ML SION2: Difference between revisions

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{{TAGDEF|ML_SION2|[real]|1.5*{{TAG|ML_SION1}}}}
{{DISPLAYTITLE:ML_SION2}}
{{TAGDEF|ML_SION2|[real]|{{TAG|ML_SION1}}}}


Description: This tag specifies the width <math>\sigma_\text{atom}</math> of the Gaussian functions used for broadening the atomic distributions of the angular descriptor <math>\rho^{(3)}_i(r)</math> within the machine learning force field method (see [[Machine learning force field: Theory#Descriptors|this section]]).
Description: This tag specifies the width <math>\sigma_\text{atom}</math> of the Gaussian functions used for broadening the atomic distributions of the angular descriptor <math>\rho^{(3)}_i(r)</math> within the machine learning force field method.
----
----
The angular descriptor is constructed from
<math>
\rho_{i}^{(3)}\left(r,s,\theta\right) = \iint d\hat{\mathbf{r}} d\hat{\mathbf{s}}  \delta\left(\hat{\mathbf{r}}\cdot\hat{\mathbf{s}} - \mathrm{cos}\theta\right) \sum\limits_{j=1}^{N_{a}} \sum\limits_{k \ne j}^{N_{a}} \rho_{ik} \left(r\hat{\mathbf{r}}\right) \rho_{ij} \left(s\hat{\mathbf{s}}\right), \quad \text{where} \quad
\rho_{ij}\left(\mathbf{r}\right) = 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 the following approximation of the delta function:
<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_SION2}} 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 system-dependent, careful testing may improve machine learning results.}}
The unit of {{TAG|ML_SION2}} is <math>\AA</math>.
The unit of {{TAG|ML_SION2}} is <math>\AA</math>.
{{BOX|tip|Our test calculations indicate that a ratio {{TAG|ML_SION2}} / {{TAG|ML_SION1}} {{=}} 1.5 results in an optimal training performance. Furthermore, a value of 0.5 was found to be a good default value for {{TAG|ML_SION2}}. Both findings together result in the default value for {{TAG|ML_SION1}}.|Background:}}


== Related Tags and Sections ==
== Related tags and articles ==
{{TAG|ML_LMLFF}}, {{TAG|ML_SION1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_RCUT2}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}}
{{TAG|ML_LMLFF}}, {{TAG|ML_SION1}}, {{TAG|ML_RCUT1}}, {{TAG|ML_RCUT2}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}}


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[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]
[[Category:INCAR tag]][[Category:Machine-learned force fields]]

Latest revision as of 13:31, 8 April 2022

ML_SION2 = [real]
Default: ML_SION2 = ML_SION1 

Description: This tag specifies the width of the Gaussian functions used for broadening the atomic distributions of the angular descriptor within the machine learning force field method.


The angular descriptor is constructed from

and is the following approximation of the delta function:

The tag ML_SION2 sets the width 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 system-dependent, careful testing may improve machine learning results.

The unit of ML_SION2 is .

Related tags and articles

ML_LMLFF, ML_SION1, ML_RCUT1, ML_RCUT2, ML_MRB1, ML_MRB2

Examples that use this tag