrt{\frac{2l+1}{2}} p_{n\nu l}^{i}\chi_{nl}\left(r\right)\chi_{\nu l}\left(s\right)P_{l}\left(\mathrm{cos}\theta\right).
</math>
 
The tag {{TAG|ML_MRB2}} sets the number <math>N_\text{R}^l</math> of radial basis functions to use in this expansion. The same number is used for all <math>l</math>.
{{NB|mind|The number of angular descriptor expansion coefficients <math>p_{n\nu l}^{i}</math> scales '''quadratically''' with <math>N_\text{R}^l</math> set by this tag. It also depends on {{TAG|ML_LMAX2}} and the number of elements.}}
 
== Related tags and articles ==
{{TAG|ML_LMLFF}}, {{TAG|ML_LMAX2}}, {{TAG|ML_MRB1}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT2}}, {{TAG|ML_SION2}}


{{sc|ML_MRB2|Examples|Examples that use this tag}}
{{sc|ML_MRB2|Examples|Examples that use this tag}}
----
----


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

Latest revision as of 11:56, 31 March 2023

ML_MRB2 = [integer]
Default: ML_MRB2 = 8 

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


The angular 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 and Legendre polynomials (see this section for more details):

The tag ML_MRB2 sets the number of radial basis functions to use in this expansion. The same number is used for all .

Mind: The number of angular descriptor expansion coefficients scales quadratically with set by this tag. It also depends on ML_LMAX2 and the number of elements.

Related tags and articles

ML_LMLFF, ML_LMAX2, ML_MRB1, ML_W1, ML_RCUT2, ML_SION2

Examples that use this tag