ML LMAX2: Difference between revisions

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{{TAGDEF|ML_FF_LMAX2_MB|[integer]|6}}
{{DISPLAYTITLE:ML_LMAX2}}
{{TAGDEF|ML_LMAX2|[integer]}}
{{DEF|ML_LMAX2|3|for {{TAG|ML_LAFILT2}} {{=}} .TRUE.|6|else}}


Description:
Description: This tag specifies the maximum angular momentum quantum number <math>L_\max</math> of spherical harmonics used to expand atomic distributions within the machine learning force field method.
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To construct an atomic environment descriptor the atomic probability density


== Related Tags and Sections ==
<math>
\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>


{{sc|ML_FF_LMAX2_MB|Examples|Examples that use this tag}}
where <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function, is expanded in terms of radial basis functions <math>\chi_{nl}(r)</math> and spherical harmonics <math>Y_{lm}\left(\hat{\mathbf{r}}\right)</math> (see [[Machine learning force field: Theory#Basis set expansion|this section]] for more details):
 
<math>
\rho_{i} \left( \mathbf{r} \right) = \sum\limits_{l=1}^{L_{\mathrm{max}}} \sum\limits_{m=-l}^{l} \sum\limits_{n=1}^{N^{l}_{ \mathrm{R}}} c_{nlm}^{i}\chi_{nl} \left( r \right) Y_{lm} \left( \hat{\mathbf{r}} \right),
</math>
 
The tag {{TAG|ML_LMAX2}} specifies the maximum angular momentum quantum number <math>L_\max</math> of spherical harmonics used in this expansion.
{{NB|mind|This tag is only relevant for the angular descriptor <math>\rho^{(3)}_i(r)</math>. The corresponding number of expansion coefficients <math>p_{n\nu l}^{i}</math> scales '''linearly''' with <math>L_\max</math> (however the calculation of the spherical harmonics scales quadratically) and is also depending on {{TAG|ML_MRB2}} and the number of elements present.}}
 
By default an angular filtering (see {{TAG|ML_LAFILT2}} and {{TAG|ML_IAFILT2}}) with a filtering parameter of {{TAG|ML_AFILT2}}=0.002 is used where a value of {{TAG|ML_LMAX2}}=3 is perfectly safe for most applications. If you need to improve the accuracy, you might also try to increase it to {{TAG|ML_LMAX2}}=4. If the angular filter is switched off, we recommend to use a value of {{TAG|ML_LMAX2}}=6 (this is then the default value).
 
== Related tags and articles ==
{{TAG|ML_LMLFF}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}}, {{TAG|ML_LAFILT2}}, {{TAG|ML_IAFILT2}}, {{TAG|ML_AFILT2}}
 
{{sc|ML_LMAX2|Examples|Examples that use this tag}}
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----


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

Latest revision as of 08:11, 9 May 2023

ML_LMAX2 = [integer] 

Default: ML_LMAX2 = 3 for ML_LAFILT2 = .TRUE.
= 6 else

Description: This tag specifies the maximum angular momentum quantum number of spherical harmonics used to expand atomic distributions within the machine learning force field method.


To construct an atomic environment descriptor the atomic probability density

where is an approximation of the delta function, is expanded in terms of radial basis functions and spherical harmonics (see this section for more details):

The tag ML_LMAX2 specifies the maximum angular momentum quantum number of spherical harmonics used in this expansion.

Mind: This tag is only relevant for the angular descriptor . The corresponding number of expansion coefficients scales linearly with (however the calculation of the spherical harmonics scales quadratically) and is also depending on ML_MRB2 and the number of elements present.

By default an angular filtering (see ML_LAFILT2 and ML_IAFILT2) with a filtering parameter of ML_AFILT2=0.002 is used where a value of ML_LMAX2=3 is perfectly safe for most applications. If you need to improve the accuracy, you might also try to increase it to ML_LMAX2=4. If the angular filter is switched off, we recommend to use a value of ML_LMAX2=6 (this is then the default value).

Related tags and articles

ML_LMLFF, ML_MRB1, ML_MRB2, ML_LAFILT2, ML_IAFILT2, ML_AFILT2

Examples that use this tag