LML fit in HEA with kACE descriptor

This section provides an example of input file to perform a linear ML (LML) fit for the equimolar Ta-Ti-V-W high entropy alloy (HEA) using the kACE descriptor (descriptor_type=300, ace_radial_chem=3), including body orders 1 to 3, chemical low-rank tensor compression, and a randomized SVD for the descriptor basis construction. The relevant files are provided in examples/lml_hea_kace.

&input_ml

!ML mode
ml_type=0

!ML model
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
weighted=.true.               !set true for multicomponent systems
fix_no_of_elements=4
chemical_elements=" Ta Ti V  W"
weight_per_element="0.8 0.9 1.0 1.1"  !for numerical stability, keep close to 1.0

!Descriptor cutoff
r_cut=4.7d0
r_cut_width=0.5d0
r_cut_in=1.2d0
r_cut_width_in=0.4d0
type_fcut=3

!Descriptor type
descriptor_type=300         !300 for ACE/kACE

ace_numax=3                  !maximum ACE body order (here up to 3)
ace_gencg=1                   !1 DRAFT redundant version; 2 SVD Dusson-Ortner version

ace_chem=1                     !chemical embedding: 0 incomplete, 1 standard, 2 TS
ace_radial_chem=3               !1 Ralf (standard ACE), 3 HSVD (kACE), 5 HSVD with random projection
ace_chem_low_rank=1              !tensor compression of the chemical basis
ace_chem_low_rank_q=8
ace_chem_low_rank_niter=10        !default is 40
ace_chem_low_rank_lambda=1.d-08

ace_svd_randomized=1              !use a randomized SVD instead of the exact one
ace_svd_randomized_oversample=10
ace_svd_randomized_power_iter=2

l_ace_order(1)=.true.
l_ace_order(2)=.true.
l_ace_order(3)=.true.
l_ace_order(4)=.false.
l_ace_order(5)=.false.
l_ace_order(6)=.false.
ace_nmax_list="4 2 1 1 1 1"
ace_lmax_list="0 4 3 2 1 1"
ace_lambda_list="3.0 3.0 3.0 3.0 3.0 3.0"
ace_radial_poly=2            !1 powPftouny, 2 expPaftouny, 3 simpBessel

&end

Note

Since the fit is linear (mld_order=1), the size of the design matrix scales only linearly with the kACE descriptor dimension, which makes it practical to use a comparatively large basis (body orders up to 3) here. See QNML fit in HEA with ACE descriptor for the same descriptor family used with a quadratic (QNML) fit, where the design matrix scales as the square of the descriptor dimension.