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# ML FF IAFILT2 MB

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.

Fig. 1: Square of filtering function.

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

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

• ML_FF_IAFILT2_MB=1: The angular filtering function is described as ${\displaystyle \eta _{{l}}={\frac {1}{(2l+1)^{{1/4}}}}}$.
• ML_FF_IAFILT2_MB=2: The angular filtering function[1] is described as ${\displaystyle \eta _{{l,a_{{{\mathrm {FILT}}}}}}={\frac {1}{1+a_{{{\mathrm {FILT}}}}[l(l+1)]^{{2}}}}}$. Using this function the parameter ${\displaystyle a_{{{\mathrm {FILT}}}}}$ 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 (labeled as TYPE1 and TYPE2, respectively). 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 ${\displaystyle l}$=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

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