ML IAFILT2: Difference between revisions

Revision as of 11:05, 11 June 2019

ML_FF_IAFILT2_MB = [integer]
Default: ML_FF_IAFILT2_MB = 2

Description: This tag specifies the type of angular filtering used in the machine learning force field method.

This tag is only used if ML_FF_LAFILT2_MB=.TRUE. is set.

Following cases are possible for the angular filtering function $\eta$ (see also here):

ML_FF_IAFILT2_MB=1: The angular filtering function is described as $\eta_{l}=\frac{1}{(2l+1)^{1/4}}$ .
ML_FF_IAFILT2_MB=2: The angular filtering function^[1] is described as $\eta_{l,a_{\mathrm{FILT}}}=\frac{1}{1+a_{\mathrm{FILT}} [l (l+1)]^{2}}$ . Using this function the parameter $a_{\mathrm{FILT}}$ has to bes defined too. It is set in the INCAR file by setting ML_FF_AFILT2_MB. This option is the default.

In the case of the power spectrum two radial basis functions are multiplied with each other (see here). Both basis functions use the same filtering function and hence the filtering is done by the square of the filtering function. This is plotted in Fig. 1 for the two different functions used for ML_FF_IAFILT2_MB=1 and 2. In the case of ML_FF_IAFILT2_MB=2 it can be seen that for the default filtering parameter ML_FF_AFILT2_MB=0.02 and $l$ =5 the function has only a contribution of 0.15. Using this filtering parameter the maximum cut off for the angular quantum number can be reduced to ML_FF_LMAX2_MB=4.

References

↑ J. P. Boyd, Chebyshev and Fourier Spectral Methods (Dover Publications, New York, 2000).

Related Tags and Sections

ML_FF_LMLFF, ML_FF_LAFILT2_MB, ML_FF_AFILT2_MB

Examples that use this tag

[boyd:book:2000-1] J. P. Boyd, Chebyshev and Fourier Spectral Methods (Dover Publications, New York, 2000).

[1]

@@ Line 10: / Line 10: @@
 *{{TAG|ML_FF_IAFILT2_MB}}=2: The angular filtering function{{cite|boyd:book:2000}} is described as <math>\eta_{l,a_{\mathrm{FILT}}}=\frac{1}{1+a_{\mathrm{FILT}} [l (l+1)]^{2}} </math>. Using this function the parameter <math>a_{\mathrm{FILT}}</math> has to bes defined too. It is set in the {{TAG|INCAR}} file by setting {{TAG|ML_FF_AFILT2_MB}}. This option is the default.
-In the case of the power spectrum two radial basis functions are multiplied with each other (see [[On-the-fly machine learning force field generation using Bayesian linear regression#Basis set expansion|here]]). Both basis functions use the same filtering function and hence the filtering is done by the square of the filtering function. This is plotted in Fig. 1 for the two different functions used for {{TAG|ML_FF_IAFILT2_MB}}=1 and 2. In the case of {{TAG|ML_FF_IAFILT2_MB}}=2 it can be seen that for the default filtering parameter {{TAG|ML_FF_AFILT2_MB}}=0.02 and <math>l</math>=5 the function has only a contribution of 0.15. Using this filtering parameter the maximum cut off for the angular quantum number can be reduced to {{TAG|ML_FF_LMAX2}}=4.
+In the case of the power spectrum two radial basis functions are multiplied with each other (see [[On-the-fly machine learning force field generation using Bayesian linear regression#Basis set expansion|here]]). Both basis functions use the same filtering function and hence the filtering is done by the square of the filtering function. This is plotted in Fig. 1 for the two different functions used for {{TAG|ML_FF_IAFILT2_MB}}=1 and 2. In the case of {{TAG|ML_FF_IAFILT2_MB}}=2 it can be seen that for the default filtering parameter {{TAG|ML_FF_AFILT2_MB}}=0.02 and <math>l</math>=5 the function has only a contribution of 0.15. Using this filtering parameter the maximum cut off for the angular quantum number can be reduced to {{TAG|ML_FF_LMAX2_MB}}=4.
 [[File:Angular filtering MLFF cropped.png|400px|thumb|Fig. 1: Square of filtering function.]]