ML LMAX2: Difference between revisions
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{{DISPLAYTITLE:ML_LMAX2}} | {{DISPLAYTITLE:ML_LMAX2}} | ||
{{TAGDEF|ML_LMAX2|[integer]}} | {{TAGDEF|ML_LMAX2|[integer]}} | ||
{{DEF|ML_LMAX2| | {{DEF|ML_LMAX2|3|for {{TAG|ML_LAFILT2}} {{=}} .TRUE.|6|else}} | ||
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. | 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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The tag {{TAG|ML_LMAX2}} specifies the maximum angular momentum quantum number <math>L_\max</math> of spherical harmonics used in this expansion. | 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> and is also depending on {{TAG|ML_MRB2}} and the number of elements present.}} | {{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}}= | 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 == | == Related tags and articles == | ||
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---- | ---- | ||
[[Category:INCAR tag]][[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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle L_\max} 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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\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), }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle g\left(\mathbf{r}\right)} is an approximation of the delta function, is expanded in terms of radial basis functions Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \chi_{nl}(r)} and spherical harmonics Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle Y_{lm}\left(\hat{\mathbf{r}}\right)} (see this section for more details):
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \rho _{{i}}\left({\mathbf {r}}\right)=\sum \limits _{{l=1}}^{{L_{{{\mathrm {max}}}}}}\sum \limits _{{m=-l}}^{{l}}\sum \limits _{{n=1}}^{{N_{{{\mathrm {R}}}}^{{l}}}}c_{{nlm}}^{{i}}\chi _{{nl}}\left(r\right)Y_{{lm}}\left({\hat {{\mathbf {r}}}}\right),
The tag ML_LMAX2 specifies the maximum angular momentum quantum number Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle L_\max} of spherical harmonics used in this expansion.
| Mind: This tag is only relevant for the angular descriptor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \rho^{(3)}_i(r)} . The corresponding number of expansion coefficients Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): p_{{n\nu l}}^{{i}} scales linearly with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle L_\max} (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