ML SION1: Difference between revisions

Latest revision as of 13:31, 8 April 2022

ML_SION1 = [real]
Default: ML_SION1 = 0.5

Description: This tag specifies the width $\sigma_\text{atom}$ of the Gaussian functions used for broadening the atomic distributions of 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 the following approximation of the delta function:

${\displaystyle g\left(\mathbf{r}\right)=\frac{1}{\sqrt{2\sigma_{\mathrm{atom}}\pi}}\mathrm{exp}\left(-\frac{|\mathbf{r}|^{2}}{2\sigma_{\mathrm{atom}}^{2}}\right). }$

The tag ML_SION1 sets the width $\sigma_\text{atom}$ of the above Gaussian function (see this section for more details).

Tip: Our test calculations indicate that ML_SION1 = ML_SION2 results in an optimal training performance. Furthermore, a value of 0.5 was found to be a good default value for both. However, the best choice is somewhat system-dependent. For instance, a smaller value for ML_SION1 can increase the number of local reference configurations, and hence ultimately the quality of the MLFF. See also here.

The unit of ML_SION1 is $\AA$ .

@@ Line 1: / Line 1: @@
-{{TAGDEF|ML_FF_SION1_MB|[real]|0.333}}
+{{DISPLAYTITLE:ML_SION1}}
+{{TAGDEF|ML_SION1|[real]|0.5}}
-Description: This tag specifies the width of the Gaussian functions used for broadening the atomic distributions for the radial descriptor within the machine learning force field method.
+Description: This tag specifies the width <math>\sigma_\text{atom}</math> of the Gaussian functions used for broadening the atomic distributions of the radial descriptor <math>\rho^{(2)}_i(r)</math> within the machine learning force field method.
 ----
+The radial descriptor is constructed from
-The unit of {{TAG|ML_FF_SION1_MB}} is in <math>\AA</math>.
+<math>
-Test calculations showed that a 1.5 smaller value for the broadening of the radial descriptor compared to the angular descriptor (see {{TAG|ML_FF_SION2_MB}}) gives optimal results.
+\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
-This tag is not used if {{TAG|ML_FF_IBROAD1_MB}}=1 (which is not the default).
+\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>
-== Related Tags and Sections ==
+and <math>g\left(\mathbf{r}\right)</math> is the following approximation of the delta function:
-{{TAG|ML_FF_LMLFF}}, {{TAG|ML_FF_SION2_MB}}, {{TAG|ML_FF_IBROAD1_MB}}, {{TAG|ML_FF_IBROAD2_MB}}
-{{sc|ML_FF_SION1_MB|Examples|Examples that use this tag}}
+<math>
+g\left(\mathbf{r}\right)=\frac{1}{\sqrt{2\sigma_{\mathrm{atom}}\pi}}\mathrm{exp}\left(-\frac{|\mathbf{r}|^{2}}{2\sigma_{\mathrm{atom}}^{2}}\right).
+</math>
+The tag {{TAG|ML_SION1}} sets the width <math>\sigma_\text{atom}</math> of the above Gaussian function (see [[Machine learning force field: Theory#Descriptors|this section]] for more details).
+{{BOX|tip|Our test calculations indicate that {{TAG|ML_SION1}} {{=}} {{TAG|ML_SION2}} results in an optimal training performance. Furthermore, a value of 0.5 was found to be a good default value for both. However, the best choice is somewhat system-dependent. For instance, a smaller value for {{TAG|ML_SION1}} can increase the number of local reference configurations, and hence ultimately the quality of the MLFF. See also [[Machine learning force field calculations: Basics#Accurate force fields|here]].
+}}
+The unit of {{TAG|ML_SION1}} is <math>\AA</math>.
+== Related tags and articles ==
+{{TAG|ML_LMLFF}}, {{TAG|ML_SION2}}, {{TAG|ML_RCUT1}}, {{TAG|ML_RCUT2}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}}
+{{sc|ML_SION1|Examples|Examples that use this tag}}
 ----
-[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]
+[[Category:INCAR tag]][[Category:Machine-learned force fields]]