Method for screening thermodynamic stability of perovskite oxide based on machine learning

Abstract

The invention provides a thermodynamic stability screening method of perovskite oxides based on machine learning. The method comprises the following steps: firstly, acquiring nuclear external energy and formation energy data of perovskite oxide, and extracting a feature descriptor strongly related to thermodynamic stability; then, training a machine learning model by using the feature descriptors; and finally, screening stable perovskite oxides by using the trained model. According to the method, the thermodynamic stability of the perovskite material is predicted based on the perovskite descriptor and machine learning, the prediction precision and efficiency can be improved, the waste of experimental resources is reduced, and the method has the advantages of automation, high throughput, high accuracy and wide applicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of material and computer integration, and specifically relates to a method for screening the thermodynamic stability of perovskite oxides based on machine learning. Background Art

[0002] The three major elements of the material genome, high-throughput computing, high-throughput experiments, and databases, correspond to the computing-driven, experiment-driven, and data-driven working modes, respectively. The computing-driven mode uses density functional theory and other methods to screen target materials, aiming to make up for the huge "trial and error" experimental costs in the experiment with less computing time; the experiment-driven mode uses a combination of parallel processing to induce qualitative changes with quantitative changes, and strives to complete the preparation and characterization of samples in a short time; the data-driven mode is the core of the material genome. Material scientists do not need to consider the physical and chemical meanings of the parameters. They can use data mining methods to directly mine valuable information from the database, and transform useful information into reliable knowledge under the guidance of theory, so as to assist material design and development. In the field of materials science, the core of data mining is to be able to select the most appropriate data from the material database, establish a model to analyze the correlation between various parameters, accurately extract laws and explain knowledge, and finally establish or predict the quantitative and qualitative relationship between "composition-process-structure-performance" under a given system. Compared with the first two modes, the data-driven mode can greatly improve the speed of material design, reduce design costs, and better screen and design materials.

[0003] In recent years, the availability of large data sets on materials combined with improvements in algorithms and exponential growth in computing power has led to an unprecedented rise in the popularity of machine learning. Predicting crystal structure based solely on knowledge of the chemical composition of a material remains one of the most important challenges in materials science, as any rational material design must be based on knowledge of the crystal structure. Unfortunately, first-principles prediction of crystal structure is extremely difficult because the combinatorial space consists of all possible atomic arrangements in three dimensions and has an extremely complex energy surface. In recent years, advances in advanced structure selection and generation algorithms, such as random sampling, simulated annealing, molecular dynamics, minimum hopping, and evolutionary algorithms, have expanded the scope of application of "classical" crystal structure prediction. However, it is impossible to find new or better high-performance materials without searching in the huge compositional and structural space. Due to the large amount of data involved, machine learning algorithms are one of the most promising candidates for this challenge.

[0004] Machine learning methods accelerate energy assessments by replacing first-principles methods with models that are several orders of magnitude faster. However, the most prominent method in inorganic solid-state physics is composition prediction, which requires selecting a prototype structure and scanning the composition space of stable materials. In this case, thermodynamic stability is a fundamental concept. Stability is usually related to whether a material can be synthesized and whether it will degrade over time at a specific temperature or pressure. Thermodynamically stable compounds are usually easier to produce and use, and play an important role in the discovery of new functional materials. The measure of thermodynamic stability is the energy distance to the convex hull, that is, the energy above the nucleus. Under certain conditions, the machine learning model will directly calculate the probability of a compound existing at a certain stage.

[0005] In terms of composition prediction, the expected output of the model is a numerical value that quantifies the probability that the compound will condense in a specific structure. Faber et al. applied KRR to calculate the formation energy of 2 million crystals composed of main group elements below bismuth. For a training set consisting of components, the reported error was about 0.1 eV / atom. At the same time, energies and data from the Materials Project were used to construct 78 phase diagrams and predict 90 new stoichiometries located on the convex hull. Schmidt et al. constructed a dataset of approximately 250,000 cubic perovskites based on DFT calculations, using all elements below bismuth, ignoring rare gases and lanthanides. After testing different machine learning methods, they finally achieved the greatest success with an average error of 0.12 eV / atom by combining extreme random trees and adaptive boosting methods. Ward et al. used random forests to combine structural information and atomic properties to predict formation energy, verifying that the model error containing only composition information was 37% higher than the model error including structural information. Kim et al. used random forests to discover quaternary Heusler compounds and identified 53 new stable structures. Ye et al. established a neural network based on element electronegativity and ionic radius to predict the formation energy of unmixed perovskites, with an average error of 30 meV / atom. CGCNNs developed by Xie et al., MGN developed by Chen et al., and MPNNs developed by Jorgensen et al. can all predict formation energy for accelerating component prediction. Balachandran et al. predicted whether the perovskite exists in the form of cubic perovskite or non-cubic perovskite, with an average cross-validation error of 94%. Oliynyk et al. used Pearson crystal data and compounds in the alloy phase diagram database to establish a random forest model to predict the possibility of forming a full Heusler compound with a specific composition, and finally successfully predicted the stability of several new full Heusler phase diagrams. Hautier et al. established a probabilistic model to predict new compositions of ABO compounds and their most likely crystal structures. In order to evaluate the stability, the energy of all decomposition channels present in the database was also calculated, and finally 355 new compounds were generated on the convex hull.

[0006] In terms of structure prediction, the focus is on distinguishing multiple crystal structures, which is usually a much more complex problem because the theory of structure space is more complex than that of composition space. Fischer et al. developed a method based on the cumulant expansion method to estimate the correlation between the stability of two structures and their composition to predict the probability of elemental composition forming a specific binary crystal structure. Olynyk et al. applied cluster-resolution feature selection to the classification of binary crystal structures, and the selected features were used as inputs to partial least squares discriminant analysis and support vector machines. Balachandran et al. used machine learning methods to study 60,000 potential perovskites, first dividing them into perovskites and non-perovskites using singular value decomposition, and then predicting the Curie temperature of these perovskites. Once a candidate perovskite was experimentally synthesized, it was added to the training set and the process was repeated. Finally, six perovskites were found with the highest Curie temperature of 898K. Graser et al. applied random forests to classify the crystal structures of 24,215 compounds in the database and studied the changes in the model's predictive ability relative to the cutoff value. The results showed that the recall rate increased with the increase of the cutoff number. Park et al. developed 255 deep convolutional neural networks using X-ray images as input and space groups, extinction groups or crystal systems as output, which were able to correctly identify the structural systems of two new compounds whose prototype structures did not appear in the database. Nouira et al. introduced a GAN-based strategy to generate stable ternary structures based on binary hydrides.

[0007] Among the methods introduced above, the machine learning-based method has the characteristics of short response time, fast speed, and generalization of extracted features. Compared with other methods, it has certain advantages in prediction effect. Summary of the invention

[0008] In order to overcome the deficiencies of the prior art, the present invention provides a method for screening the thermodynamic stability of perovskite oxides based on machine learning. First, the exonuclear energy and formation energy data of the perovskite oxide are obtained, and feature descriptors that are strongly related to thermodynamic stability are extracted; then, the feature descriptors are used to train the machine learning model; finally, the trained model is used to screen stable perovskite oxides. The present invention predicts the thermodynamic stability of perovskite materials based on perovskite descriptors and machine learning, which can improve the accuracy and efficiency of prediction, reduce the waste of experimental resources, and has the advantages of automation, high throughput, high accuracy, and wide applicability.

[0009] A method for screening thermodynamic stability of perovskite oxides based on machine learning, characterized by the following steps:

[0010] Step 1: Obtain the nuclear exo-energy and formation energy data of perovskite oxides from the open source materials database Materials Project;

[0011] Step 2: Use data preprocessing methods to extract features from perovskite oxide data to obtain a set of feature variables, and select features that are strongly related to the thermodynamic stability of perovskite oxides through feature selection to form a set of feature descriptors;

[0012] Step 3: Selecting the nuclear external energy of 36 meV / atom as the cutoff value, taking the data in the feature descriptor set as input, and taking the classification results of stable and unstable perovskite oxides as output, the random forest model is trained; the random forest model predicts the thermodynamic stability of the perovskite oxide according to the feature data, and gives the stability classification result of the perovskite oxide by integrating the voting mechanism of multiple decision trees;

[0013] Step 4: Input the feature data set of perovskite oxides after feature selection into the trained random forest model, and output the classification results of stable and unstable perovskite oxides.

[0014] Specifically, the material gene analysis software package Pymatgen was used to download the nuclear exo-energy and formation energy data of perovskite oxides from the materials database Materials Project.

[0015] Specifically, the process of feature extraction using the preprocessing method is as follows: first, according to the elemental composition of the perovskite oxide, the elemental property type characteristics are constructed using the physical and chemical properties of the atoms; then, different elemental property type characteristics are combined using statistical methods to obtain elemental property type derived characteristics; then, spatial structure type characteristics are constructed based on the crystal structure of the perovskite oxide; finally, the elemental property type derived characteristics and the spatial structure type characteristics are combined, and all combined characteristics constitute the final characteristic variable set.

[0016] Specifically, the characteristics related to the thermodynamic stability of perovskite oxides include atomic radius, electronegativity, atomic mass, oxidation state, ionic radius, bond length, bond angle, lattice constant, band structure, valence band top position, conduction band bottom position, electron affinity, formation energy, atomic arrangement, and electronic structure characteristics of the material; among them, strongly correlated features refer to features whose correlation coefficient with the thermodynamic stability of perovskite oxides is higher than a set threshold, or features that have significantly contributed to the predicted stability screened out by machine learning methods including recursive feature elimination methods and feature selection methods based on importance scores.

[0017] Specifically, when training the random forest model, the grid search method is used to search in the hyperparameter space of the model, continuously optimize the model parameters, and obtain the optimal parameters of the model.

[0018] Specifically, the element property type features include two types: continuous and discrete. The creation process of the continuous element property type features is as follows: first, the continuous element properties of the highest component elements at the A and B positions are used to generate features. Then, the average, difference, and ratio of the corresponding continuous element property values ​​of the highest component element atoms at the A and B positions are calculated, and added to the features. Next, the weighted average, maximum, minimum, and value range of the continuous element properties of all element atoms at the A position are calculated, as well as the weighted average, maximum, minimum, and value range of the continuous element properties of all element atoms at the B position, and these are added to the features to obtain the final continuous element property type feature vector.

[0019] The creation process of discrete element property type features is as follows: first, all discrete element properties of the highest component elements at position points A and B are used to generate features, and then the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at position point A, as well as the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at position point B are calculated, and added to the features to obtain the final discrete element property type feature vector.

[0020] Specifically, the combination methods of combining different element property type characteristics using statistical methods to obtain the final element property type derived characteristics include weighted average method, ratio method, extreme value method and main element method.

[0021] Specifically, the spatial structure type characteristics include the tolerance factor, octahedral factor, AO bond length, BO bond length, AB bond length calculated by Shannon atomic radius, and the tolerance factor and octahedral factor calculated by ionic radius.

[0022] Specifically, all features in the feature variable set are normalized to have zero-unit mean and standard deviation.

[0023] The beneficial effects of the present invention are as follows: the present invention predicts the thermodynamic stability of perovskite materials based on perovskite descriptors and machine learning, which can improve the accuracy and efficiency of prediction, reduce the waste of experimental resources, and has the advantages of automation, high throughput, high accuracy, and wide applicability. By selecting appropriate feature descriptors, redundant information in complex feature spaces can be reduced, thereby improving the generalization ability of the model. At the same time, the use of machine learning models to screen the thermodynamic stability of materials avoids the time-consuming and labor-intensive trial and error process in traditional experiments, allowing researchers to more quickly screen out perovskite materials with excellent stability; in addition, the present invention can process large-scale material data, greatly speeding up the process of material screening, helping researchers to quickly understand the trend of material properties and provide information for material discovery; the use of the present invention can significantly improve efficiency in the design and development of new materials, and promote the practical application of perovskite materials in energy, electronics, photovoltaics and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flow chart of the thermodynamic stability screening method of perovskite oxides based on machine learning of the present invention;

[0025] Figure 2 It is a schematic diagram of the model training process of the present invention;

[0026] Figure 3 It is a diagram of the number of compounds of corresponding elements at position A and position B in the data set of the present invention. DETAILED DESCRIPTION

[0027] The present invention is further described below in conjunction with the accompanying drawings and embodiments. The present invention includes but is not limited to the following embodiments.

[0028] The present invention provides a method for screening the thermodynamic stability of perovskite oxides based on machine learning, such as Figure 1 As shown, the specific implementation process is as follows:

[0029] 1. Obtain the nuclear exokinetic energy and formation energy data of perovskite oxides from the open source materials database Materials Project.

[0030] The data used in the present invention for predicting the thermodynamic stability of perovskite oxides mainly come from Materials Project, i.e., the materials engineering database. Currently, the interface of this website has been integrated into the materials gene analysis software package Pymatgen, and this tool can be used to download material data.

[0031] Pymatgen is a robust and very powerful open source Python library that is widely used in materials analysis. Its main features include: highly flexible classes used to represent molecules, elements, and structural objects with high portability; support for a wide range of input and output formats, including VASP, ABINIT, CIF, and other file formats; powerful analysis tools, including generation of phase diagrams (the main function used in this experiment) and diffusion analysis; analysis of electronic structure, such as state density and band structure. Pymatgen can also perform continuous integration on Linux and Windows platforms to ensure that each submission can fully pass unit tests, and a fairly comprehensive documentation has been written to help researchers quickly master it. In addition, many core numerical methods in Pymatgen have been optimized by vectorizing in numpy / scipy, so coordinate processing can be performed quickly.

[0032] The thermodynamic stability of perovskite oxides is a key material property, and its value may determine the effectiveness of perovskites in specific applications. If a compound is predicted to be thermodynamically stable, then it should be synthesizable. Potential energy calculations and potential energy analysis based on first principles of density functional theory can be used to screen the catalytic activity and thermodynamic stability of perovskite oxides. All perovskite oxide materials calculated based on density functional theory appear in the open source database Materials Project, which contains 1,900 perovskite oxides and their energy above hull and formation energy. The energy above hull of the compounds in the data set is less than 400 meV / atom, so it is possible to exclude a small number of highly unstable materials that may have a negative impact on the accuracy of the model.

[0033] The main parameter controlling stability is the energy above the hull, which is a measure of the energy required to decompose a compound into a linear combination of stable phases on a phase diagram. Energy above the hull can directly measure the thermodynamic stability of perovskite oxides. The data in this data set were obtained under the environmental conditions of T = 1073k and p(O2) = 0.2atm, corresponding to an oxidation potential of -6.25eV / O, i.e., the approximate working conditions of the cathode of a solid oxide fuel cell. Since many technological applications involving the use of perovskite oxides operate at high temperatures, and in addition, stability tests are performed at a temperature of 1073k, where cation movement is fast enough to cause phase decomposition, the data set selected based on this thermodynamic condition is suitable for accurate prediction of the high temperature stability of perovskites under p(O2) = 0.2atm.

[0034] The perovskite oxides in the dataset consist of a set of candidate elements, where the A-site candidate element set is {Ba, La, Y, Pr, Gd, Dy, Ho, Nd, Sm, Ca, Sr, Bi, Cd, Sn, Zn} and the B-site candidate element set is {Fe, V, Cr, Mn, Sc, Co, Ti, Mg, Ni, Zr, Ga, Hf, Nb, Ta, Re, Tc, Ir, Os, Ru, Rh, Al, Cu, Pt, Zn} and the X-site represents oxygen (O). In total, the dataset consists of 65 ternary perovskite oxides (e.g., LaMnO3), 1238 quaternary perovskite oxides (e.g., La 0.75 Sr 0.25 MnO3), 588 pentad perovskite oxides (such as La 0.5 Sr 0.5 Co 0.25 Fe 0.75 O3) and 9 six-membered perovskite oxides. All data were simulated as fully stoichiometric (no O vacancies), and all compounds containing more than 3 elements (including O) were simulated as a single-order structure to ensure that a large number of density functional theory (DFT) calculations are easy to handle. Referring to the successful application cases of predecessors, the elemental composition of the A position and the B position is combined in a ratio of 1 / 8.

[0035] The perovskite oxide 36meV / atom extranuclear energy is selected as a threshold value to separate stable and unstable perovskite oxide compounds, that is, when the perovskite oxide extranuclear energy is less than 36meV / atom, it is considered to be a stable compound. In theory, any compound not on the convex hull is unstable, however, density functional theory (DFT) error analysis of compounds from the Materials Project database shows that the perovskite oxide extranuclear energy of 36meV / atom is the most likely reasonable cutoff point for separating stable or unstable materials. The perovskite material data set used in the present invention, the possible perovskite oxide composition space represented is a very small part. Therefore, the data-driven method based on machine learning will help predict the stability of more perovskite oxides.

[0036] 2. Use data preprocessing methods to extract features from the data of perovskite oxides, generate a sufficiently large set of feature variables describing perovskite oxides, and screen out feature sets that are strongly related to the thermodynamic stability of perovskite oxides through feature selection, thereby obtaining a set of compound feature descriptors.

[0037] Any compound is composed of a series of atoms. This compound can be described by the type of atomic elements that constitute the compound and its surrounding environment, and the surrounding environment depends on other atoms. Based on the existing perovskite oxide data set, the present invention constructs a descriptor that describes the thermodynamic stability of perovskite oxides, that is, to perform feature engineering of perovskite oxide compounds. The basic features are mainly constructed from three aspects: (1) Element property type features: These features are based on the chemical composition of perovskite oxides and are constructed from the atomic physicochemical properties (such as atomic radius, electronegativity, oxidation state, electronic configuration, etc.), including continuous and discrete features; (2) Spatial structure type features: These features are constructed based on the specific spatial arrangement of perovskite oxides, such as tolerance factor, octahedral factor, bond length, bond angle, etc. These features are related to the geometric shape and crystal structure of the oxide and are usually continuous features; (3) Generation of derived features: After obtaining the basic features, statistical methods (weighted average method, ratio method, extreme value method, main element method, etc.) are used to combine different features to generate complex derived features. The combination here should not be limited to element property type features, but should also include spatial structure type features. For example, combining the electronegativity difference of the constituent elements with the bond length in the spatial structure, or combining the atomic radius ratio with the tolerance factor, can generate derived features with physical significance. Finally, a sufficiently large feature set is generated, and the combination methods include weighted average method, ratio method, extreme value method, main element method, etc.

[0038] In order to construct the feature matrix for training the machine learning model, the elemental property type features are constructed based on the elemental composition of the perovskite oxides and the physicochemical properties of the atoms. The data set in step 1 contains 1,900 perovskite oxide compounds. According to the chemical formula of each compound, the type and number of elements at the A position, B position, and X position that constitute the chemical formula are analyzed. For any material, the more complete the set of characteristic variables that describe the material, the more properties of the material can be predicted. Therefore, it is necessary to generate a sufficiently large set of characteristic variables that describe the perovskite oxides, and then screen out the feature set that is strongly related to the thermodynamic stability of the perovskite oxides through feature selection. In order to construct the perovskite oxide descriptor, the present invention collects the physical and chemical properties of more than 100 elements in the periodic table, which cover all elements that may appear at the A, B, and X positions, and saves these element properties in an Excel file, including: (1) continuous element properties, such as ion radius, elastic modulus, covalent radius, ionization energy, Mendeleev number, first ionization potential, second ionization potential, and thermal conductivity, etc. 39 element properties; (2) discrete element properties, such as period, group, whether it is a cubic element, whether it is a boron element, whether it is a halogen element, whether it is a noble gas, whether it is a transition metal, and the most stable oxidation state. State) and other 43 element properties. The data is read through Python and used to construct the characteristic vector of perovskite oxide.

[0039] For the creation of continuous element property type features, first use the element properties of the highest component elements at the A and B positions to generate features. For example, for Ba 0.125 Sr 0.875VO3, there are Ba and Sr at the A site, and the highest component element is Sr; there is V at the B site, and the highest component element is V, thus generating new features, namely the element quantity of Sr atoms and V atoms and all their continuous element properties, in the format of "host_Asite0_A continuous element properties" and "host_Bsite0_B continuous element properties". Then, considering the changes in element type and element quantity in the A site and B site of the perovskite oxide, the average, difference, and ratio of the corresponding continuous element property values ​​of the highest component element atoms at the A site and the B site are calculated, in the format of "continuous element properties_AB_avg", "continuous element properties_AB_diff", and "continuous element properties_AB_ratio", thereby creating derived features. Next, continue to add derived features by calculating the weighted average, maximum, minimum and range of continuous element properties of all element atoms at position A, in the format of "Asite_continuous element properties_weighted_avg / max / min / range", and the weighted average, maximum, minimum and range of continuous element properties of all element atoms at position B, in the format of "Bsite_continuous element properties_weighted_avg / max / min / range".

[0040] For the creation of discrete element property type features, first use all discrete element properties of the highest component elements at the A and B positions to generate features, in the format of "host_Asite0_A discrete element properties" and "host_Bsite0_B discrete element properties". Then, calculate the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at the A position, in the format of "Asite_discrete element properties_weighted_avg / max / min / range", and the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at the B position, in the format of "Bsite_discrete element properties_weighted_avg / max / min / range", and create derived features.

[0041] This ensures that there are an equal number of features, so that the set of feature variables specifically incorporates the stoichiometric information for each compound.

[0042] However, using only elemental properties to describe a compound is often not comprehensive, so spatial structure environment information is introduced to create additional features, and the created spatial structure type features are added to the feature matrix.

[0043] The present invention is aimed at the unique structure of perovskite oxide materials, and the characteristics of the introduced spatial structure type are: tolerance factor, octahedral factor, AO bond length, BO bond length, AB bond length calculated by Shannon atomic radius, and tolerance factor and octahedral factor calculated by ionic radius. The main range of Shannon atomic radius is determined by the orbital position of the outer electron, i.e., the valence electron, but it is known that the orbital function of the valence electron is greatly affected by the microenvironment in which the atom is located. Therefore, the Shannon atomic radius varies greatly in different valence and bond types. Considering that perovskite crystals are generally ionic compounds, the tolerance factor and octahedral factor calculated by the ionic radius are introduced at the same time.

[0044] Among them, the calculation formulas for AO bond length, BO bond length, and AB bond length are:

[0045] A_O = r A + r O (1)

[0046] B_O = r B + r O (2)

[0047] A_B = r A + r B (3)

[0048] Among them, r A 、r B 、r O Respectively represent the Shannon atomic radius of the elements at positions A, B, and X. The tolerance factor is considered to be a criterion for the structural stability of perovskite compounds. It can characterize the degree of distortion and stability of perovskite materials. Its calculation formula is:

[0049]

[0050] Among them, r′ A , r′ B , r′ O Respectively represent the ionic radius of the elements at the A, B, and X positions, goldschmidt_TF represents the tolerance factor for Shannon atomic radius calculation, and goldschmidt_TF_ionic represents the tolerance factor for ionic radius calculation. The octahedral factor can be calculated using the following formula:

[0051]

[0052] Among them, octahedral represents the octahedral factor for Shannon atomic radius calculation, and octahedral_ionic represents the octahedral factor for ionic radius calculation.

[0053] The tolerance factor and octahedron factor measure the deviation of the spatial structure from the ideal cubic geometry.

[0054] The basic features will be constructed mainly from three aspects: (1) Elemental property type features: These features are based on the chemical composition of perovskite oxides and are constructed from the atomic physicochemical properties (such as atomic radius, electronegativity, oxidation state, electronic configuration, etc.), including continuous and discrete features; (2) Spatial structure type features: These features are constructed based on the specific spatial arrangement of perovskite oxides, such as tolerance factor, octahedral factor, bond length, bond angle, etc. These features are related to the geometric shape and crystal structure of the oxides and are usually continuous features; (3) Generation of derived features: After obtaining the basic features, different features are combined using statistical methods (weighted average method, ratio method, extreme value method, main element method, etc.) to generate complex derived features. The combination here should not be limited to elemental property type features, but should also include spatial structure type features. For example, combining the electronegativity difference of the constituent elements with the bond length in the spatial structure, or combining the atomic radius ratio with the tolerance factor, can generate physically meaningful derived features. After all are combined, there are 900 features in total, including 500 continuous features and 400 discrete features.

[0055] Before performing feature selection, all features are normalized to have a unit mean and standard deviation of zero. This normalization is used to ensure that all features are scaled in the same way, which is a common requirement for many machine learning models.

[0056] The features strongly correlated with the thermodynamic stability of perovskite oxide in the feature vector set are screened out by feature selection to form a feature descriptor set. The features related to the thermodynamic stability of perovskite oxide include atomic radius, electronegativity, atomic mass, oxidation state, ionic radius, bond length, bond angle, lattice constant, band structure, valence band top position, conduction band bottom position, electron affinity, formation energy, atomic arrangement mode and electronic structure characteristics of materials, etc. These features can effectively characterize the thermodynamic behavior of materials at different temperatures and pressures. Strongly correlated features can be carried out in the following manner: first, the correlation coefficient of each feature and the thermodynamic stability of perovskite oxide is calculated, usually using statistical methods such as Pearson correlation coefficient and Spearman correlation coefficient. Then, a correlation threshold (such as 0.7 or 0.8) is set, and when the absolute value of the correlation coefficient of the feature is higher than the threshold, it is defined as the feature of "strong correlation" with thermodynamic stability. In addition, machine learning methods such as recursive feature elimination (RFE) and feature selection based on importance scores (such as through random forest, XGBoost and other models) can be used to further screen out features that contribute significantly to predictive stability.

[0057] 3. The nuclear external energy of 36 meV / atom was selected as the cutoff value, the data in the feature descriptor set was used as input, and the classification results of stable and unstable perovskite oxides were used as output to train the random forest model.

[0058] Traditional experimental and computational studies, such as high-throughput density functional theory, can screen out the thermodynamic stability of perovskite oxides, so that they can be used as cathodes for solid oxide fuel cells. However, both computational and experimental studies require a lot of time for large-scale screening studies, and high-throughput density functional theory requires high computational costs. Therefore, the present invention uses the structural and composition information, i.e., descriptors, that is, strongly related to the task of stabilizing perovskites obtained in step 2, and introduces the best machine learning method to quickly screen stable perovskite oxides, significantly reducing the density functional theory calculation time and workload, so that the trend of material properties can be quickly understood and key information for the discovery of new materials can be provided.

[0059] Bagging is a representative of parallel ensemble learning methods, based on the self-service sampling method. Its core is to randomly sample the training sample set, collect a fixed number of samples from the original training set, and each collection is sampled with replacement, and the new training sample set obtained is used to train the weak learner. The collection strategy of bagging is simple. For classification tasks, a simple voting method is usually used, and the category with more votes is used as the final output result; for regression tasks, a simple arithmetic average method is used, and the results obtained by several weak learners are arithmetic averaged as the final model output. Since the complexity of the sampling process and the voting / averaging process is very small, the complexity of training a bagging ensemble is the same as the complexity of directly using the base learning algorithm to train a learner, so bagging efficiency is very high. The random forest model used in the present invention is a kind of bagging ensemble method.

[0060] The random forest model improves the bagging algorithm. The random forest uses the CART decision tree as a weak learner and improves the generation of decision trees on this basis. For ordinary decision trees, the best feature is selected from all n features on the node to divide the left subtree and the right subtree. The random forest model mainly uses resampling technology to randomly extract input variables in the data set and feature variables in the feature set. Each decision tree randomly selects n when splitting a node. sub features, where n sub<n, use the best split feature to divide the left subtree and the right subtree. In the process of generating decision trees, it is necessary to keep the probability of random sampling unchanged and independently extract samples, and finally generate a series of decision trees. Since random forest contains many decision trees, the final prediction result is the vote or arithmetic average of the prediction results of each decision tree. This can reduce the prediction error of a single decision tree, thereby enhancing the generalization ability of the model. If n sub =n, then the CART decision tree of the random forest is no different from the ordinary CART decision tree. Usually, n sub The smaller it is, the more robust the model will be, but the fit to the training set will become worse.

[0061] The performance of support vector machine, neural network, decision tree, gradient boosting tree and random forest model in terms of accuracy, precision, recall and F1 score is compared. According to the experiment, except for the decision tree, the F1 score of all classification models exceeds 0.85 and the accuracy exceeds 0.92. Both random forest model and gradient boosting tree belong to ensemble learning. Since ensemble learning combines multiple learners to fit the data, it has better generalization performance than a single learner and has more obvious advantages. It can reflect that the ensemble learning algorithm based on tree model has obvious superiority in the problem of screening stable perovskite oxides. Compared with the gradient boosting tree, the random forest model is not only better than the gradient boosting tree algorithm in various indicators, but also its classification performance is much less sensitive to parameter adjustment. The algorithm based on bagging ensemble performs well for data sets with unbalanced data. It can be concluded that the random forest model has strong generalization performance and adaptability. Therefore, the random forest model is selected as the best model and applied to the problem of screening stable perovskite oxides.

[0062] The nuclear external energy of 36 meV / atom was selected as the cutoff value, the data in the feature descriptor set was used as input, and the classification results of stable and unstable perovskite oxides were used as output to train the random forest model.

[0063] In the process of building a model through training, adjusting and continuously optimizing parameters is a key task. The process of parameter optimization is as follows Figure 2 As shown in the figure, the grid search method is used to adjust the parameters. This method searches in the model's hyperparameter space, continuously optimizes the model parameters, and records the best parameters of the model. Since this method uses an exhaustive search method, all parameters use default parameters under initial conditions. The initial model performance is checked by fitting data and measured by F1. The parameters are first roughly adjusted and then fine-tuned to continuously narrow the search range and improve the generalization ability of the model.

[0064] Specifically, calling model_select.GridSearchCV in the Scikit-learn library can achieve this function. Using the RandomForestClassifier package in Skikit-learn to build a model, four parameters, n_estimators, max_features, max_depth, and min_samples_leaf, are selected for optimization. n_estimators is a hyperparameter of the random forest framework. If the value is too small, it will cause underfitting, and if it is too large, it will cause the code to slow down. Therefore, a reasonable value of this parameter can not only improve the prediction accuracy, but also ensure the running speed. In addition, max_depth, min_samples_leaf, and max_features represent the parameters of the base learner. max_depth represents the maximum growth depth of the tree. By default, it represents the highest complexity. Reducing max_depth will reduce the model complexity. min_samples_leaf represents the minimum number of leaf samples. The default minimum limit is 1, that is, the highest complexity. Increasing this value can reduce the model complexity. The larger the maximum number of selected features max_features, the higher the model complexity, and vice versa.

[0065] After training, the best random forest model can be obtained.

[0066] 4. Input the feature data set of perovskite oxides after feature selection into the trained random forest model, and output the classification results of stable and unstable perovskite oxides. The data set includes a set of preprocessed feature descriptors, such as atomic radius, electronegativity, oxidation state, formation energy, lattice constant, electronic structure and other key features. The random forest model predicts the thermodynamic stability of perovskite oxides based on these features, and gives the stability classification results of perovskite oxides by integrating the voting mechanism of multiple decision trees, thereby screening out perovskite materials with high thermodynamic stability.

[0067] Figure 3 The number of compounds of the corresponding elements in the A position and the B position in the data set of the present invention is given (i.e., the value in each square in the figure). Different subsets of perovskite oxide components are removed from the complete data set as test data, and a total of five test sets are selected, whose perovskite oxide numbers are 55, 54, 53, 47 and 42, respectively. For each set of test sets, a trained (hyperparameters determined) random forest model is used to screen stable perovskite oxides in different component subsets.

[0068] Among them, the perovskite oxide in test set 1 contains alkaline earth elements at position A, and the alkaline earth elements (Ba and Ca) are frequently sampled in the complete data set, and its prediction accuracy can reach 100%; set 3 contains the most frequently sampled elements in the complete data set, and its prediction accuracy can also reach 100%; set 5 has the least sampled elements from the complete data set, most of the stable perovskite oxides have nuclear extrinsic energies around 0meV / atom, and most of the unstable perovskite oxides have very high nuclear extrinsic energies, and its prediction accuracy is 95%; set 4 contains a set of moderately sampled elements from the complete data set, many of these perovskite oxides are unstable, and their nuclear extrinsic energies are near the cutoff value of stability and instability of 36meV / atom, so it will be more difficult to screen out stable perovskite oxides in this set, and its prediction accuracy is 80%; set 2 contains rare earth elements at position A, and the problem it faces is similar to that of set 4, that is, the nuclear extrinsic energies of many compounds are near the cutoff value of 36meV / atom, and its prediction accuracy is 89%. It can be seen that choosing a suitable cutoff value is extremely important for the task of rapid screening of stable perovskite oxides.

[0069] In general, even when the number of compounds in a specific set is limited, the present invention can show good classification performance and achieve accurate prediction of frequently sampled compounds. The present invention can be used to quickly screen the stability of perovskite oxides in the cathode component space of highly active solid fuel cells, and can also be used to predict the extranuclear energy and formation energy related to the thermodynamic stability of materials, thereby helping researchers to quickly understand the trends of material properties and provide information for material discovery.

[0070] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. A person skilled in the art may modify or make equivalent substitutions for the technical solutions of the present invention without departing from the spirit and scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for screening the thermodynamic stability of perovskite oxides based on machine learning, characterized in that Here are the steps: Step 1: Obtain the nuclear exo-energy and formation energy data of perovskite oxides from the open source materials database Materials Project; Step 2: Use data preprocessing methods to extract features from perovskite oxide data to obtain a set of feature variables, and select features that are strongly related to the thermodynamic stability of perovskite oxides through feature selection to form a set of feature descriptors; Step 3: Selecting the nuclear external energy of 36 meV / atom as the cutoff value, taking the data in the feature descriptor set as input, and taking the classification results of stable and unstable perovskite oxides as output, the random forest model is trained; the random forest model predicts the thermodynamic stability of the perovskite oxide according to the feature data, and gives the stability classification result of the perovskite oxide by integrating the voting mechanism of multiple decision trees; Step 4: Input the feature data set of perovskite oxides after feature selection into the trained random forest model, and output the classification results of stable and unstable perovskite oxides.

2. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 1, characterized in that: The material gene analysis software package Pymatgen was used to download the nuclear external energy and formation energy data of perovskite oxides from the materials database Materials Project.

3. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 1, characterized in that: The process of feature extraction using the preprocessing method is as follows: first, according to the elemental composition of the perovskite oxide, the elemental property type characteristics are constructed using the physical and chemical properties of the atoms; then, different elemental property type characteristics are combined using statistical methods to obtain elemental property type derived characteristics; then, spatial structure type characteristics are constructed based on the crystal structure of the perovskite oxide; finally, the elemental property type derived characteristics and the spatial structure type characteristics are combined, and all combined characteristics constitute the final characteristic variable set.

4. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 1, characterized in that: The characteristics related to the thermodynamic stability of perovskite oxides include atomic radius, electronegativity, atomic mass, oxidation state, ionic radius, bond length, bond angle, lattice constant, band structure, valence band top position, conduction band bottom position, electron affinity, formation energy, atomic arrangement, and electronic structure characteristics of the material; among them, strongly correlated features refer to features whose correlation coefficient with the thermodynamic stability of perovskite oxides is higher than a set threshold, or features that have significantly contributed to the predicted stability screened out by machine learning methods including recursive feature elimination methods and feature selection methods based on importance scores.

5. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 1, characterized in that: When training the random forest model, the grid search method is used to search in the model's hyperparameter space, continuously optimize the model parameters, and obtain the optimal parameters of the model.

6. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 3, characterized in that: The element property type features include two types: continuous and discrete. The creation process of the continuous element property type features is as follows: first, the continuous element properties of the highest component elements at the A and B positions are used to generate features. Then, the average value, difference, and ratio of the corresponding continuous element property values ​​of the highest component element atoms at the A and B positions are calculated, and added to the features. Next, the weighted average value, maximum value, minimum value, and value range of the continuous element properties of all element atoms at the A position are calculated, as well as the weighted average value, maximum value, minimum value, and value range of the continuous element properties of all element atoms at the B position, and these are added to the features to obtain the final continuous element property type feature vector. The creation process of discrete element property type features is as follows: first, all discrete element properties of the highest component elements at position points A and B are used to generate features, and then the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at position point A, as well as the weighted average, maximum, minimum and value range of the discrete element properties of all element atoms at position point B are calculated, and added to the features to obtain the final discrete element property type feature vector.

7. The method for screening thermodynamic stability of perovskite oxides based on machine learning according to claim 3, characterized in that: The combination method of combining different element property type characteristics using statistical methods to obtain the final element property type derived characteristics includes weighted average method, ratio method, extreme value method and main element method.

8. The method for screening thermodynamic stability of perovskite oxides based on machine learning as claimed in claim 3, characterized in that: The spatial structure type characteristics include the tolerance factor, octahedral factor, AO bond length, BO bond length, AB bond length calculated from the Shannon atomic radius, and the tolerance factor and octahedral factor calculated from the ionic radius.

9. The method for screening thermodynamic stability of perovskite oxides based on machine learning as claimed in claim 3, characterized in that: Normalize all features in the feature variable set to have zero-unit mean and standard deviation.

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