ML LMAX2: Difference between revisions
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{{TAGDEF| | {{DISPLAYTITLE:ML_LMAX2}} | ||
{{TAGDEF|ML_LMAX2|[integer]}} | |||
{{DEF|ML_LMAX2|3|for {{TAG|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. | 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. | ||
---- | ---- | ||
To construct an atomic environment descriptor the atomic probability density | |||
<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> | |||
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): | |||
{{sc| | <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}} | |||
---- | ---- | ||
[[Category:INCAR]][[Category:Machine | [[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 [math]\displaystyle{ L_\max }[/math] 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
[math]\displaystyle{ \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]
where [math]\displaystyle{ g\left(\mathbf{r}\right) }[/math] is an approximation of the delta function, is expanded in terms of radial basis functions [math]\displaystyle{ \chi_{nl}(r) }[/math] and spherical harmonics [math]\displaystyle{ Y_{lm}\left(\hat{\mathbf{r}}\right) }[/math] (see this section for more details):
[math]\displaystyle{ \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 ML_LMAX2 specifies the maximum angular momentum quantum number [math]\displaystyle{ L_\max }[/math] of spherical harmonics used in this expansion.
| Mind: This tag is only relevant for the angular descriptor [math]\displaystyle{ \rho^{(3)}_i(r) }[/math]. The corresponding number of expansion coefficients [math]\displaystyle{ p_{n\nu l}^{i} }[/math] scales linearly with [math]\displaystyle{ L_\max }[/math] (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