ML RCUT2: Difference between revisions

Latest revision as of 13:35, 9 May 2023

ML_RCUT2 = [real]
Default: ML_RCUT2 = 5.0

Description: This flag sets the cutoff radius $R_\text{cut}$ for the angular descriptor $\rho^{(3)}_i(r)$ in the machine learning force field method. The unit of the cut-off radius is $\AA$ .

The angular descriptor is constructed from

${\displaystyle \rho_{i}^{(3)}\left(r,s,\theta\right) = \iint d\hat{\mathbf{r}} d\hat{\mathbf{s}} \delta\left(\hat{\mathbf{r}}\cdot\hat{\mathbf{s}} - \mathrm{cos}\theta\right) \sum\limits_{j=1}^{N_{a}} \sum\limits_{k \ne j}^{N_{a}} \rho_{ik} \left(r\hat{\mathbf{r}}\right) \rho_{ij} \left(s\hat{\mathbf{s}}\right), \quad \text{where} \quad \rho_{ij}\left(\mathbf{r}\right) = f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right) }$

and $g\left(\mathbf{r}\right)$ is an approximation of the delta function. A basis set expansion of $\rho^{(3)}_i(r)$ yields the expansion coefficients $p_{n\nu l}^{i}$ which are used in practice to describe the atomic environment (see this section for details). The tag ML_RCUT2 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 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 $\AA$ (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 $\AA$ can improve the accuracy,

@@ Line 10: / Line 10: @@
 \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 accuraof the descriptor cy '''and''' speed.}}
+{{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> might improve the accuracy,
+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,
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