Kernel regression using polynomial kernel

Here we provide an example of input file to perform kernel noise ML (KNML) fit for W. The relevant files are provided in examples/kernel_poly_w_bso4.

For the models like kernel are performed using ml_type=1. However, any kernel fit requires one pre-processing step, which actually are two :). Here are listed all three:

1. perfrom a LML fit with the same descriptor that you intend to perform kernel fit: ml_type=0

2. get the representative environements from your databases:ml_type=-2. Those atomic environements will define your kernel.

3. perform the kernel fit: ml_type=1.

Note

All these steps should be run in the same directory. Lets take, one by one.

Problem: we want a kernel fit based on BSO4 descriptor, for W.

The input of each step are stored in vacancy.ml_01, vacancy.ml_02 and vacancy.ml_03 files. At each step please copy all of them in vacancy.ml

1. LML fit Typical ml file vacancy.ml_01 file:

&input_ml
debug=.false.


!ML model
ml_type=0               !set 0 to perform the fit using basis functions
mld_order=1            !set 1 for linear regression
mld_fit_type=4         !lapack full SVD with rank estimation
desc_forces=.true.      !set true to fit the forces

!Define your system
fix_no_of_elements=1    !the number of chemical species in the system
chemical_elements=" W " !the system composition, ordered as in DB files

!Descriptor settings
r_cut=4.7d0             !set the cutoff distace Rc
descriptor_type=9       !set 9 for bispectrum SO4
j_max=4.0               !angular moment for bispectrum SO4

&end

2. Selection of kernel points The selection in this example is done using MCD/Mahalanobis distance. You should define the classes that define the MCD class and the exponent Please note: ml_type=-2 and write_kernel_matrix=.true. The content of the file vacancy.ml_02

&input_ml
debug=.false.

!ML model
ml_type=-2                 !set -2 to perform kernel selection
mld_order=1               !set 1 for linear regression
mld_fit_type=4            !lapack full SVD with rank estimation
desc_forces=.true.         !set true to fit the forces

!Define your system
fix_no_of_elements=1       !the number of chemical species in the system
chemical_elements=" W "    !the system composition, ordered as in DB files

!Descriptor settings
r_cut=4.7d0                !set the cutoff distace Rc
descriptor_type=9          !set 9 for bispectrum SO4
j_max=4.0                  !angular moment for bispectrum SO4

!Kernel dump settings
write_kernel_matrix=.true. !write or not the selected kernel.
n_pca=3                    !set 3 (default)
classes_for_mcd="07 08 13" !classes used for the MCD reference.

!Choose the classes more close to the bulk, MD bulk, deformed bulk etc
power_mcd=0.05d0           !exponent used for the grid of selction of kernel.
np_kernel_ref=1000         !number of proposed points in the MCD class
np_kernel_full=4000        !number of points outside the MCD class
kernel_dump=2              !set 2 for MCD/MAHALANOBIS
&end

3. kernel fit.

Just change in previous ml file: ml_type=1 and write_kernel_matrix=.false. and set the characteristic of kernel. Let’s look to the vacancy.ml_03 file.

&input_ml
debug=.false.

!ML model
ml_type=1                  !set 1 to perform kernel fit
mld_order=1               !set 1 for linear regression
mld_fit_type=4            !lapack full SVD with rank estimation
desc_forces=.true.         !set true to fit the forces

!Define your system
fix_no_of_elements=1       !the number of chemical species in the system
chemical_elements=" W "    !the system composition, ordered as in DB files

!Descriptor settings
r_cut=4.7d0                !set the cutoff distace Rc
descriptor_type=9          !set 9 for bispectrum SO4
j_max=4.0                  !angular moment for bispectrum SO4

!Kernel dump settings
write_kernel_matrix=.false. !write or not the selected kernel.!set 3 (default)
n_pca=3                    !set 3 (default)
classes_for_mcd="07 08 13" !classes used for the MCD reference.

!Choose the classes more close to the bulk, MD bulk, deformed bulk etc
power_mcd=0.05d0           !exponent used for the grid of selction of kernel.
np_kernel_ref=1000         !number of proposed points in the MCD class
np_kernel_full=4000        !number of points outside the MCD class
kernel_dump=3              !set 3 dump by MCD/MAHALANOBIS

!Kernel settings
kernel_type=4              !set 4 for polynomial kernel.
kernel_power=4             !order of polynomial kernel
length_kernel=0.05         !hyperparameter, test more!
sigma_kernel=0.d0          !hyperparameter, set 0 in milady

&end