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 $R_\text{cut}$ for the radial descriptor $\rho^{(2)}_i(r)$ in $\AA$ .

The radial descriptor for machine-learned force fields 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. A basis set expansion of $\rho^{(2)}_i(r)$ yields the expansion coefficients $c_{n00}^{i}$ , 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 $R_\text{cut}$ at which the cutoff function $f_{\mathrm{cut}}\left(r_{ij}\right)$ decays to zero.

Mind: The cutoff radius determines how many neighbor atoms

N_\mathrm{a}

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 $\AA$ .

@@ Line 11: / Line 11: @@
 </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 (see [[Machine learning force field: Theory#Descriptors|this section]] 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.
+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.}}

Latest revision as of 06:34, 11 May 2023

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