ML MRB1: Difference between revisions

Latest revision as of 08:06, 9 May 2023

ML_MRB1 = [integer]
Default: ML_MRB1 = 12

Description: This tag sets the number $N_\text{R}^0$ of radial basis functions used to expand the radial descriptor $\rho^{(2)}_i(r)$ within the machine learning force field method.

The radial descriptor is constructed from

${\displaystyle \rho_{i}^{(2)}\left(r\right) = \frac{1}{4\pi} \int \rho_{i}\left(r\hat{\mathbf{r}}\right) d\hat{\mathbf{r}}, \quad \text{where} \quad \rho_{i}\left(\mathbf{r}\right) = \sum\limits_{j=1}^{N_{\mathrm{a}}} f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right) }$

and $g\left(\mathbf{r}\right)$ is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions $\chi_{n0}(r)$ (see this section for more details):

${\displaystyle \rho_{i}^{(2)}\left(r\right) = \frac{1}{\sqrt{4\pi}} \sum\limits_{n=1}^{N^{0}_{\mathrm{R}}} c_{n00}^{i} \chi_{n0}\left(r\right). }$

The tag ML_MRB1 sets the number $N_\text{R}^0$ of radial basis functions to use in this expansion.

@@ Line 1: / Line 1: @@
-{{TAGDEF|ML_MRB1|[integer]|8}}
+{{DISPLAYTITLE:ML_MRB1}}
+{{TAGDEF|ML_MRB1|[integer]|12}}
-Description: This tag sets the number <math>N_\text{R}^0</math> of radial basis functions used to expand the atomic distribution for the radial descriptor within the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors|this section]].
+Description: This tag sets the number <math>N_\text{R}^0</math> of radial basis functions used to expand the radial descriptor <math>\rho^{(2)}_i(r)</math> within the machine learning force field method.
 ----
-The value of {{TAG|ML_MRB1}} is the default value for {{TAG|ML_MRB2}}.
+The radial descriptor 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. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions <math>\chi_{n0}(r)</math> (see [[Machine learning force field: Theory#Basis set expansion|this section]] for more details):
+<math>
+\rho_{i}^{(2)}\left(r\right) = \frac{1}{\sqrt{4\pi}} \sum\limits_{n=1}^{N^{0}_{\mathrm{R}}} c_{n00}^{i} \chi_{n0}\left(r\right).
+</math>
+The tag {{TAG|ML_MRB1}} sets the number <math>N_\text{R}^0</math> of radial basis functions to use in this expansion.
+== Related tags and articles ==
-== Related Tags and Sections ==
 {{TAG|ML_LMLFF}}, {{TAG|ML_MRB2}}, {{TAG|ML_W1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_SION1}}
@@ Line 12: / Line 25: @@
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-[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]
+[[Category:INCAR tag]][[Category:Machine-learned force fields]]