\(\renewcommand{\AA}{\text{Å}}\)
compute slcsa/atom command
Syntax
compute ID group-ID slcsa/atom twojmax nclasses db_mean_descriptor_file lda_file lr_decision_file lr_bias_file maha_file value
ID, group-ID are documented in compute command
slcsa/atom = style name of this compute command
twojmax = band limit for bispectrum components (non-negative integer)
nclasses = number of crystal structures used in the database for the classifier SL-CSA
db_mean_descriptor_file = file name of file containing the database mean descriptor
lda_file = file name of file containing the linear discriminant analysis matrix for dimension reduction
lr_decision_file = file name of file containing the scaling matrix for logistic regression classification
lr_bias_file = file name of file containing the bias vector for logistic regression classification
maha_file = file name of file containing for each crystal structure: the Mahalanobis distance threshold for sanity check purposes, the average reduced descriptor and the inverse of the corresponding covariance matrix
c_ID[*] = compute ID of previously required compute sna/atom command
Examples
compute b1 all sna/atom 9.0 0.99363 8 0.5 1.0 rmin0 0.0 nnn 24 wmode 1 delta 0.3
compute b2 all slcsa/atom 8 4 mean_descriptors.dat lda_scalings.dat lr_decision.dat lr_bias.dat maha_thresholds.dat c_b1[*]
Description
New in version 7Feb2024.
Define a computation that performs the Supervised Learning Crystal Structure Analysis (SL-CSA) from (Lafourcade) for each atom in the group. The SL-CSA tool takes as an input a per-atom descriptor (bispectrum) that is computed through the compute sna/atom command and then proceeds to a dimension reduction step followed by a logistic regression in order to assign a probable crystal structure to each atom in the group. The SL-CSA tool is pre-trained on a database containing \(C\) distinct crystal structures from which a crystal structure classifier is derived and a tutorial to build such a tool is available at SL-CSA.
The first step of the SL-CSA tool consists in performing a dimension reduction of the per-atom descriptor \(\mathbf{B}^i \in \mathbb{R}^{D}\) through the Linear Discriminant Analysis (LDA) method, leading to a new projected descriptor \(\mathbf{x}^i=\mathrm{P}_\mathrm{LDA}(\mathbf{B}^i):\mathbb{R}^D \rightarrow \mathbb{R}^{d=C-1}\):
where \(\mathbf{C}^T_\mathrm{LDA} \in \mathbb{R}^{D \times d}\) is the reduction coefficients matrix of the LDA model read in file lda_file, \(\mathbf{B}^i \in \mathbb{R}^{D}\) is the bispectrum of atom \(i\) and \(\mu^\mathbf{B}_\mathrm{db} \in \mathbb{R}^{D}\) is the average descriptor of the entire database. The latter is computed from the average descriptors of each crystal structure read from the file mean_descriptors_file.
The new projected descriptor with dimension \(d=C-1\) allows for a good separation of different crystal structures fingerprints in the latent space.
Once the dimension reduction step is performed by means of LDA, the new descriptor \(\mathbf{x}^i \in \mathbb{R}^{d=C-1}\) is taken as an input for performing a multinomial logistic regression (LR) which provides a score vector \(\mathbf{s}^i=\mathrm{P}_\mathrm{LR}(\mathbf{x}^i):\mathbb{R}^d \rightarrow \mathbb{R}^C\) defined as:
with \(\mathbf{b}_\mathrm{LR} \in \mathbb{R}^C\) and \(\mathbf{D}_\mathrm{LR} \in \mathbb{R}^{C \times d}\) the bias vector and decision matrix of the LR model after training both read in files lr_fil1 and lr_file2 respectively.
Finally, a probability vector \(\mathbf{p}^i=\mathrm{P}_\mathrm{LR}(\mathbf{x}^i):\mathbb{R}^d \rightarrow \mathbb{R}^C\) is defined as:
from which the crystal structure assigned to each atom with descriptor \(\mathbf{B}^i\) and projected descriptor \(\mathbf{x}^i\) is computed as the argmax of the probability vector \(\mathbf{p}^i\). Since the logistic regression step systematically attributes a crystal structure to each atom, a sanity check is needed to avoid misclassification. To this end, a per-atom Mahalanobis distance to each crystal structure CS present in the database is computed:
where \(\mathbf{\mu}^\mathbf{x}_\mathrm{CS} \in \mathbb{R}^{d}\) is the average projected descriptor of crystal structure CS in the database and where \(\mathbf{\Sigma}_\mathrm{CS} \in \mathbb{R}^{d \times d}\) is the corresponding covariance matrix. Finally, if the Mahalanobis distance to crystal structure CS for atom i is greater than the pre-determined threshold, no crystal structure is assigned to atom i. The Mahalanobis distance thresholds are read in file maha_file while the covariance matrices are read in file covmat_file.
The SL-CSA framework provides an automatic computation of the different matrices and thresholds required for a proper classification and writes down all the required files for calling the compute slcsa/atom command.
The compute slcsa/atom command requires that the compute sna/atom command is called before as it takes the resulting per-atom bispectrum as an input. In addition, it is crucial that the value twojmax is set to the same value of the value twojmax used in the compute sna/atom command, as well as that the value nclasses is set to the number of crystal structures used in the database to train the SL-CSA tool.
Output info
By default, this compute computes the Mahalanobis distances to the different crystal structures present in the database in addition to assigning a crystal structure for each atom as a per-atom vector, which can be accessed by any command that uses per-atom values from a compute as input. See the Howto output page for an overview of LAMMPS output options.
Restrictions
This compute is part of the EXTRA-COMPUTE package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.
Default
none
(Lafourcade) Lafourcade, Maillet, Denoual, Duval, Allera, Goryaeva, and Marinica, Comp. Mat. Science, 230, 112534 (2023)