CN111091878A - Method for rapidly predicting perovskite dielectric constant - Google Patents

Abstract

The invention relates to a method for rapidly predicting perovskite dielectric constant. It comprises the following steps: finding ABO synthesized by sol-gel method from literature₃And (3) taking the chemical formula, the experimental numerical value of the dielectric constant, the calcining temperature and the calcining time of the inorganic perovskite material as a data set sample. And generating a corresponding descriptor according to the chemical formula by using an OCPMDM (optical character matching model) of a data mining platform, and deleting the sample of the defect numerical value in the descriptor generation process. The data set samples are randomly divided into training and test sets. Taking the dielectric constant logarithm value as a target variable, and taking descriptors such as generated atomic parameters and the like as independent variables; carrying out independent variable screening on the training set by combining a genetic algorithm with a support vector machine leave-one-out method, selecting an optimal independent variable subset for modeling, establishing a rapid prediction model of perovskite dielectric constant, and carrying out parameter optimization andleave one out for cross validation. And according to the established rapid prediction model of the dielectric constant of the perovskite and the chemical formula of the perovskite to be detected, rapidly predicting the dielectric constant of the perovskite to be detected. The invention is based on reliable literature data and a modeling method, and the established prediction model of the perovskite dielectric constant has the advantages of simplicity, convenience, rapidness, low cost, no pollution and the like.

Description

Method for rapidly predicting perovskite dielectric constant

Technical Field

The invention relates to the field of electrical properties of inorganic perovskite, in particular to a method for rapidly predicting perovskite dielectric constant by combining genetic algorithm with a support vector machine, which can be applied to the technical field of perovskite property characterization and analysis testing.

Technical Field

Perovskite in the narrow sense means CaTiO₃By itself, perovskite in the broadest sense is meant to have the structure ABX₃The perovskite type compound has a structure generally of an octahedron structure, wherein the apex angle of the lattice is occupied by an A ion with a larger radius, and the center is occupied by a common angle formed by a B ion and an X. Wherein the cation A is generally metal ion or organic small molecule, the cation B is generally 2-valent or 3-valent metal ion, and can be replaced by two different cations to form double-layer perovskite, and the anion X is generally chalcogen or halogen. The perovskite has the advantages of stable crystal structure, low manufacturing cost, simple synthesis process and excellent photoelectric property, and is widely applied to the fields of piezoelectricity, catalysis, solar cells and the like.

The dielectric constant, also called permittivity or absolute conductivity, is the ratio of the capacitance of the same substance in the same capacitor in a dielectric and in a vacuum, and represents the relative ability of the dielectric to store electrostatic energy in an electric field, i.e. the ability to hold a charge, and is often expressed as epsilon. The dielectric constant ε can be measured experimentally in the form of an electrostatic field: testing the capacitance C of a capacitor while vacuum is applied between two plates₀The capacitance C is then measured using the same distance between the capacitor plates but with the dielectric between the plates_xThe dielectric constant can be calculated by the following formula ∈ ═ Cx/C₀. The dielectric constant is one of important data for representing the electrical property of a dielectric or insulating material and is an important index for selecting the dielectric material, so that the research on the dielectric constant of the perovskite is of great significance.

The Genetic Algorithm (Genetic Algorithm) is a calculation model of a biological evolution process for simulating natural selection and Genetic mechanism of Darwin biological evolution theory, is a method for searching an optimal solution by simulating the natural evolution process, is provided by Holland professor in the United states, and has the core idea that the principle of 'excellence and disadvantage' in the biological evolution theory is adopted to generate better and better approximate solutions by generation evolution according to the survival principle of fittest. The genetic algorithm has the rapid searching capability irrelevant to the problem field, iteration is carried out from a group based on an evaluation function during searching, and the method has better parallelism and randomness. Therefore, the genetic algorithm can embody the high efficiency and the practicability when solving optimization problems of multiple targets, multiple variables, nonlinearity and the like.

A Support Vector Machine (SVM) is a new Machine Learning method established by mathematicians vladimix n. vapnik and the like on the basis of a Statistical Learning Theory (SLT), and includes a Support Vector Classification (SVC) algorithm and a Support Vector Regression (SVR) algorithm. The method of support vector machine is based on statistical learning theoryVC vitaminOn the basis of the principle of minimum theoretical and structural risks, an optimal compromise is sought between the complexity of the model (i.e. the learning accuracy of a specific training sample) and the learning ability (i.e. the ability to identify any sample without error) according to limited sample information so as to obtain the best popularization ability. The work was modeled using a support vector regression method.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide a method for quickly predicting the dielectric constant of inorganic perovskite by combining a genetic algorithm with a support vector machine, wherein the genetic algorithm is simple, convenient, quick, low in cost, comprehensive and accurate in data and free of experiments and complicated calculation processes.

The purpose of the invention can be realized by the following technical scheme:

a method for rapidly predicting the dielectric constant of inorganic perovskite based on genetic algorithm combined with a support vector machine comprises the following steps:

1) finding ABO synthesized by sol-gel method from literature₃Chemical formula, experimental dielectric constant value and calcination of inorganic perovskite materialTemperature and calcination time as data set samples.

2) And generating a corresponding descriptor according to the chemical formula by using an OCPMDM (optical character matching model) of a data mining platform, and deleting the sample of the defect numerical value in the descriptor generation process.

3) Randomly dividing the data set samples obtained in the step 1) into a training set and a testing set.

4) Taking the logarithmic value of the dielectric constant collected in the step 1) as a target variable, and the descriptors such as the atomic parameters generated in the step 2) as independent variables; and (4) carrying out independent variable screening on the training set by combining a genetic algorithm with a support vector machine leave-one-out method, and selecting the optimal independent variable subset for modeling.

5) And (3) establishing a rapid prediction model of the perovskite dielectric constant by using a support vector machine, and performing parameter optimization and leave-one-out cross validation.

6) And according to the established rapid prediction model of the dielectric constant of the perovskite and the chemical formula of the perovskite to be detected, rapidly predicting the dielectric constant of the perovskite to be detected.

Compared with the prior art, the invention has the following advantages:

firstly, the prediction of the perovskite dielectric constant is simple and rapid: according to the method, the perovskite dielectric constant is forecasted by combining a genetic algorithm with a support vector machine method, the result is cross-validated, the collected atomic parameters are used for generating the descriptors, the obtained descriptors are imported into the model, the calculation result can be obtained in a few seconds, and the method is convenient and rapid and can be completed by only one person.

Secondly, the cost is low: the method utilizes the genetic algorithm and the support vector machine to quickly predict the dielectric constant of the inorganic perovskite, and has simple operation and low cost for predicting the sample of the dielectric constant to be measured.

Thirdly, the data are comprehensive and accurate: the invention reduces the dimension of independent variable by using genetic algorithm, reduces original multidimensional data to 9 most representative data, maintains original information as much as possible while reducing data dimension, and has simple model and convenient calculation.

Fourthly, no pollution is caused: the invention does not relate to experiments in the whole process, does not use chemical drugs and has no pollution to the environment.

Drawings

FIG. 1 is a graph of the results of modeling a support vector machine regression model of perovskite dielectric constant.

FIG. 2 is a graph of the results of one-out-of-one cross-validation of a support vector machine regression model of perovskite dielectric constant.

FIG. 3 is a graph of the results of an independent test set of a support vector machine regression model for perovskite dielectric constant.

Detailed Description

The invention is described in detail below with reference to the drawings and preferred embodiments.

Example 1: modeling results of a perovskite dielectric constant quantitative prediction model established based on 39 samples, as shown in fig. 1; the method comprises the following steps:

(1) finding ABO synthesized by sol-gel method from literature₃The chemical formula, the experimental numerical value of dielectric constant, the calcination temperature and the calcination time of the inorganic perovskite material are used as data set samples, 104 inorganic perovskite materials are found in total, and table 1 is a data sample set of the chemical formula, the experimental numerical value of dielectric constant, the calcination temperature and the calcination time of partial perovskite materials:

table 1: data sample set of perovskites in literature

Chemical formula (II)	Dielectric constant ε	Calcination temperature/K	Calcination time/h
				MnFeO3	41.87	1073	7
Gd0.2Mn0.8Fe0.98Cu0.02O3	18.57	1073	7
				Gd0.4Mn0.6Fe0.96Cu0.04O3	14.89	1073	7
Gd0.6Mn0.4Fe0.94Cu0.06O3	10.59	1073	7
				Gd0.8Mn0.2Fe0.92Cu0.08O3	7.95	1073	7
GdFe0.9Cu0.1O3	5.53	1073	7
				Na0.425K0.075Bi0.5TiO3	400	973	0.05
Na0.425K0.075Bi0.5TiO3	519	937	0.083
				SrTiO3	504	1473	4
Pb0.5Sr0.5FeO3	788	773	6
				Pb0.5Sr0.5Ti0.99Fe0.01O3	704	773	6
Pb0.5Sr0.5Ti0.95Fe0.05O3	442	773	6
				Pb0.5Sr0.5Ti0.9Fe0.1O3	396	773	6
BiFeO3	45.5	823	0.5
				Bi0.95Ba0.05FeO3	31.4	823	0.5
Bi0.95Sr0.05FeO3	18.8	823	0.5
				Bi0.95Ca0.05FeO3	4.5	823	0.5
Ba0.8Ca0.2TiO3	368	1073	8
				Ba0.8Sr0.2TiO3	225	1073	8
Ba0.7Sr0.3TiO3	573	1023	2

(2) And generating corresponding descriptors according to the chemical formula by using an OCPMDM (optical character matching model) of a data mining platform, and deleting samples of the defect numerical values in the descriptor generation process, wherein the number of the samples with complete data is 48 after deletion. The OCPMDM generates 21 descriptors, and the calcination time and the calcination temperature collected in the literature are added to 23 descriptors, and the expression method and the physical meaning are shown in the following table 2:

table 2: descriptor and physical meaning

(3) Randomly dividing 48 data set samples obtained in the step 2) into a training set and a testing set, wherein the ratio is 4:1, and the sample amount of the training set and the sample amount of the testing set are 39 and 9 respectively; the training set is used for variable screening, leave-one-out cross validation and modeling; the test set is used for independent test validation.

(4) Taking the logarithm value of the dielectric constant of the perovskite collected in the step 2) as a target variable, taking a descriptor generated by OCPMDM, a calcination temperature and calcination time as independent variables, verifying by combining a genetic algorithm and a support vector machine one-out method to carry out variable screening on a modeling set, and selecting 9 optimal variables, wherein the selected optimal variables are shown in a table 3;

table 3: optimal variables selected by genetic algorithm

Radius_B	Za	Zb	B_ionic	A_Tm
					B_Hfus	B_Density	CT	AH

The genetic algorithm screening variables comprises the following specific steps:

4-1) initialization: setting an evolution algebra counter T to be 0, setting a maximum evolution algebra T, and randomly generating M individuals as initial individuals P (0);

4-2) evaluation of individuals: calculating the fitness of each individual in the population P (t);

4-3) selection operation: acting a selection operator on a group, directly transmitting the optimized individual heredity to the next generation or generating a new individual heredity by pairing and crossing, wherein the selection operation is established on the basis of self-adaptive evaluation of individuals in the group;

4-4) intersection operation: applying a crossover operator to the population, wherein crossover refers to the generation of new individuals by replacing and recombining partial structures of two parent individuals;

4-5) mutation operation: mutation operators are applied to the population, i.e., the gene values at certain loci of the individual strings in the population are varied. The group P (t) is subjected to selection, crossing and mutation operations to obtain a next generation group;

4-6) judging termination conditions: if the termination condition of the iterative computation is met, outputting the individual with the maximum fitness obtained in the evolution process as an optimal solution, and computing a final value;

the support vector machine regression algorithm comprises the following specific steps:

4-7) setting sampleThe collection is as follows: (y)₁，x₁)，…，(y_l，x_l) The nonlinear regression function is represented by the following regression function:

lagrange undetermined coefficient α_i ^*，α_iAnd kernel function K (x)_i,x_j) This can be found from the following equation:

the lagrangian constraint is:

0≤α_i≤C,i＝1,…,l

e is an offset value, and C is a set penalty factor value;

4-8)K(x_i,x_j) Instead of using a suitable kernel function, a radial basis kernel function is used, namely:

σ is a function parameter;

4-9) find the regression function f (x).

(5) And (3) establishing a rapid prediction model of the perovskite dielectric constant by using a support vector machine, and performing parameter optimization and leave-one-out cross validation. The penalty factor C of the optimal parameters of the support vector machine, the parameter gamma of the kernel function of the radial machine and the insensitive loss function epsilon are 0.1011, 1.8880 and 0.2253 respectively.

(6) And according to the established rapid prediction model of the dielectric constant of the perovskite and the chemical formula of the perovskite to be detected, rapidly predicting the dielectric constant of the perovskite to be detected.

In this embodiment, a support vector machine regression algorithm is used to perform regression modeling on 39 perovskite sample data, and a support vector machine regression quantitative model of inorganic perovskite dielectric constant is established. The correlation coefficient between the predicted value and the experimental value of the perovskite dielectric constant model is 0.9278. According to the method, an efficient and rapid forecasting model is established through sample data from documents, and the method has the advantages of rapidness, convenience, low cost, environmental friendliness, and can also play a guiding role in actual experimental operation and avoid blindness.

Example 2: in this example, the same as example 1, and the leave-one-out internal cross validation result of the quantitative prediction model of perovskite dielectric constant, which is established by using 39 samples, is shown in fig. 2.

In this embodiment, the method is characterized in that the 39 samples in the training set are numbered a1, a2 … … a 54. In the first step, A1 and A2 … … A39 are used as training sets, the same optimal independent variable subsets as in the first embodiment are used for establishing a model 1, and the Curie temperature of A39 is forecasted by using the model 1. In the second step, a1, a2 … … a37 and a39 are used as training sets, the same optimal independent variable subset as in the first embodiment is adopted, model 2 is established, and the curie temperature of a38 is forecasted by using the model 2. By analogy, after 38 models are established, the stability and reliability of the data modeling method are judged through the error between the predicted value and the true value.

The method adopts a leave-one-out method to carry out internal cross validation on the quantitative prediction model of the perovskite Curie temperature established by 39 sample data by using a support vector machine, and the correlation coefficient of the model prediction value and the experimental value of the perovskite dielectric constant in the leave-one-out method is 0.8965. According to the method, the forecasting model of the one-out-of-one-training-set cross validation is established through the sample data from the literature, the advantages of rapidness, convenience, low cost and environmental friendliness are achieved, and meanwhile the stability and reliability of the data modeling method can be evaluated.

Example 3: independent test set prediction results based on 9 established quantitative prediction models of perovskite dielectric constant are shown in fig. 3.

The method is characterized in that the established support vector machine quantitative prediction model of the perovskite dielectric constant is used for predicting 9 samples in an independent test set, and a better result is obtained. The correlation coefficient of the model prediction value and the experimental value of the perovskite dielectric constant is 0.8958, the method establishes an efficient and rapid prediction model through sample data from documents, has the advantages of rapidness, convenience, low cost, environmental friendliness, and can also play a guiding role in practical experiment operation to avoid blindness.

Claims (2)

1. A method for rapidly predicting the dielectric constant of perovskite, comprising the steps of: :

1) finding ABO synthesized by sol-gel method from literature₃The chemical formula, the experimental numerical value of the dielectric constant, the calcination temperature and the calcination time of the inorganic perovskite material are used as data set samples;

2) generating a corresponding descriptor according to the chemical formula by using an OCPMDM (optical code matching model) of a data mining platform, and deleting a sample of a defect numerical value in the descriptor generation process;

3) randomly dividing the data set samples obtained in the step 1) into a training set and a testing set;

4) taking the dielectric constant logarithm value collected in the step 1) as a target variable, and taking the generated atomic parameter descriptor in the step 2) as an independent variable; carrying out independent variable screening on the training set by combining a genetic algorithm with a support vector machine leave-one-out method to select an optimal independent variable subset for modeling;

5) establishing a rapid prediction model of perovskite dielectric constant by using a support vector machine, and performing parameter optimization and leave-one-out cross validation;

6) and according to the established rapid prediction model of the dielectric constant of the perovskite and the chemical formula of the perovskite to be detected, rapidly predicting the dielectric constant of the perovskite to be detected.

2. The method for rapidly predicting the perovskite dielectric constant according to claim 1, wherein the step 4) specifically comprises the following steps:

the genetic algorithm screening variables comprises the following specific steps:

4-1) initialization: setting an evolution algebra counter T to be 0, setting a maximum evolution algebra T, and randomly generating M individuals as initial individuals P (0);

4-2) evaluation of individuals: calculating the fitness of each individual in the population P (t);

4-3) selection operation: acting a selection operator on a group, directly transmitting the optimized individual heredity to the next generation or generating a new individual heredity by pairing and crossing, wherein the selection operation is established on the basis of self-adaptive evaluation of individuals in the group;

4-4) intersection operation: applying a crossover operator to the population, wherein crossover refers to the generation of new individuals by replacing and recombining partial structures of two parent individuals;

4-5) mutation operation: applying mutation operators to the population, i.e., varying the gene values at certain loci of the individual strings in the population; the group P (t) is subjected to selection, crossing and mutation operations to obtain a next generation group;

4-6) judging termination conditions: if the termination condition of the iterative computation is met, outputting the individual with the maximum fitness obtained in the evolution process as an optimal solution, and computing a final value;

the support vector machine regression algorithm comprises the following specific steps:

4-7) set the sample set to: (y)₁，x₁)，…，(y_l，x_l) The nonlinear regression function is represented by the following regression function:

α_i ^*，α_iand K (x)_i,x_j) The following equation is used to solve:

the lagrangian constraint is:

0≤α_i≤C,i＝1,…,l

e is an offset value, and C is a set penalty factor value;

4-8)K(x_i,x_j) Instead of using a suitable kernel function, a radial basis kernel function is used, namely:

σ is a function parameter;

4-9) find the regression function f (x).

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