ML MRB1: Difference between revisions
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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_{ | 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> | <math> | ||
\rho_{i}^{(2)}\left(r\right) = \frac{1}{\sqrt{4\pi}} \sum\limits_{n=1}^{N^{0}_{\mathrm{R}}} c_{n00}^{i} \chi_{ | \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> | </math> | ||
Revision as of 12:55, 13 October 2021
ML_MRB1 = [integer]
Default: ML_MRB1 = 8
Description: This tag sets the number [math]\displaystyle{ N_\text{R}^0 }[/math] of radial basis functions used to expand the radial descriptor [math]\displaystyle{ \rho^{(2)}_i(r) }[/math] within the machine learning force field method.
The radial descriptor 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. 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]\displaystyle{ \chi_{n0}(r) }[/math] (see this section for more details):
[math]\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). }[/math]
The tag ML_MRB1 sets the number [math]\displaystyle{ N_\text{R}^0 }[/math] of radial basis functions to use in this expansion. The value of ML_MRB1 is the default value for ML_MRB2.
Related Tags and Sections
ML_LMLFF, ML_MRB2, ML_W1, ML_RCUT1, ML_SION1