ML RCUT2: Difference between revisions
No edit summary |
m (Type corrected.) |
||
| (15 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{TAGDEF| | {{DISPLAYTITLE:ML_RCUT2}} | ||
{{TAGDEF|ML_RCUT2|[real]|5.0}} | |||
Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method. The unit of the cut-off radius is <math>\AA</math>. | |||
---- | |||
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 an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{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_RCUT2}} 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 taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuracy '''and''' speed.}} | |||
For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> can improve the accuracy, | |||
== Related tags and articles == | |||
{{TAG|ML_LMLFF}}, {{TAG|ML_RCUT1}}, {{TAG|ML_W1}}, {{TAG|ML_SION1}}, {{TAG|ML_SION2}}, {{TAG|ML_MRB1}}, {{TAG|ML_MRB2}} | |||
{{sc| | {{sc|ML_RCUT1|Examples|Examples that use this tag}} | ||
---- | ---- | ||
[[Category:INCAR]][[Category:Machine | [[Category:INCAR tag]][[Category:Machine-learned force fields]] | ||
Latest revision as of 13:35, 9 May 2023
ML_RCUT2 = [real]
Default: ML_RCUT2 = 5.0
Description: This flag sets the cutoff radius [math]\displaystyle{ R_\text{cut} }[/math] for the angular descriptor [math]\displaystyle{ \rho^{(3)}_i(r) }[/math] in the machine learning force field method. The unit of the cut-off radius is [math]\displaystyle{ \AA }[/math].
The angular descriptor is constructed from
[math]\displaystyle{ \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]\displaystyle{ g\left(\mathbf{r}\right) }[/math] is an approximation of the delta function. A basis set expansion of [math]\displaystyle{ \rho^{(3)}_i(r) }[/math] yields the expansion coefficients [math]\displaystyle{ p_{n\nu l}^{i} }[/math] which are used in practice to describe the atomic environment (see this section for details). The tag ML_RCUT2 sets the cutoff radius [math]\displaystyle{ R_\text{cut} }[/math] at which the cutoff function [math]\displaystyle{ f_{\mathrm{cut}}\left(r_{ij}\right) }[/math] decays to zero.
| Mind: The cutoff radius determines how many neighbor atoms [math]\displaystyle{ N_\mathrm{a} }[/math] are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuracy and speed. |
For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 [math]\displaystyle{ \AA }[/math] (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 [math]\displaystyle{ \AA }[/math] can improve the accuracy,
Related tags and articles
ML_LMLFF, ML_RCUT1, ML_W1, ML_SION1, ML_SION2, ML_MRB1, ML_MRB2