ML RCUT1: Difference between revisions
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{{TAGDEF|ML_RCUT1|[real]| | {{DISPLAYTITLE:ML_RCUT1}} | ||
{{TAGDEF|ML_RCUT1|[real]|8.0}} | |||
Description: | Description: Sets the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_i(r)</math> in <math>\AA</math>. | ||
---- | ---- | ||
The radial descriptor for machine-learned force fields 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. A basis set expansion of <math>\rho^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{i}</math>, which are used in practice to describe the atomic environment; refer to the [[Machine learning force field: Theory#Descriptors|theory of machine-learned force fields]] for details. The tag {{TAG|ML_RCUT1}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero. | |||
{{NB|mind|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are considered to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is too small. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent. Therefore, different values should be tested to achieve satisfying accuracy '''and''' speed.}} | |||
The unit of the cut-off radius is <math>\AA</math>. | The unit of the cut-off radius is <math>\AA</math>. | ||
== Related | == Related tags and articles == | ||
{{TAG|ML_LMLFF}}, {{TAG|ML_RCUT2}}, {{TAG|ML_W1}}, {{TAG|ML_SION1}}, {{TAG|ML_SION2}} | {{TAG|ML_LMLFF}}, {{TAG|ML_RCUT2}}, {{TAG|ML_W1}}, {{TAG|ML_SION1}}, {{TAG|ML_SION2}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}} | ||
{{sc|ML_RCUT1|Examples|Examples that use this tag}} | {{sc|ML_RCUT1|Examples|Examples that use this tag}} | ||
---- | ---- | ||
[[Category:INCAR]][[Category:Machine | [[Category:INCAR tag]][[Category:Machine-learned force fields]] | ||
Latest revision as of 06:34, 11 May 2023
ML_RCUT1 = [real]
Default: ML_RCUT1 = 8.0
Description: Sets the cutoff radius [math]\displaystyle{ R_\text{cut} }[/math] for the radial descriptor [math]\displaystyle{ \rho^{(2)}_i(r) }[/math] in [math]\displaystyle{ \AA }[/math].
The radial descriptor for machine-learned force fields is constructed from
[math]\displaystyle{ \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]\displaystyle{ g\left(\mathbf{r}\right) }[/math] is an approximation of the delta function. A basis set expansion of [math]\displaystyle{ \rho^{(2)}_i(r) }[/math] yields the expansion coefficients [math]\displaystyle{ c_{n00}^{i} }[/math], which are used in practice to describe the atomic environment; refer to the theory of machine-learned force fields for details. The tag ML_RCUT1 sets the cutoff radius [math]\displaystyle{ R_\text{cut} }[/math] at which the cutoff function [math]\displaystyle{ f_{\mathrm{cut}}\left(r_{ij}\right) }[/math] decays to zero.
| Mind: The cutoff radius determines how many neighbor atoms [math]\displaystyle{ N_\mathrm{a} }[/math] are considered to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is too small. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent. Therefore, different values should be tested to achieve satisfying accuracy and speed. |
The unit of the cut-off radius is [math]\displaystyle{ \AA }[/math].
Related tags and articles
ML_LMLFF, ML_RCUT2, ML_W1, ML_SION1, ML_SION2, ML_MRB1, ML_MRB2