ML RCUT1: Difference between revisions

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].

@@ Line 1: / Line 1: @@
-{{TAGDEF|ML_FF_RCUT1_MB|[logical]|{{TAG|}ML_FF_RCUT2_MB}}}
+{{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
-== Related Tags and Sections ==
+<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>
-{{sc|ML_FF_RCUT1_MB|Examples|Examples that use this tag}}
+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>.
+== Related tags and articles ==
+{{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}}
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-[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]]
+[[Category:INCAR tag]][[Category:Machine-learned force fields]]