m a i s e - bingweb
TRANSCRIPT
Module for Ab Initio Structure Evolution: Overview
slides 20-24
train & test NNs for compounds
slides 2-5
find space groupcompare structures
slides 6-14
relax structureset up MD & EVOS
slides 15-20
create & select data for NN fitting
Referencedata generation
evolutionary sampling
NN modelconstruction
stratifiedtraining
StructureSimulation
local/global optimizationMD, Phonons
StructureAnalysis
symmetry (spglib)fingerprints (RDF)
StructureAnalysis & Prediction
M A I S ENeural Network
Modeling
For neural network (NN) users
For NN developers
Command Line Options
POSCAR
-spg find space group number with SPGLIB
-rdf find RDF and nearest neighbor distances
-cxc compute dot product for two structures
-cmp compare two structures using RDF and SPGLIB
-cif convert str.cif into conventional unit cell CONV
-sup make a supercell specified by Na x Nb x Nc
-rot rotate a nanoparticle along eigenvectors of moments of inertia
-dim find structure periodicity
-vol compute volume per atom for crystal or nano structures
-box reset the box size for nanoparticles
Cu NP
1.000000
20.00000000 0.00000000 0.00000000
0.00000000 20.00000000 0.00000000
0.00000000 0.00000000 20.00000000
Cu
36
Cartesian
8.78504090 8.78512670 10.00000000
11.75961210 9.10945610 10.00000000
9.10951520 11.75965600 10.00000000
10.16741660 10.16741750 11.98894980
[...]
Command line applications aredesignated to perform structureanalysis and manipulation operationsgiven one POSCAR or two POSCAR0and POSCAR1 input files.
2
maise/XX-app/
Symmetry Analysis with SPGLIB
str.cif CONV PRIM
_symmetry_Int_Tables_number 12
_cell_length_a 4.2624856597999239
_cell_length_b 3.0000000000000000
_cell_length_c 3.0000006666665926
_cell_angle_alpha 90.0000000000000000
_cell_angle_beta 134.6956664078110180
_cell_angle_gamma 90.0000000000000000
_chemical_formula_sum
'Cu '
loop_
Cu1 Cu 2 a 0.0000000000000000 0.0000000000000000 0.0000000000000000
#End
[1] [1] Run the SG solver with a given tolerance (0.01 default) to get
SG numberPearson symbolSG international symbol used tolerancesimilarity cxc
$ maise –spg 0.01
139 tI2 I4/mmm 1.0E-02 1.0000
$ maise –spg 0.0005
12 mS2 C2/m 5.0E-04 1.0000
$ maise –spg -0.1
229 cI2 Im-3m 1.0E-01 0.6891
139 tI2 I4/mmm 3.0E-02 1.0000
12 mS2 C2/m 1.0E-03 1.0000
[2]
bcc-Cu
1.00000000000000
3.03000000000000 0.00000000000000 0.00000000000000
0.00200000000000 3.00000000000000 0.00000000000000
0.00000000000000 0.00000000000000 3.00000000000000
Cu
2
direct
0.00000000000000 0.00000000000000 0.00000000000000
0.50000000000000 0.50000000000000 0.50000000000000
With the [-spg] flag, maise uses thespglib solver to find the space group(SG) symmetry of a given POSCARstructure. The tolerance for thesymmetry analysis can be adjusted.The output is a symmeterizedstructure in the cif and VASP formats(CONV for conventional and PRIM forprimitive unit cells).
maise/01-spg/
3
[2] With a given negative tolerance, maise will scan the [ |tol|, 10-12 ] range and output the closest tolerance values corresponding to a SG symmetry change
POSCAR
https://atztogo.github.io/spglib/
Structure Analysis
list.dat RDF.dat rdf.dat
# R total AA AB BB
[...]
2.996667 5.917243 2.958621 0.000000 2.958621
2.998333 5.979203 2.989601 0.000000 2.989601
3.000000 6.000000 3.000000 0.000000 3.000000
[...]
[1][2]
[1] Distance from the origin in Å
$ maise -rdf 300 4.5 5 0.02
Max number of nearest neighbors 300
Soft cutoff for finding neighbors 4.500000
Hard cutoff for finding neighbors 5.000000
Gaussian spread for smearing bonds 0.020000
Neighbor list written to list.dat
Normalized RDF written to RDF.dat
Original RDF written to rdf.dat
Cu Ag
1.00000000000000
3.00000000000000 0.00000000000000 0.00000000000000
0.00000000000000 3.00000000000000 0.00000000000000
0.00000000000000 0.00000000000000 3.00000000000000
Cu Ag
1 1
direct
0.00000000000000 0.00000000000000 0.00000000000000
0.50000000000000 0.50000000000000 0.50000000000000
Using [-rdf] flag, maise calculates theradial distribution function (RDF) foran input structure and outputs thelist of nearest neighbor distances(list.dat) and RDF (normalized andtotal) patterns.
4
maise/00-rdf/
A.N. Kolmogorov et al., PRL 105, 217003 (2010)
[2] Normalized RDF for each combination of species
POSCAR
RDF1.dat
$ maise -cmp 300 6 7 0.06
STR vol/atom space group number RDF scalar product
number A^3/atom 10^-1 10^-2 10^-4 10^-8 0 1
0 13.500000 221 221 221 221 1.000000 0.979452
1 13.635000 221 123 10 10 0.979452 1.000000
$ maise -cxc 300 6 7 0.06
0.979452
[2] -cxc flag: quick calculation of RDF products.
[1]
[1] Dot product of RDFs for POSCAR0 and POSCAR1 as a measure of structural similarity: 1.0 representing similar and 0.0 dissimilar structures.
Zn
1.00000000000000
8.59556541588277 0.00000000000000 0.00000000000000
0.00000000000000 2.96067416794937 0.00000000000000
0.00000000000000 0.00000000000000 4.91525475045491
Zn
8
direct
0.42517529285620 0.50000000000000 0.14065768796726
0.18890882824820 0.50000000000000 0.61011420106387
0.57482470714380 0.50000000000000 0.85934231203274
0.81109117175180 0.50000000000000 0.38988579893613
0.92517529285620 0.00000000000000 0.14065768796726
0.68890882824820 0.00000000000000 0.61011420106387
0.07482470714380 0.00000000000000 0.85934231203274
0.31109117175180 -0.00000000000000 0.38988579893613
POSCAR1
RDF0.datlist1.datlist0.dat
Cu-Ag
1.00000000000000
3.00000000000000 0.00000000000000 0.00000000000000
0.00000000000000 3.00000000000000 0.00000000000000
0.00000000000000 0.00000000000000 3.00000000000000
Cu Ag
1 1
direct
0.00000000000000 0.00000000000000 0.00000000000000
0.50000000000000 0.50000000000000 0.50000000000000
The list of nearest neighbors and anormalized list of RDF for each inputstructure is outputted after thestructure comparison.
maise/02-cmp/
Structure Comparison 5
POSCAR0
[2]
A.N. Kolmogorov et al., PRL 105, 217003 (2010)
MAISE
Structure Simulation: Built-in Options
INPUT POSCAR setup model
OUTPUT CONTCAR OUTCAR ...
6
neural networkGuptaSutton-Chen...
structure potential type
local relaxationmolecular dynamicsΓ-point phonons...
simulation type
-----------------------------------------------------------------------------
| neural network general information |
-----------------------------------------------------------------------------
| model unique ID | 0357EDA0 |
| number of species | 1 |
| species types | 29 |
| species names | Cu |
| number of layers | 4 |
| architecture | 51 10 10 1 |
| number of weights | 641 |
| reference | doi |
-----------------------------------------------------------------------------
| performance |
-----------------------------------------------------------------------------
| train energy error | 0.001731 eV/atom |
| test Energy error | 0.001833 eV/atom |
| train force error | 0.010072 eV/Ang |
| test Force error | 0.010170 eV/Ang |
-----------------------------------------------------------------------------
B2A Scaling
0.529177249 1.25
...
Rc 1 11.338
-----------------------------------------------------------------------------
Structure Simulation: Available Model Types 7
model
-----------------------------------------------------------------------------
| Gupta potential |
-----------------------------------------------------------------------------
| model unique ID | XXXXXXXX |
| number of species | 1 |
| species types | 29 |
| species names | Cu |
| reference | https://doi.org/10.1007/s11051-017-3907-6 |
-----------------------------------------------------------------------------
| parameters |
-----------------------------------------------------------------------------
| A rep (eV) Cu | 0.0855 |
| p rep (Ang) Cu | 10.96 |
| B att (eV) Cu | 1.2240 |
| q att (Ang) Cu | 2.278 |
| r0 (Ang) Cu | 2.556 |
| Rmin (Ang) Cu | 100.0000 |
| Rmax (Ang) Cu | 110.0000 |
-----------------------------------------------------------------------------
model
Naming convention: nn_Cu_d3_v0neural network for Cu periodic structure version 0
Architecture: 51 inputs, 2 hidden layers, 1 output641 = (51+1)*10 + (10+1)*10 + (10+1)*1
Typical energy accuracy: 1-10 meV/atomTypical force accuracy 10-50 meV/Å
Interaction range (Rc)( 11.338 * B2A * 1.25 ) Å = 7.5 Å
Naming convention: gp_Cu_d3_vpGupta potential for Cu clusters version p
Parameters taken from DOI10.1007/s11051-017-3907-6
Effective accuracy ~ 30 meV/atom10.1021/acs.jpcc.9b08517
Rmax is set to 110 Å to include all neighborsFor bulk structures it should be set to ~ 10 Å
model setupPOSCAR
OUTCAR OSZICAR CONTCAR
POSITION (Angst) TOTAL-FORCE (eV/Angst) ATOM ENERGY (eV)
---------------------------------------------------------------------------------------------------
0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -4.099140027504
0.000000 1.817187 1.817187 0.000000 0.000000 0.000000 -4.099140027504
1.817187 0.000000 1.817187 0.000000 0.000000 0.000000 -4.099140027504
1.817187 1.817187 0.000000 0.000000 0.000000 0.000000 -4.099140027504
---------------------------------------------------------------------------------------------------
Total 0.00000001 0.00000001 0.00000001 0.00000000 0.00000000 0.00000000
in kB 0.00001015 0.00001015 0.00001015 0.00000000 0.00000000 0.00000000
---------------------------------------------------------------------------------------------------
iter 8 total enthalpy= -16.39656011 energy= -16.39656011 -4.09914003 -4.09914003
---------------------------------------------------------------------------------------------------
Total CPU time used (sec): 7.22000000 wall time (sec): 1.65885300
[5]
[5] enthalpy and energy per atom
[4]
[4] energy for each atom
[1] NPAR sets the number of cores used in parallel execution. It should be multiple of the number of atoms.
[2]
MAISE can perform local structurerelaxation given model, setup, andPOSCAR files. The OUTCAR output(compatible with the VASP format)includes the relaxed structure, totaland atomic energies, forces, etc.
Structure Simulation: Relaxation 8
maise/03-rlx/
$ maise
0 -7.9926743659805801
1 -8.1223228263625700 -0.1296484603819898
[...]
INI -7.99267437
DIF -0.20441123
FIN -8.19708559
[2] NDIM sets the periodicity of the simulation cell. Cells are either periodic (3) or non-periodic (0).
[3] MITR sets the max number of cell relaxation steps. Set it to 0 for a single-point calculation.
[1]
[3]
=====================================================================================
JOBT 20 cell relaxation
NPAR 4 number of cores for parallel run
NDIM 3 (3) crystal; (0) cluster;
MITR 100 number of cell optimization steps
RLXT 3 cell optimization type: (2) force only; (3) full cell; (7) volume;
PGPA 0.0 pressure in GPa
ETOL 1e-8 error tolerance for cell optimization convergence
COUT 12 OUTCAR output options
MINT 0 minimizer type: (0) BFGS2; (1) CG-FR; (2) CG-PR; (3) steepest descent;
MMAX 500 maximum number of nearest neighbors
=====================================================================================
model setup
=====================================================================================
JOBT 21 molecular dynamics
NPAR 16 number of cores for parallel run
NDIM 3 3) crystal; (0) cluster;
MDTP 20 MD type (10) NVE (20) NVT Nose-Hoover (30) NPT Nose-Hoover + Berendsen
PGPA 0.0 pressure in GPa
TMIN 1300.0 min temperature in MD runs
TMAX 1500.0 max temperature in MD runs
TSTP 100.0 temperature step in MD runs
DELT 2.0 time step in femtoseconds
NSTP 100 number of steps
CPLT 25.0 thermostat coupling constant
CPLP 100.0 barostat coupling constant
ICMP 0.01 isothermal compressibility (in 1/GPa)
=====================================================================================
POSCAR
MAISE can perform NVE, NVT, andNPT molecular dynamics simulationsgiven model, setup, and POSCARfiles. The main output file ave-out.datcontains the averages for thepotential and kinetic energies, latticeconstants (for NPT), and Lindemannindex at each temperature.
Structure Simulation: Molecular Dynamics 9
maise/07-nvt/
Example: linear thermal expansion coefficient in fcc-Ag (NPT)
S. Hajinazar et al., arxiv:2005.12131 (2020)
External engine PHON, PyChemia, MAISE, ...Simulation type Phonon analysis, evolutionary search, ...
Structure Simulation: External Usage 10
External engine PHON, PyChemia, MAISE, ...Simulation type Phonon analysis, evolutionary search, ...
MAISE
INPUT POSCAR setup model
OUTPUT CONTCAR OUTCAR ...
neural networkGuptaSutton-Chen...
structure potential type
local relaxationmolecular dynamicsΓ-point phonons...
simulation type
Structure Simulation: Examples of External Usage 11
MAISE Atomic forces with NNs
new stable Mg-Ca phases at high T, P
S. Hajinazar, J. Shao, and A.N. Kolmogorov, PRB 95, 014114 (2017) W. Ibarra-Hernandez, S. Hajinazar, et al., PCCP 20, 27545 (2018)
PHON Frozen phonon methodD. Alfe, 10.1016/j.cpc.2009.03.010
phonon dispersion, free energy corrections
MAISE Local relaxation with NNs
PyChemia Minima hopping searchA. Romero, https://pypi.org/project/pychemia/
0 20 40 60 80
E (
eV/a
tom
)
generation numbergeneration 0
initialize
relax
generation 1
mate
relax
rank
select
Structure Simulation: Evolutionary Search 12
Structure Simulation: Evolutionary Search 13
MAISE Local relaxation with NNs
MAISE Evolutionary search
=============================================================================================================
EVOLUTIONARY SEARCH GENERAL SETTINGS
=============================================================================================================
JOBT 10 evolutionary search run (10); soft exit (11); hard exit (12); analysis (13)
NMAX 48 maximum number of atoms
MMAX 500 maximum number of neighbors within cutoff radius
NSPC 2 number of species types
TSPC 12 20 species types
ASPC 8 4 atom number of each species
CODE 2 MAISE-INT (0); VASP-EXT (1); MAISE-EXT (2)
QUET 1 queue type: torque (0); slurm (1)
NDIM 3 structure type: crystal (3); film (2); cluster (0)
NPOP 32 population size
SITR 0 starting iteration
NITR 100 number of iterations
TINI 0 starting options if SITR=0
TIME 1200 max time per relaxation
PGPA 0.0 pressure in GPa
SEED 0 random number generator seed (0 for system time)
=============================================================================================================
EVOLUTIONARY OPERATION SETTINGS
=============================================================================================================
MATE 0.7 crossover with planar cut
MUTE 0.3 mutation via distortion
=============================================================================================================
MCRS 0.5 mutation rate in crossover
SCRS 0.1 swapping rate in crossover
LCRS 0.1 lattice vector distortion in crossover
ACRS 0.1 atomic position distortion in crossover
SDST 0.1 swapping rate in mutation
LDST 0.15 lattice vector distortion in mutation
ADST 0.15 atomic position distortion in mutation
MAGN 10000000 max number of tries for crossover
=============================================================================================================
setup
Structure Simulation: Evolutionary Search Performance 14
3D crystals 0D clusters
Crossover operation critical for N > 10 atoms
No input information: 3000-10000 relaxations for 12 ≲ N ≲ 30
Lattice constant input: only 100-200 relaxations for 20 ≲ N ≲ 30
tI56-CaB6 found w/o any input among largest confirmed
Kolmogorov et al., PRL 95, 109, 075501 (2012)
V (Å3/atom)
H–
HcP
7(e
V/a
tom
)
Hajinazar et al., PCCP 20, 27545 (2018); Thorn et al., JPCC 21, 8729 (2019)
Convenient TETRIS-like generation of clusters
Alternative evolutionary operations for efficiency analysis
Dramatic efficiency boost with multitribe co-evolution
New putative DFT ground states for Au with 30-80 atoms
{ Ri } = { Rij , θijk }
Behler-Parrinellosymmetry functions
{ Ri }
generate a database of relevant structures
E, Fiα, sαβ
convert atomic positions into NN input
tune NN parametersto produce energy & forces
{ xin }
Construction of Neural Network Interatomic Models: Overview 15
MAISE-NETevolutionary sampling
MAISEdata parsing
MAISEstratified training
arbitraryenvironments
2007symmetry functions
Behler-ParrinelloPRL 98, 146401
(2007)
constant #of neighbors
1999-2004atomistic RBF-NN
AKPhD thesis
unpublished (2004)
constant #of atoms
1995-system-
specific NNsreviewed in
JCTC 1, 14 (2005)
1 2 1 0
1 3 1 1
arbitraryenvironments
2013-SOAP (Bartók, Kondor, Csányi)
PRB 87, 184115 (2013)moment tensor (Shapeev), etc.
MMS 14, 1153 (2016)completeness (Pozdnyakov et al.)
arXiv:2001.11696 (2020)
r1 r2 ... rN atom Δr1 Δr2 ... ΔrN n n1 n2 ... nN f n1 n2 ... nN f
Our focus: Develop a practical NN tool for unconstrained prediction of stable alloys
Construction of Neural Network Interatomic Models: A Perspective 16
Evolutionary sampling guidelines
• Sample configurations relevant for EVOS• Add EOS structures with short distances• Eliminate similar structures• Expand datasets iteratively after NN testing
Reference data and NN generation with MAISE-NET 17
DFT
Data generation approaches
• Randomization of given structures• Molecular dynamics• Evolutionary sampling (2017)
S. Hajinazar, J. Shao, and A.N. Kolmogorov, PRB 95, 014114 (2017) S. Hajinazar et al., arxiv:2005.12131 (2020)
NN
Reference Data Organization and Selection 18
TEFS 1 train NN for (0) E (1) EF
FMRK 0.5 fraction of atoms used for EF training
EMAX 0.90 fraction of lowest-enthalpy structures
FMAX 100.0 do not parse data with larger force
VMIN 0.0 do not parse data with lower volume
VMAX 45.0 do not parse data with larger volume
RAND 5 optional for fixed parsing
DEPO ./DATA location of DFT data
setup
-7.99786290
in kB -78.764 40.695 -54.435 19.213 -102.114 -17.84928
POSITION TOTAL-FORCE (eV/Angst)
--------------------------------------------------------
3.14733 -0.05179 1.34028 0.225348 0.299805 -0.262492
2.39085 -1.67936 2.83105 -0.225348 -0.299805 0.262492
-------------------------------------------------------
pressure 10.00000000
dat.dat
if present, tag fileoverwrites setup
and assigns the full subset to training
DATA/eosbcc
tag 00/ 01/ ...
Data is divided into subsets with same compositionsame pressuresame dimensionality
POSCARDATA/evo01/01
DATA/evo01
00/ 01/ ...
DATA/evo00
00/ 01/ ...
ECUT = 0.90 means that 10% of highest-enthalpy structures
are discarded
remainingstructures are splitinto training (90%)
& testing (10%) sets
FMRK fraction of forces are selected
PARS/e*
$ maise
dir poscars Emin Emax Ecut path
0 113 112 226 -1.453728145000 3.385686635000 3.385686635000 ./DATA/000/
1 250 225 225 -3.308694100000 0.009592215000 -2.603072180966 ./DATA/100/
2 61 60 122 -3.070987127500 2.247194970000 2.247194970000 ./DATA/200/
Total 424 POSCAR.0 files are found in ./DATA/*
Structures marked for: TRAIN= 0 TEST= 0 TRAIN+TEST= 397 DISCARD= 27
Successfully parsed 397 POSCAR.0 out of total 424 structures!
setup DATA/ basis
JOBT 30 job type: data parsing (30)
NPAR 8 number of cores for parsing
NSPC 2 number of species types
TSPC 29 47 species types
NSYM 30 number of Behler-Parrinello symmetry functions
NCMP 82 total number of NN inputs
TEFS 1 train NN for: (0) E; (1) EF;
FMRK 0.5 fraction of atoms used for EF training
ECUT 0.90 parse only this fraction of lowest-energy structures (from 0 to 1)
EMAX 5.0 maximum energy from the lowest-energy structure that is parsed
FMAX 50.0 do not parse data with larger force
RAND 5 seed for random number generator
DEPO ./DATA path to the DFT dataset to be parsed
DATA ./PARS location of the parsed data to write the parsed data
PARS/index.dat PARS/stamp.dat PARS/ve.dat PARS/RDFP.dat
e000000 ./DATA/000/109/
e000001 ./DATA/000/066/
e000002 ./DATA/000/091/
e000003 ./DATA/000/069/
e000004 ./DATA/000/048/
e000005 ./DATA/000/141/
e000006 ./DATA/000/057/
e000007 ./DATA/200/38/
e000008 ./DATA/000/084/
[...]
Parsing the DFT-based data forconstruction of training dataset of aneural network model.
maise/04-prs/
Reference Data Parsing 19
Parsing produces a set of e* files that contained the parsed information for each structure.
The index.dat file contains the the list of e* files and the path to the corresponding structure.
A summary of parsing task is provided in the stamp.dat file. A list of volume-energy data, and average RDF for the dataset is provided in ve.dat and RDFP.dat files.
Behler-Parrinello symmetry functions can be customized in the basis file: number, types, parameters, Rcut.
$ maise
Loading list of parsed data from ./PARS/index.dat
Total number of parameters: 1902
BFGS2 relaxation: 1040 adjustable parameters
1 1.1180920333757309 0.779057 5.034344 0.938831 7.022223
2 0.6960607178739942 0.623539 1.941889 0.660513 2.726337
[...]
Test error ENE FRC TOT 0.027726 0.180121 0.026405 39 102
setup
JOBT 41 training type: full training (40); stratified training (41)
NPAR 16 number of cores for parallel NN training
MINT 0 gsl minimizer type: (0) BFGS2; (1) CG-FR; (2) CG-PR; (3) steepest descent;
MITR 100 maximum N for NN training or cell optimization steps
ETOL 1e-6 error tolerance for training
NSPC 2 number of species types
TSPC 29 47 species types
NSYM 30 number of Behler-Parrinello symmetry functions
NCMP 82 total number of NN inputs
TEFS 1 train NN for: (0) E; (1) EF;
LREG 1e-8 regularization parameter
NTRN -90 number of structures for training (negative means percentage)
NTST -10 number of structures for testing (negative means percentage)
NNNN 2 number of hidden layers in MLP
NNNU 10 10 number of neurons in hidden layers in MLP
Training neural network models. Theoutput includes model, err-out.dat(optimization steps), and energy andforce errors for testing set (err-ene.dat and err-frc.dat).
maise/05-trn/
NN Model Construction: Training 20
NNET/model NNET/err-out.dat NNET/err-ene.dat NNET/err-frc.dat
-----------------------------------------------------------------------------
| number of species | 2 |
| species names | Cu Ag |
| architecture | 82 10 10 1 |
| number of weights | 1902 |
-----------------------------------------------------------------------------
| train energy data | 357 |
| test energy data | 39 |
| train force data | 906 |
| test force data | 102 |
-----------------------------------------------------------------------------
| number of epochs | 100 |
| train energy error | 0.030774 eV/atom |
| test Energy error | 0.027726 eV/atom |
| train force error | 0.180638 eV/Ang |
| test Force error | 0.180121 eV/Ang |
-----------------------------------------------------------------------------
NN Model Construction: Training 21
NN accuracy shows little dependence on
number of layers (1 or 2)number of neurons (20-40)weight initialization (random or restart)
Typical E&F training time for 100,000 steps
elements weights data CPU hours
unary 641 38,000 300 binary 1,880 42,000 900ternary 1,290 55,000 1,500
Standard fitting procedure
Stratified Construction of NN Models for Compounds 22
CuCu PdPd
CuCu CuPd PdPd PdCu
E(Cu) ≠ E(Cu)
Cudata
Pddata
CuPddata
Cudata
Pddata
CuPd
CuPddata
NNCu
model
Cu structure
NNCuPd
model
NNCu
model
NNPd
model
binary NNCuPd
model
E(Cu) = E(Cu)
NNCu
model
Cu structure
NNCuPd
model
Stratified fitting procedure
S. Hajinazar, J. Shao, and A.N. Kolmogorov, PRB 95, 014114 (2017)
Binary data affects elemental weights
Unphysical change in subsystem description
Elemental weights in the binary NN are fixed
Consistent unchanged subsystem description
Stratified Construction of NN Models for Alloys 23
S. Hajinazar, J. Shao, and A.N. Kolmogorov, PRB 95, 014114 (2017); S. Hajinazar et al., arxiv:2005.12131 (2020)
Stratified training procedure
has been previously used for tight-binding models and traditional potentials
allows for proper description of screening, charge transfer, etc. in multielement systems
is most natural for compounds with elements similar in size, electronegativity, etc.
speeds up training due to division of adjustable parameters
enables construction of reusable libraries of NN models
has been tested on several metals (e.g., Cu-Pd-Ag, Mg-Ca, etc.)
has been recently generalized for an arbitrary number of species
NN library built with MAISE-NETStratified training from the bottom up
Are NNs better than traditional potentials for guiding ab initio search?
search
DFT NN~ 10
meV/atom
NN+
~ 5 meV/atom
buildsearch
check
EAM, GP, SC ~ 30
meV/atom
A. Thorn, J. Rojas-Nunez, S. Hajinazar, S.E. Baltazar, and A.N. Kolmogorov, JPCC (2019)
build
search
check
build
search+check
check
CPU time
Structure Search Acceleration with Pre-trained NNs 24
perform search with coarse
but fast method
examine small low-E pool with
accurate method
~ΔE
cost of Au50 calculation
GP : NN : DFT1 : 102 : 106
MAISE present features
space group solver SPGLIB interface https://atztogo.github.io/spglib/fingerprint structure comparison with RDF PRL 105, 217003 (2010)global optimization DFT evolutionary search PRL 109, 075501 (2012), etc.NN data generation Python MAISE-NET script PRB 95, 014114 (2017); arXiv:2005.12131NN development stratified training PRB 95, 014114 (2017)NN application structure prediction PCCP 20, 27545 (2018); JPCC 21, 8729 (2019)
Summary 25
MAISE development information
MAISE 2.7 OpenMP parallelized C code (14364 lines)MAISE-NET 2.0 Python script (3889 lines)2009-present A. Kolmogorov, S. Hajinazar, E. Sandoval, A. Thorn, S. Kharabadze
MAISE resources
open source code https://github.com/maise-guideNN model library https://github.com/maise-guide/maise/tree/master/modelsforum http://harvey0.binghamton.edu/~akolmogo/forumwiki documentation http://maise.binghamton.edu/wikiA. Kolmogorov contact for development of new simulation features and NN models for alloys
TransdisciplinaryAreas of Excellence
DMR 1410514DMR 1821815
Generalized Stratified Training of NN for Compounds E1