CN113255083B - Elastic modulus prediction method based on molecular dynamics and elastic network regression model - Google Patents

Elastic modulus prediction method based on molecular dynamics and elastic network regression model Download PDF

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CN113255083B
CN113255083B CN202110715862.2A CN202110715862A CN113255083B CN 113255083 B CN113255083 B CN 113255083B CN 202110715862 A CN202110715862 A CN 202110715862A CN 113255083 B CN113255083 B CN 113255083B
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elastic modulus
elastic
constructing
glass
cation
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CN113255083A (en
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赵明
赵谦
刘鑫
陈阳
匡宁
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Nanjing Fiberglass Research and Design Institute Co Ltd
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Abstract

The invention discloses an elastic modulus prediction method based on molecular dynamics and an elastic network regression model, and belongs to the field of glass performance prediction. According to the method, crystal and amorphous structures of oxides in the glass are established based on molecular dynamics, long-range disorder and short-range order of the glass are considered, the method is more consistent with the rule of actual glass, and aiming at the property of the glass, namely the elastic modulus, the binding energy of unit cations in the crystal, the elasticity tensor constant of a unit cell and the product of the body modulus and the shear modulus of the unit cell are innovatively provided as performance parameters, and descriptors used in an elastic network regression model are correspondingly constructed, so that the accurate prediction of the elastic modulus of the glass is realized; and based on the molecular dynamics calculation descriptor and Newton's law, the system is simple in structure, the action of each electron does not need to be considered, but the electronic mechanism of the system is equivalent to the potential energy function in the atom, so that the calculation process is greatly simplified, and the calculation time is saved.

Description

Elastic modulus prediction method based on molecular dynamics and elastic network regression model
Technical Field
The invention relates to an elastic modulus prediction method based on molecular dynamics and an elastic network regression model, and belongs to the field of glass performance prediction.
Background
The elastic modulus is an important performance parameter of engineering materials, and is a measure for the resistance of an object to elastic deformation in a macroscopic view and is a reflection of the bonding strength between atoms, ions or molecules in a microscopic view. All factors influencing the bonding strength can influence the elastic modulus of the material, such as bonding mode, crystal structure, chemical composition, microstructure, temperature and the like. The elastic modulus can be regarded as an index for measuring the difficulty of the material in elastic deformation, and the larger the value of the elastic modulus, the larger the stress for causing the material to generate certain elastic deformation, that is, the higher the rigidity of the material, that is, the smaller the elastic deformation generated under the action of certain stress.
The modulus of elasticity of the material is very important in engineering design, for example, in the use of wind power blades, the blade mass is also increased significantly as the length of the blade is increased. The substantial increase in mass can present a number of challenges to the design of the blade: for example, the risk of layering between the main beam cap and the skin is greatly increased, the natural frequency and the rotating frequency of the blade are closer, the transportation and hoisting difficulty of the blade is greatly increased, and the unit needs to bear larger load. Therefore, the current research focus is on improving the structural rigidity of the wind turbine blade spar cap, particularly reflecting on the raw materials, and improving the tensile modulus of the used glass fiber.
Due to the appearance of big data, a plurality of methods for predicting material performance based on a machine learning algorithm are available at present, the methods establish a prediction model based on a neural network or a support vector machine and train and verify the prediction model to obtain a model under optimal parameters, but the methods predict the percentage of material components as input, so that the prediction accuracy is not high, a method for predicting the glass performance by using a descriptor calculated by molecular dynamics as the input of the machine learning algorithm is not available at present, a method for accurately predicting the elastic modulus by using the machine learning algorithm of the molecular dynamics is not provided aiming at an influence factor of the elastic modulus, and the method for predicting the elastic modulus is a key problem to be solved urgently at present.
Disclosure of Invention
In order to solve the problem that the elastic modulus of glass cannot be intuitively, quickly and accurately predicted in the prior art, the invention provides an elastic modulus prediction method based on molecular dynamics and an elastic network regression model, which comprises the following steps:
step 1, acquiring elastic modulus data of oxide glass materials with different component compositions, and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
step 2, constructing an atomic structure model of oxide crystals with different symmetries in the oxide glass material based on molecular dynamics, and using cations per unitiBinding energy of
Figure 403853DEST_PATH_IMAGE001
Elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 821059DEST_PATH_IMAGE002
And
Figure 54595DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 416306DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 754009DEST_PATH_IMAGE005
Constructing a descriptor of the elastic modulus comprising a "material gene" as a performance parameter;
step 3, constructing a training set, a verification set and a test set based on the elastic modulus database constructed in the step 1 and the descriptor constructed in the step 2;
step 4, constructing an elastic modulus prediction model based on the elastic network regression model, and training the constructed elastic modulus prediction model according to the training set, the verification set and the test set constructed in the step 3 to obtain a trained elastic modulus prediction model;
step 5, aiming at the glass material to be predicted, obtaining a descriptor containing a material gene according to the composition of the components of the glass material; and predicting the elastic modulus of the glass material to be predicted by using the trained elastic modulus prediction model.
Optionally, step 2 includes:
step 2-1, constructing atomic structure models of oxide crystals with different symmetries as unit cells of molecular dynamics calculation;
step 2-2 for each cell structure constructed in step 2-1, performing molecular dynamics calculation to obtain cell energy
Figure 150355DEST_PATH_IMAGE006
；
Step 2-3, obtaining a performance parameter set of each crystal cell structure obtained in the step 2-1 through further calculation, and constructing a descriptor for machine learning
Figure 554791DEST_PATH_IMAGE007
：
Figure 544744DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power-averaged exponent, and takes on all non-zero integers between-4 and + 4;
Figure 60039DEST_PATH_IMAGE009
is the set of all cations;
Figure 310892DEST_PATH_IMAGE010
is a corresponding cationiThe component ratio of (A);
Figure 886230DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 347167DEST_PATH_IMAGE012
means when the power exponent is
Figure 666153DEST_PATH_IMAGE013
When is a cation
Figure 771512DEST_PATH_IMAGE014
Is corresponding to
Figure 517751DEST_PATH_IMAGE015
Individual performance parameters;
Figure 951138DEST_PATH_IMAGE016
,3；
Figure 73814DEST_PATH_IMAGE007
is a power exponent of
Figure 33680DEST_PATH_IMAGE013
When is a cation
Figure 950821DEST_PATH_IMAGE014
Is corresponding tomA descriptor; the performance parameters include the cation per unit of each crystaliBinding energy of
Figure 884885DEST_PATH_IMAGE001
Elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 545674DEST_PATH_IMAGE002
And
Figure 360046DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 713667DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 121646DEST_PATH_IMAGE005
The product of (a).
Optionally, the cation per unitiBinding energy of
Figure 320546DEST_PATH_IMAGE001
The calculation method comprises the following steps:
using the cell energy obtained in step 2-2
Figure 255004DEST_PATH_IMAGE006
Subtracting the sum of the energies of the single atoms of the same number and kind, and calculating by the formula:
Figure 779526DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,Mfor cations in crystal cellsiThe number of the (c) component (a),
Figure 658489DEST_PATH_IMAGE018
and
Figure 926659DEST_PATH_IMAGE019
are each a single cationiAnd a single oxygen atom, O, in one unit cell.
Alternatively, the step 2-1 of constructing an atomic structure model of oxide crystals having different symmetries as a unit cell of molecular dynamics calculation includes:
(1) for cations with a valence of +1, according to CaF2The structure is crystal, oxygen ions form a face-centered cubic structure, and cations are in tetrahedral gaps of the face-centered cubic structure;
(2) for + 2-valent cations, crystals are constructed according to a NaCl structure, the cations form a face-centered cubic structure, and oxygen ions are in hexahedral gaps of the face-centered cubic structure;
(3) for cations with a valence of +3, according to α -Al2O3A structural structure crystal;
(4) for cations with a valence of +4, according to CaF2The structure makes crystal, the positive ions form a face-centered cubic structure, and the oxygen ions are in the tetrahedral gaps of the face-centered cubic structure.
Optionally, when the elastic modulus database is constructed in step 1, the method further includes preprocessing the elastic modulus data of the oxide glass materials with different components:
judging whether the following two conditions are simultaneously satisfied or not according to the two glass components:
condition 1: in the glass components, the molar ratio difference value of the components of each oxide component is less than or equal to a first preset threshold, and the unit is percentage;
condition 2: the difference value of the elastic moduli of the two glasses is greater than a second preset threshold value, and the unit is percentage;
and if the two glass components are simultaneously satisfied, removing the corresponding two glass components and the corresponding elastic modulus data from the elastic modulus database.
Optionally, the first preset threshold is 2%, and the second preset threshold is 20%.
Optionally, in the elastic network regression model, the elastic modulus is predictedyAnd descriptors
Figure 715624DEST_PATH_IMAGE007
The following relationship is satisfied:
Figure 286414DEST_PATH_IMAGE020
wherein the content of the first and second substances,Perin order to be a set of performance parameters,
Figure 793618DEST_PATH_IMAGE021
is composed of
Figure 599900DEST_PATH_IMAGE007
Corresponding regression coefficients, n being a non-zero integer from-4 to 4;
the loss function of the elastic network regression model is:
Figure 243371DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 735795DEST_PATH_IMAGE023
for the loss function, N is the number of samples,
Figure 464716DEST_PATH_IMAGE024
in order to predict the value of the target,
Figure 74689DEST_PATH_IMAGE025
in the form of an actual value of the value,
Figure 838246DEST_PATH_IMAGE026
in order to be a penalty term,
Figure 485259DEST_PATH_IMAGE027
for adjusting the over-parameters
Figure 967056DEST_PATH_IMAGE028
；
The present application further provides an elastic modulus prediction system based on molecular dynamics and elastic network regression algorithm, the system comprising:
the elastic modulus database construction module is used for acquiring elastic modulus data of glass materials with different component compositions and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
a descriptor construction module for constructing a descriptor containing a 'material gene' of the elastic modulus of the oxide glass material based on molecular dynamics;
the training data construction module is used for constructing a training set, a verification set and a test set on the basis of the elastic modulus database constructed by the elastic modulus database construction module and the descriptor constructed by the descriptor construction module;
the model construction training module is used for constructing an elastic modulus prediction model based on an elastic network regression model tree, and training the constructed elastic modulus prediction model according to a training set, a verification set and a test set constructed by the training data construction module to obtain a trained elastic modulus prediction model;
and the prediction module is used for constructing an elastic modulus prediction model trained by the training module by utilizing the model to predict the elastic modulus of the glass material to be predicted.
Optionally, the descriptor building module constructs a descriptor containing a "material gene" of the elastic modulus of the oxide glass material, including
Constructing an atomic structure model of oxide crystals with different symmetries as a unit cell for molecular dynamics calculation;
for each cell structure obtained by construction, molecular dynamics calculation is carried out to obtain unit cell energy
Figure 115140DEST_PATH_IMAGE006
；
For each cell structure obtained by construction, a performance parameter set is obtained by further calculationConstructing descriptors for machine learning
Figure 733204DEST_PATH_IMAGE007
：
Figure 800386DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power-averaged exponent, and takes on all non-zero integers between-4 and + 4;
Figure 503899DEST_PATH_IMAGE009
is the set of all cations;
Figure 455675DEST_PATH_IMAGE010
is a corresponding cationiThe component ratio of (A);
Figure 928245DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 182639DEST_PATH_IMAGE012
means when the power exponent is
Figure 373449DEST_PATH_IMAGE013
When is a cation
Figure 863337DEST_PATH_IMAGE014
Is corresponding to
Figure 455992DEST_PATH_IMAGE015
Individual performance parameters;
Figure 894670DEST_PATH_IMAGE016
,3；
Figure 307197DEST_PATH_IMAGE007
is a power exponent of
Figure 600775DEST_PATH_IMAGE013
When is a cation
Figure 923303DEST_PATH_IMAGE014
The m-th descriptor corresponding to the structure of (1); the performance parameters include the cation per unit of each crystaliBinding energy of
Figure 644134DEST_PATH_IMAGE001
Elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 809537DEST_PATH_IMAGE002
And
Figure 641226DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 67528DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 959261DEST_PATH_IMAGE005
The product of (a).
The present application further provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.
The invention has the beneficial effects that:
1) the crystal and amorphous structures of the oxides in the glass are established, the long-range disorder and short-range order of the glass are considered, the rule of the actual glass is better met, and the calculation result is accurate.
2) Based on the molecular dynamics calculation descriptor and Newton's law, the system is simple in structure, the action of each electron does not need to be considered, the electronic mechanism of the system is equivalent to the potential energy function in the atom, the calculation process is greatly simplified, and the calculation time is saved.
3) By adopting the elastic network regression model, global linear regression does not need to be considered for samples with more sample characteristics and complex nonlinear relations among the characteristics, the elastic network regression model divides the sample characteristics into a plurality of piecewise linear regressions, the interpretability of the tree is stronger, and the training model time of the algorithm is short.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for predicting glass modulus based on molecular dynamics in one embodiment.
FIG. 2 is a flow diagram for constructing descriptors based on molecular dynamics, in one embodiment.
FIG. 3 shows CaF2Structural diagram of crystal form.
FIG. 4 is a view showing a structure of NaCl type crystals.
FIG. 5 shows a-Al2O3Structural diagram of crystal form.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The first embodiment is as follows:
the present embodiment provides an elastic modulus prediction method based on molecular dynamics and elastic network regression algorithm, referring to fig. 1, the method includes:
step 1, acquiring elastic modulus data of glass materials with different component compositions, and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
step 2, constructing descriptors containing 'material genes' of the elastic modulus of the oxide glass material based on molecular dynamics, and referring to fig. 2;
2-1 constructing an atomic structure model of oxide crystals with different symmetries as a unit cell for molecular dynamics calculation;
2-2 for each crystal cell structure constructed in the step 2-1, performing molecular dynamics calculation to obtain optimized unit cell energy
Figure 80801DEST_PATH_IMAGE006
；
2-3 are directed to the structures of the above crystals comprising various symmetries optimized by molecular dynamics calculations; and further calculating to obtain a performance parameter set thereof, and constructing a descriptor for machine learning
Figure 981761DEST_PATH_IMAGE007
：
Figure 278881DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power-averaged exponent, takes on all non-zero integers between-4 and +4,
Figure 341515DEST_PATH_IMAGE009
is the set of all the cations that are present,
Figure 215930DEST_PATH_IMAGE010
is a corresponding cationiThe ratio of the components (A) to (B),
Figure 389422DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 291782DEST_PATH_IMAGE012
means when the power exponent is
Figure 525317DEST_PATH_IMAGE013
When is a cation
Figure 887028DEST_PATH_IMAGE014
Is corresponding to
Figure 864211DEST_PATH_IMAGE015
Individual performance parameters;
Figure 135924DEST_PATH_IMAGE029
，
Figure 805940DEST_PATH_IMAGE007
is a power exponent of
Figure 389368DEST_PATH_IMAGE013
When is a cation
Figure 294876DEST_PATH_IMAGE014
Is corresponding tomA descriptor.
The set of performance parameters includes the following performance parameters:
(1) cation per unit of each crystaliBinding energy of
Figure 545728DEST_PATH_IMAGE001
In eV/atom;
calculation of binding energy by using optimized unit cell energy
Figure 121066DEST_PATH_IMAGE006
Subtracting the sum of the energies of the single atoms with the same number and the same type to obtain the product, wherein the calculation formula is as follows:
Figure 191790DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,Mfor cations in crystal cellsiThe number of the (c) component (a),
Figure 386142DEST_PATH_IMAGE018
and
Figure 491502DEST_PATH_IMAGE019
are each a single cationiAnd the energy of a single oxygen atom O in one unit cell can be calculated through the command statements of computer ke/atom and computer pe/atom of Lammps software;
(2) elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 237741DEST_PATH_IMAGE030
And
Figure 61340DEST_PATH_IMAGE003
；
(3) volume of each unit cell of cubic crystals containing cation A
Figure 565044DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 790489DEST_PATH_IMAGE005
The product of (a);
step 3, constructing a training set, a verification set and a test set based on the elastic modulus database constructed in the step 1 and the descriptor constructed in the step 2;
step 4, constructing an elastic modulus prediction model based on the elastic network regression model, and training the constructed elastic modulus prediction model according to the training set, the verification set and the test set constructed in the step 3 to obtain a trained elastic modulus prediction model;
and 5, aiming at the glass material to be predicted, predicting the elastic modulus of the glass material by using the trained elastic modulus prediction model.
Example two:
the embodiment provides an elastic modulus prediction method based on molecular dynamics and elastic network regression algorithm, which includes:
step 1, acquiring elastic modulus data of glass materials with different component compositions, and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
for the acquired elastic modulus data, in practical application, the method further comprises preprocessing the acquired elastic modulus data, wherein the preprocessing comprises the following steps:
judging whether the following two conditions are simultaneously satisfied or not according to the two glass components:
condition 1: in the glass components, the molar ratio difference value of the components of each oxide component is less than or equal to a first preset threshold, and the unit is percentage;
condition 2: the difference value of the elastic moduli of the two glasses is greater than a second preset threshold value, and the unit is percentage;
if the two glass components are simultaneously satisfied, the corresponding two glass components and the corresponding elastic modulus data are removed from the database.
Wherein, the first preset threshold and the second preset threshold in the above two conditions can be determined by the technicians in the field according to the prior knowledge, in the present application, the first preset threshold is 2%, and the second preset threshold is 20%
Step 2, constructing a descriptor containing a material gene of the elastic modulus of the oxide glass material based on molecular dynamics;
2-1 constructing an atomic structure model of oxide crystals with different symmetries as a unit cell for molecular dynamics calculation;
specifically, the method comprises the following steps:
(1) for cations with a valence of +1, according to CaF2The structure is crystal, oxygen ions form a face-centered cubic structure, and cations are in tetrahedral gaps of the face-centered cubic structure, as shown in figure 3;
(2) for +2 valent cations, crystals are constructed according to the NaCl structure, the cations form a face-centered cubic structure, and oxygen ions are in hexahedral gaps of the face-centered cubic structure, as shown in FIG. 4;
(3) for cations with a valence of +3, according to α -Al2O3A structural structure crystal, as shown in fig. 5;
(4) for cations with a valence of +4, according to CaF2The structure makes crystal, the positive ions form a face-centered cubic structure, and the oxygen ions are in the tetrahedral gaps of the face-centered cubic structure;
2-2 for each crystal cell structure constructed in the step 2-1, performing molecular dynamics calculation to obtain optimized unit cell energy
Figure 707630DEST_PATH_IMAGE006
；
Specifically, the method can be realized by adopting the software LAMMPS of molecular dynamics calculation, and the optimized unit cell energy is obtained according to the following steps
Figure 752946DEST_PATH_IMAGE006
：
(a) Selecting a potential function of the system as a Morse potential:
Figure 554680DEST_PATH_IMAGE031
the parameters used for the different oxide elements are shown in the following table:
table 1: parameters adopted by Morse potential
Figure 634632DEST_PATH_IMAGE032
（eV）
Figure 722673DEST_PATH_IMAGE033
(
Figure 379920DEST_PATH_IMAGE034
)
Figure 844399DEST_PATH_IMAGE035
(
Figure 778857DEST_PATH_IMAGE036
)
Figure 37800DEST_PATH_IMAGE037
(eV
Figure 933075DEST_PATH_IMAGE038
)
Li-O 0.001114 3.429506 2.681360 1.0
Na-O 0.023363 1.763867 3.006315 5.0
K-O 0.011162 2.062605 3.305308 5.0
Mg-O 0.038908 2.281000 2.586153 5.0
Ca-O 0.030211 2.241334 2.923245 5.0
Ba-O 0.065011 1.547596 3.393410 5.0
Si-O 0.340554 2.006700 2.100000 0.9
Al-O 0.361581 1.900442 2.164818 1.0
Ti-O 0.024235 2.254703 2.708943 1.0
Sr-O 0.019623 1.886000 3.328330 3.0
(b) Determining initial conditions, given an initial configuration and an initial velocity of the particles (a reasonable initial configuration may accelerate the system towards equilibrium), and according to the boltzmann distribution, assigning initial velocities (v) to the atoms:
Figure 201245DEST_PATH_IMAGE039
(c) the energy conservation of the system is controlled during the simulation using a micro-canonical ensemble (NEV). The temperature and pressure eventually reach equilibrium.
(d) The time step length adopted by simulation is 1fs, the simulation time is 30ps, and the truncation radius is 10
Figure 990210DEST_PATH_IMAGE040
。
(e) After the system reaches the equilibrium, the configuration integral of the system is solved through the tracks (r, F) along the phase space, and then the energy of the unit cell is further calculated based on the result of the configuration integral
Figure 420054DEST_PATH_IMAGE006
。
(f) Single cation is calculated through the command statements of computer ke/atom and computer pe/atom of Lammps softwareiAnd a single oxygen atom O in a unit cell
Figure 553357DEST_PATH_IMAGE018
And
Figure 359639DEST_PATH_IMAGE019
。
2-3 are directed to the structures of the above crystals comprising various symmetries optimized by molecular dynamics calculations; and further calculating to obtain a performance parameter set thereof, and constructing a descriptor for machine learning
Figure 3110DEST_PATH_IMAGE007
：
Figure 869435DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power average exponentAll non-zero integers between-4 and +4,
Figure 473723DEST_PATH_IMAGE009
is the set of all the cations that are present,
Figure 83696DEST_PATH_IMAGE010
is a corresponding cationiThe ratio of the components (A) to (B),
Figure 581673DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 618899DEST_PATH_IMAGE012
means when the power exponent is
Figure 959751DEST_PATH_IMAGE013
When is a cation
Figure 107835DEST_PATH_IMAGE014
Is corresponding to
Figure 725898DEST_PATH_IMAGE015
Individual performance parameters;
Figure 934026DEST_PATH_IMAGE029
，
Figure 512906DEST_PATH_IMAGE007
is a power exponent of
Figure 464681DEST_PATH_IMAGE013
When is a cation
Figure 937251DEST_PATH_IMAGE014
Is corresponding tomA descriptor.
Cationic in predicting elastic modulus herein
Figure 205028DEST_PATH_IMAGE014
The structures of (1) correspond to 3 performance parameters and three performance parameters respectivelyRespectively as follows:
(1) cation per unit of each crystaliBinding energy of
Figure 395838DEST_PATH_IMAGE001
In eV/atom;
calculation of binding energy by using optimized unit cell energy
Figure 885725DEST_PATH_IMAGE006
Subtracting the sum of the energies of the single atoms with the same number and the same type to obtain the product, wherein the calculation formula is as follows:
Figure 478380DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,Mfor cations in crystal cells
Figure 638097DEST_PATH_IMAGE014
The number of the (c) component (a),
Figure 316203DEST_PATH_IMAGE018
and
Figure 609782DEST_PATH_IMAGE019
are each a single cation
Figure 56943DEST_PATH_IMAGE014
And the energy of a single oxygen atom, O, in a unit cell;
(2) elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 902408DEST_PATH_IMAGE030
And
Figure 802231DEST_PATH_IMAGE003
；
(3) volume of each unit cell of cubic crystals containing cation A
Figure 633921DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 201169DEST_PATH_IMAGE005
The product of (a);
the ElaStic tensor constant of the hexagonal crystal can be calculated through the tool software ElaStac of Quantum Espresso
Figure 968268DEST_PATH_IMAGE030
，
Figure 355387DEST_PATH_IMAGE041
，
Figure 990767DEST_PATH_IMAGE042
，
Figure 412521DEST_PATH_IMAGE003
And
Figure 101254DEST_PATH_IMAGE043
. Volume of the hexagonal crystal
Figure 975669DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 149161DEST_PATH_IMAGE005
The calculation formula is as follows:
Figure 425422DEST_PATH_IMAGE044
Figure 534323DEST_PATH_IMAGE045
using a set of data in a database as an example, the application is introduced to construct descriptors for machine learning
Figure 161614DEST_PATH_IMAGE007
The process of (2) is as follows:
a group collected from the databaseThe data are as follows: the glass structure contains A mol SiO2，B mol Al2O3，C mol Na2O, the elastic modulus of the component glass is y GPa.
The total number of ions was calculated to be (3A + 5B + 3C) mol, where Si4+Proportion of ions
Figure 138797DEST_PATH_IMAGE046
Comprises the following steps:
Figure 394198DEST_PATH_IMAGE047
Al3+the proportion is as follows:
Figure 798634DEST_PATH_IMAGE048
Na+the proportion is as follows:
Figure 382062DEST_PATH_IMAGE049
when predicting the modulus of elasticity, for each cationi（Si，Al，Na），
Figure 162937DEST_PATH_IMAGE011
All consist of the 3 types of parameters mentioned above:
Figure 148210DEST_PATH_IMAGE050
elastic constant of
Figure 598914DEST_PATH_IMAGE030
And
Figure 200797DEST_PATH_IMAGE003
modulus parameter (body modulus)
Figure 519783DEST_PATH_IMAGE004
And shear modulus
Figure 248311DEST_PATH_IMAGE005
The product of (d).
n =1 is as follows:
Figure 994550DEST_PATH_IMAGE051
Figure 818150DEST_PATH_IMAGE052
Figure 675247DEST_PATH_IMAGE053
n =2 as follows:
Figure 510479DEST_PATH_IMAGE054
Figure 693199DEST_PATH_IMAGE055
Figure 738515DEST_PATH_IMAGE056
by analogy, the rest can be constructednDescriptor (n = -4, -3, -2, -1, 3, 4) case of value (each case)nThe value has 3 descriptors).
Step 3, constructing a training set, a verification set and a test set based on the elastic modulus database constructed in the step 1 and the descriptor constructed in the step 2;
the method specifically comprises the following steps:
step 3-1, from the elastic modulus database according to the total data quantity N
Figure 399304DEST_PATH_IMAGE057
Randomly extracting data as a first test subset { T }1}；
Step 3-2, for the rest
Figure 603889DEST_PATH_IMAGE058
Screening out data with elastic modulus value smaller than third preset threshold value, and randomly selecting data
Figure 691931DEST_PATH_IMAGE059
As a second test subset { T }2}；
Step 3-3, test subset for divide { T }1}、{T2Acquiring the residual data, acquiring the glass components of the concerned specific components in a preset section, and then randomly selecting the glass components from the glass components
Figure 224543DEST_PATH_IMAGE060
As a third test subset { T }3}；
And 3-4, combining the three test subsets to form a test set { T } = { T } of the model1，T2，T3The rest data are used as a training set and a verification set of the model, and the data are used as the training set and the verification set of the model
Figure 689023DEST_PATH_IMAGE061
、
Figure 498847DEST_PATH_IMAGE062
And
Figure 757790DEST_PATH_IMAGE063
the value of (A) is to ensure that the data ratio of the training set plus the verification set ({ D } + { V }) to the test set { T } is 9: 1.
And 3-4, taking the rest data as a training set and a verification set of the model, wherein the specific division process comprises the following steps:
constructing a training set { D } and a verification set { V } by adopting a k-fold cross validation method, and specifically comprising the following steps:
step 3-4-1, arranging the rest 90% N data in the database according to the elastic modulus value in an ascending order, and then averagely dividing the data into k disjoint subsets { S1，S2，S3……Sk}；
Step 3-4-2, 1 subset S of the data is taken each timehAs a verification set { V }hH =1, 2, 3 … … k, the remaining k-1 subsets as training set { D }hWill train set { DhV and verification sethAs cross validation data.
Step 4, constructing an elastic modulus prediction model based on the elastic network regression model, and training the constructed elastic modulus prediction model according to the training set, the verification set and the test set constructed in the step 3 to obtain a trained elastic modulus prediction model;
step 4-1, establishing an elastic network regression model, and setting a predicted elastic modulus y and a descriptor
Figure 777698DEST_PATH_IMAGE007
The following relationship is satisfied:
Figure 780289DEST_PATH_IMAGE020
whereinPerIn order to be a set of performance parameters,
Figure 195352DEST_PATH_IMAGE021
is composed of
Figure 890776DEST_PATH_IMAGE007
Corresponding regression coefficients, n being a non-zero integer from-4 to 4;
step 4-2, establishing a loss function of the elastic network regression model according to the following formula:
Figure 397981DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 938684DEST_PATH_IMAGE023
for the loss function, N is the number of samples,
Figure 723100DEST_PATH_IMAGE024
in order to predict the value of the target,
Figure 323846DEST_PATH_IMAGE025
in the form of an actual value of the value,
Figure 318346DEST_PATH_IMAGE026
in order to be a penalty term,
Figure 662740DEST_PATH_IMAGE027
for adjusting the over-parameters
Figure 550930DEST_PATH_IMAGE028
；
Step 4-3, adjusting the hyper-parameters for a group
Figure 588157DEST_PATH_IMAGE027
Coefficient of performance
Figure 804374DEST_PATH_IMAGE064
Solving for minimization
Figure 952459DEST_PATH_IMAGE023
Optimization of lower correspondence
Figure 445888DEST_PATH_IMAGE027
Hyper-parameters;
the specific process comprises the following steps:
step 4-3-1, in
Figure 654016DEST_PATH_IMAGE065
Under the condition, the training set { D obtained in the step 3 is adoptedhV and verification sethTraining models in turnkThen, and calculatekNext-in verification set { VhMean square error MSE value in (j):
Figure 357529DEST_PATH_IMAGE066
in the formula (I), the compound is shown in the specification,
Figure 43726DEST_PATH_IMAGE067
in order to verify the amount of data in a set,
Figure 405044DEST_PATH_IMAGE068
in order to verify the predictive value of a set,
Figure 784072DEST_PATH_IMAGE025
actual values for the validation set;
step 4-3-2, calculating
Figure 974882DEST_PATH_IMAGE069
Under the condition ofkAverage of fold-cross validation
Figure 464769DEST_PATH_IMAGE070
：
Figure 667212DEST_PATH_IMAGE071
Step 4-3-3, adjusting model parameters of elastic network regression
Figure 217142DEST_PATH_IMAGE027
Setting the adjusting parameters in sequence
Figure 895248DEST_PATH_IMAGE072
Coefficient of
Figure 188826DEST_PATH_IMAGE073
To adjust the over-parameters
Figure 760621DEST_PATH_IMAGE074
Coefficient of
Figure 215874DEST_PATH_IMAGE075
Repeating the steps 4-3-1 to 4-3-2, and calculating the corresponding
Figure 381276DEST_PATH_IMAGE076
；
Step 4-3-4, selecting the smallest
Figure 212965DEST_PATH_IMAGE077
Corresponding to
Figure 655579DEST_PATH_IMAGE078
Value as optimal hyper-parameter of model
Figure 281733DEST_PATH_IMAGE027
。
Step 4-4, all training sets { D in the database are takenhV and verification sethThe sum of the parameters is used as a training set of the final model after parameter adjustment is finished, namely { S }1，S2，S3……Sk}；
Step 4-5, training set { S ] based on the elastic network regression model in step 4-11，S2，S3……SkAfter training, a series of regression coefficients of the model are obtained
Figure 934431DEST_PATH_IMAGE079
And forming an elastic modulus prediction model.
And 5, aiming at the glass material to be predicted, predicting the elastic modulus of the glass material by using a trained elastic modulus prediction model, wherein the specific process comprises the following steps of:
step 5-1, according to the process of step 2, constructing a descriptor of the glass material to be predicted
Figure 569812DEST_PATH_IMAGE007
；
Step 5-2, the descriptor is processed
Figure 352085DEST_PATH_IMAGE007
And substituting the model into the elastic modulus prediction model to obtain the predicted elastic modulus.
To verify the effectiveness of the method of the present application, 10 sets of glass materials with known values of elastic modulus were predicted by the method of the present invention, and the results are shown in table 2 below.
Table 2: comparison of predicted value and true value of glass elastic modulus predicted by the method
Figure 414719DEST_PATH_IMAGE080
As can be seen from the above table 2, the maximum error between the elastic modulus value of the glass predicted by the method provided by the invention and the true value is only 5.4%, and compared with the existing method, the method provided by the invention can relatively accurately predict the elastic modulus value and verify the effectiveness of the method. Moreover, the method of the invention is adopted to predict the elastic modulus of the glass with unknown elastic modulus, can quickly estimate the elastic modulus of the glass with different component proportions, can greatly reduce the trial and error cost for glass research and development, and has great significance for research and development targets with strict requirements on the elastic modulus of the glass.
Example three:
the embodiment provides an elastic modulus prediction system based on molecular dynamics and elastic network regression algorithm, the system includes:
the elastic modulus database construction module is used for acquiring elastic modulus data of glass materials with different component compositions and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
a descriptor construction module for constructing a descriptor containing a 'material gene' of the elastic modulus of the oxide glass material based on molecular dynamics;
the training data construction module is used for constructing a training set, a verification set and a test set on the basis of the elastic modulus database constructed by the elastic modulus database construction module and the descriptor constructed by the descriptor construction module;
the model construction training module is used for constructing an elastic modulus prediction model based on an elastic network regression model, and training the constructed elastic modulus prediction model according to a training set, a verification set and a test set constructed by the training data construction module to obtain a trained elastic modulus prediction model;
and the prediction module is used for constructing an elastic modulus prediction model trained by the training module by utilizing the model to predict the elastic modulus of the glass material to be predicted.
For specific definition of the elastic modulus prediction system based on molecular dynamics, reference may be made to the definition of the elastic modulus prediction method based on molecular dynamics, which is not described herein again.
The modules in the above-described system for predicting elastic modulus based on molecular dynamics can be implemented in whole or in part by software, hardware, and combinations thereof.
The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
Example four:
the embodiment provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the following steps:
step 1, acquiring elastic modulus data of a glass material, and constructing an elastic modulus database, wherein the database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
step 2, constructing a descriptor containing a material gene of the elastic modulus of the oxide glass material based on molecular dynamics;
step 3, constructing a training set, a verification set and a test set based on the elastic modulus database and the descriptor constructed in the step 2;
step 4, constructing an elastic modulus prediction model based on an elastic network regression model;
and 5, aiming at the glass material to be predicted, predicting the elastic modulus of the glass material by using the elastic modulus prediction model.
For the specific definition of each step, reference may be made to the definition of the elastic modulus prediction method based on molecular dynamics, which is not described herein again.
In one embodiment, a computer-readable storage medium is provided, having stored thereon a computer program which, when executed by a processor, performs the steps of:
step 1, acquiring elastic modulus data of a glass material, and constructing an elastic modulus database, wherein the database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
step 2, constructing a descriptor containing a material gene of the elastic modulus of the oxide glass material based on molecular dynamics;
step 3, constructing a training set, a verification set and a test set based on the elastic modulus database and the descriptor constructed in the step 2;
step 4, constructing an elastic modulus prediction model based on the elastic network regression model;
and 5, aiming at the glass material to be predicted, predicting the elastic modulus of the glass material by using the elastic modulus prediction model.
For the specific definition of each step, reference may be made to the definition of the elastic modulus prediction method based on molecular dynamics, which is not described herein again.
Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A method for predicting elastic modulus based on molecular dynamics and elastic network regression models, the method comprising:
step 1, acquiring elastic modulus data of oxide glass materials with different component compositions, and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
step 2, constructing atomic structures of oxide crystals with different symmetries in the oxide glass material based on molecular dynamicsModel and in terms of cations per unitiBinding energy of
Figure 541517DEST_PATH_IMAGE001
Elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 112307DEST_PATH_IMAGE002
And
Figure 619512DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 102490DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 886907DEST_PATH_IMAGE005
Constructing a descriptor of the elastic modulus comprising a "material gene" as a performance parameter;
step 3, constructing a training set, a verification set and a test set based on the elastic modulus database constructed in the step 1 and the descriptor constructed in the step 2;
step 4, constructing an elastic modulus prediction model based on the elastic network regression model, and training the constructed elastic modulus prediction model according to the training set, the verification set and the test set constructed in the step 3 to obtain a trained elastic modulus prediction model;
step 5, aiming at the glass material to be predicted, obtaining a descriptor containing a material gene according to the composition of the components of the glass material; and predicting the elastic modulus of the glass material to be predicted by using the trained elastic modulus prediction model.
2. The method of claim 1, wherein the step 2 comprises:
step 2-1, constructing atomic structure models of oxide crystals with different symmetries as unit cells of molecular dynamics calculation;
step 2-2 for each cell structure constructed in step 2-1, performing molecular dynamics calculation to obtain cell energy
Figure 753232DEST_PATH_IMAGE006
；
Step 2-3, obtaining a performance parameter set of each crystal cell structure obtained in the step 2-1 through further calculation, and constructing a descriptor for machine learning
Figure 934683DEST_PATH_IMAGE007
：
Figure 154443DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power-averaged exponent, and takes on all non-zero integers between-4 and + 4;
Figure 183579DEST_PATH_IMAGE009
is the set of all cations;
Figure 643641DEST_PATH_IMAGE010
is a corresponding cationiThe component ratio of (A);
Figure 266384DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 414468DEST_PATH_IMAGE012
means when the power exponent is
Figure 422744DEST_PATH_IMAGE013
When is a cation
Figure 568555DEST_PATH_IMAGE014
Is corresponding to
Figure 537648DEST_PATH_IMAGE015
Individual performance parameters;
Figure 849943DEST_PATH_IMAGE016
,3；
Figure 853671DEST_PATH_IMAGE007
is a power exponent of
Figure 108066DEST_PATH_IMAGE013
When is a cation
Figure 485827DEST_PATH_IMAGE014
Is corresponding tomA descriptor; the performance parameters include the cation per unit of each crystaliBinding energy of
Figure 241293DEST_PATH_IMAGE001
Elastic tensor constant of each unit cell of cubic crystal containing cation A
Figure 709315DEST_PATH_IMAGE002
And
Figure 524824DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 891345DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 60290DEST_PATH_IMAGE005
The product of (a).
3. The method of claim 2, wherein said per unit cation isiBinding energy of
Figure 773031DEST_PATH_IMAGE001
The calculation method comprises the following steps:
using the cell energy obtained in step 2-2
Figure 618496DEST_PATH_IMAGE006
Subtracting the sum of the energies of the single atoms of the same number and kind, and calculating by the formula:
Figure DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,Mfor cations in crystal cellsiThe number of the (c) component (a),
Figure 252739DEST_PATH_IMAGE018
and
Figure 976107DEST_PATH_IMAGE019
are each a single cationiAnd a single oxygen atom, O, in one unit cell.
4. The method according to claim 3, wherein the step 2-1 constructs an atomic structure model of the oxide crystal having different symmetries as a unit cell of molecular dynamics calculation, comprising:
(1) for cations with a valence of +1, according to CaF2The structure is crystal, oxygen ions form a face-centered cubic structure, and cations are in tetrahedral gaps of the face-centered cubic structure;
(2) for + 2-valent cations, crystals are constructed according to a NaCl structure, the cations form a face-centered cubic structure, and oxygen ions are in hexahedral gaps of the face-centered cubic structure;
(3) for cations with a valence of +3, according to α -Al2O3A structural structure crystal;
(4) for cations with a valence of +4, according to CaF2The structure makes crystal, the positive ions form a face-centered cubic structure, and the oxygen ions are in the tetrahedral gaps of the face-centered cubic structure.
5. The method according to claim 4, wherein the step 1 of constructing the elastic modulus database further comprises preprocessing the acquired elastic modulus data of oxide glass materials with different compositions:
judging whether the following two conditions are simultaneously satisfied or not according to the two glass components:
condition 1: in the glass components, the molar ratio difference value of the components of each oxide component is less than or equal to a first preset threshold, and the unit is percentage;
condition 2: the difference value of the elastic moduli of the two glasses is greater than a second preset threshold value, and the unit is percentage;
and if the two glass components are simultaneously satisfied, removing the corresponding two glass components and the corresponding elastic modulus data from the elastic modulus database.
6. The method according to claim 5, wherein the first predetermined threshold is 2% and the second predetermined threshold is 20%.
7. The method of claim 6, wherein the elastic network regression model predicts the elastic modulusyAnd descriptors
Figure 277775DEST_PATH_IMAGE007
The following relationship is satisfied:
Figure 310454DEST_PATH_IMAGE020
wherein the content of the first and second substances,Perin order to be a set of performance parameters,
Figure DEST_PATH_IMAGE021
is composed of
Figure 681261DEST_PATH_IMAGE007
Corresponding regression coefficients, n being a non-zero integer from-4 to 4;
the loss function of the elastic network regression model is:
Figure 926429DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 613762DEST_PATH_IMAGE023
for the loss function, N is the number of samples,
Figure 364811DEST_PATH_IMAGE024
in order to predict the value of the target,
Figure 380172DEST_PATH_IMAGE025
in the form of an actual value of the value,
Figure 819243DEST_PATH_IMAGE026
in order to be a penalty term,
Figure 485717DEST_PATH_IMAGE027
for adjusting the over-parameters
Figure 984831DEST_PATH_IMAGE028
。
8. An elastic modulus prediction system based on molecular dynamics and elastic network regression algorithm, the system comprising:
the elastic modulus database construction module is used for acquiring elastic modulus data of glass materials with different component compositions and constructing an elastic modulus database, wherein the elastic modulus database comprises glass components mapped one by one and elastic moduli corresponding to the glass components;
a descriptor construction module for constructing a descriptor containing a 'material gene' of the elastic modulus of the oxide glass material based on molecular dynamics;
the training data construction module is used for constructing a training set, a verification set and a test set on the basis of the elastic modulus database constructed by the elastic modulus database construction module and the descriptor constructed by the descriptor construction module;
the model construction training module is used for constructing an elastic modulus prediction model based on an elastic network regression model tree, and training the constructed elastic modulus prediction model according to a training set, a verification set and a test set constructed by the training data construction module to obtain a trained elastic modulus prediction model;
and the prediction module is used for constructing an elastic modulus prediction model trained by the training module by utilizing the model to predict the elastic modulus of the glass material to be predicted.
9. The elastic modulus prediction system of claim 8, wherein the descriptor construction module is configured to construct a descriptor containing a "material gene" of the elastic modulus of the oxide glass material, comprising
Constructing an atomic structure model of oxide crystals with different symmetries as a unit cell for molecular dynamics calculation;
for each cell structure obtained by construction, molecular dynamics calculation is carried out to obtain unit cell energy
Figure 284226DEST_PATH_IMAGE006
；
For each cell structure obtained by construction, obtaining a performance parameter set thereof through further calculation, and constructing a descriptor for machine learning
Figure 887508DEST_PATH_IMAGE007
：
Figure 283854DEST_PATH_IMAGE008
In the formula (I), the compound is shown in the specification,nis a power-averaged exponent, and takes on all non-zero integers between-4 and + 4;
Figure 829236DEST_PATH_IMAGE009
is the set of all cations;
Figure 865194DEST_PATH_IMAGE010
is a corresponding cationiThe component ratio of (A);
Figure 318172DEST_PATH_IMAGE011
is one of a set of performance parameters,
Figure 460703DEST_PATH_IMAGE012
means when the power exponent is
Figure 708144DEST_PATH_IMAGE013
When is a cation
Figure 231398DEST_PATH_IMAGE014
Is corresponding to
Figure 815964DEST_PATH_IMAGE015
Individual performance parameters;
Figure 62268DEST_PATH_IMAGE016
,3；
Figure 808507DEST_PATH_IMAGE007
is a power exponent of
Figure 66662DEST_PATH_IMAGE013
When is a cation
Figure 330284DEST_PATH_IMAGE014
The m-th descriptor corresponding to the structure of (1); the performance parameters include the cation per unit of each crystaliBinding energy of
Figure 555729DEST_PATH_IMAGE001
Each of the cubic crystals containing the cation ASpring tensor constant of unit cell
Figure 597503DEST_PATH_IMAGE002
And
Figure 268918DEST_PATH_IMAGE003
volume of each unit cell of cubic crystals containing cation A
Figure 195286DEST_PATH_IMAGE004
And Voigt average shear modulus
Figure 947341DEST_PATH_IMAGE005
The product of (a).
10. A computer device comprising a memory, a processor and a computer program stored on the memory and running on the processor, characterized in that the steps of the method of any of claims 1 to 7 are implemented when the computer program is executed by the processor.
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