CN113963758A

CN113963758A - Prediction recommendation method, device and terminal for thermodynamic stable structure of disordered material

Info

Publication number: CN113963758A
Application number: CN202111357893.1A
Authority: CN
Inventors: 温晓东; 袁晓泽; 周余伟; 杨勇; 李永旺
Original assignee: Shanxi Institute of Coal Chemistry of CAS
Current assignee: Shanxi Institute of Coal Chemistry of CAS
Priority date: 2021-11-16
Filing date: 2021-11-16
Publication date: 2022-01-21

Abstract

The invention belongs to the technical field of disordered structure materials, and discloses a method, equipment and a terminal for predicting and recommending a thermodynamically stable structure of a disordered material, wherein all possible non-redundant structures in a specified substitution/defect/co-occupation state are generated by adopting an existing program; clustering the structure by adopting a clustering algorithm in machine learning; recommending and obtaining a structure to be optimized by adopting a density functional theory from each clustering result; optimizing the recommended structure by adopting a density functional theory method; preparing a training set from the trajectory of the optimized structure; training a machine learning potential model; optimizing a structure without relaxation by adopting a trained machine learning potential model; judging whether a set termination condition is reached or not by adopting a multi-generation operation mode; and after the termination condition is met, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization. The method is suitable for predicting and recommending the thermodynamically stable structure and the crystal structure of the disordered material.

Description

Prediction recommendation method, device and terminal for thermodynamic stable structure of disordered material

Technical Field

The invention belongs to the technical field of disordered structure materials, and particularly relates to a method, equipment and a terminal for predicting and recommending a thermodynamically stable structure of a disordered material.

Background

Currently, when two (or more) atoms or ions occupy a certain position in a crystal structure, the structure is called disordered structure (disorder structure) if their distribution to each other is arbitrary, i.e. the probability that they occupy any one of the positions is the same. The category of disordered structures falls into a variety of forms (including substitution/defect/co-occupation, etc.). Disordered structure materials are widely used in the fields of semiconductors, high temperature superconductors, metal alloys, ceramics, zeolite catalysts, and the like due to their unique properties. Studying the structure of disordered materials is of great importance to understand the properties of disordered materials.

In the experiment, the structure of the material can be represented by various means, the diffraction technology can provide average long-range structural information, and the spectrum of the solid-state nuclear magnetic resonance, Raman, infrared or X-ray absorption near-edge structure and the like can provide local structural related information. However, the local structure-related information provided by such spectra is often difficult to interpret by experimentation alone. This makes molecular modeling critical for an in-depth understanding of such systems. The supercell approximation is one of the most common methods for dealing with disordered structures, by constructing a large periodic cell, which reflects as much as possible the local structural properties of the disordered system within its boundaries: composition, coordination, etc. At present, many programs (SOD, supercell, enumb, disarder, etc.) can realize the creation of a supercell structure model in different unordered states (substitution/defect/co-occupation), thereby effectively reducing the supercell structures to be considered. However, as the size of the supercell increases or in the case of special substitution/defect/co-occupation, the number of non-redundant structures obtained by these procedures is still large, and how to find out the thermodynamically stable structure from these non-redundant structures is a very important issue, and currently the most common practice is as follows: firstly, a random mode is adopted, a plurality of structures are randomly selected and optimized by adopting a density functional theory, and the optimized structures are used as candidate structures; secondly, calculating the energy of all structures in a relatively cheap mode (such as an empirical potential function), sorting the energy from low to high, selecting the first structures, optimizing the first structures by adopting a density functional theory, and taking the optimized structures as candidate structures; thirdly, optimizing all non-redundant structures by adopting an exhaustion method and adopting a density functional theory, and then selecting the structure with the lowest energy as the most candidate structure. Several approaches that are common today either provide unreliable candidates (methods one and two) or require high computational resources and time costs (method three). In the process of explaining experimental spectrogram information, sometimes, the most thermodynamically stable structure is not found completely, and a plurality of structures with energy close to that of the most thermodynamically stable structure are needed to be subjected to statistical averaging to obtain a result consistent with the experimental spectrogram information. Therefore, it is necessary to find out the most thermodynamically stable structure from the non-redundant structures and find out many structures with energies close to the most stable structure.

Through the above analysis, the problems and defects of the prior art are as follows:

(1) the number of non-redundant structures obtained by procedures (SOD, supercell, enumb, reorder, etc.) is still large with increasing supercell sizes or in special substitution/defect/co-occupancy cases.

(2) The existing random approach and the relatively inexpensive approach taken provide unreliable candidates; the exhaustive methods adopted in the prior art require high computational resources and time costs.

(3) In the process of explaining experimental spectrogram information, sometimes, the most thermodynamically stable structure is not found completely, and a plurality of structures with energy close to that of the most thermodynamically stable structure are needed to be subjected to statistical averaging to obtain a result consistent with the experimental spectrogram information.

The difficulty in solving the above problems and defects is: the optimization of a large number of non-redundant structures using density functional theory requires a significant time cost and a significant amount of computational resources. For example, BaScO2F has O/F co-occupation (O/F: 0.667/0.333). In order to obtain the most favorable distribution configuration of O and F in BaScO2F, when the size of a supercell is 2 multiplied by 2, the number of non-redundant structures is 2664, about 0.5h is averagely needed for optimizing a structure with the number of one unit cell atoms being 40 by adopting the density functional theory on a computer with 72 cores, about 55 days is needed for optimizing the 2664 structures, and 95904 elements are needed for commercial super calculation charge calculated according to 0.10 element/core/hour; when the supercell size is 2 × 2 × 3, the number of non-redundant structures increases to 6849807, which requires more time cost and computational resources.

The significance of solving the problems and the defects is as follows: the method greatly saves time cost and money cost, provides prediction recommendation of the thermodynamically stable structure of the disordered material from a plurality of non-redundant structures quickly and reliably, is favorable for the structural characterization process of the experimentally disordered material, and accelerates the research and development process of the disordered material. Specifically, the time cost of 55 days and the monetary cost of 95904 yuan required to optimize 2664 structures using the density functional theory in the BaScO2F 2 × 2 × 2 supercell of the above example can be reduced to the time cost of 7 days and the monetary cost of 209 yuan required to optimize only 29 structures using the density functional theory.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a prediction and recommendation method, equipment and a terminal for a thermodynamically stable structure of a disordered material.

The invention is realized in such a way that a prediction recommendation method for a thermodynamically stable structure of a disordered material comprises the following steps:

step one, adopting an existing program (such as a supercell program) to generate all possible non-redundant structures in a specified substitution/defect/co-occupation state; a large number of symmetrical equivalent structures are removed by using symmetry, the number of configurations needing to be considered is greatly reduced, all non-redundant structures in a specified substitution/defect/co-occupation state can be quickly obtained, and a total structure set is provided for subsequent steps.

Secondly, clustering the structure by adopting a clustering algorithm in machine learning; clustering can effectively realize differential sampling, so that diversity of recommendation results can be guaranteed, a training set can cover a richer sampling space, and model prediction capability is improved.

Recommending and obtaining a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, wherein the recommending principle follows energy priority and diversity priority; the recommendation principle considering both energy and diversity greatly improves the prediction recommendation probability of the recommended candidate structure becoming the disordered material thermodynamic stable structure.

Fourthly, optimizing the recommended structure by adopting a density functional theory method; by adopting the density functional theory optimization structure, the configuration is more reasonable, the potential energy surface is close to a low-energy region, and a training set can be provided for establishing a machine learning potential model on line.

Step five, preparing a training set from the track of the optimized structure; the information in the structure optimization process can be effectively captured by adopting the optimized track to prepare the training set, so that the trained model is more suitable for performing structure relaxation by adopting machine learning potential subsequently.

Step six, training a machine learning situation model; the integration method can effectively improve the accuracy and the robustness of the model, and the trained machine learning potential model can replace the energy and the force of a high-precision density functional theory calculation structure, so that the time is greatly saved, and the calculation cost is reduced.

Step seven, optimizing a structure without relaxation by adopting a trained machine learning potential model; the trained machine learning potential model is adopted to optimize the structure without relaxation, so that the configuration is more reasonable, the structure is close to a low-energy region of a potential energy surface, and the probability that the configuration becomes a local minimum value is improved.

Step eight, judging whether a set termination condition is reached or not by adopting a multi-generation operation mode, and if not, repeating the step two to the step eight until the termination condition is met; the multi-generation running mode can continuously increase training sets and update the machine learning model, so that the model prediction capability is continuously improved, and the prediction and recommendation capability is effectively improved.

And step nine, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition. The probability of finding the most stable structure of thermodynamics is effectively improved, and a batch of structures with energy similar to the most stable structure of thermodynamics are effectively provided.

Further, in the second step, clustering the structure by using a clustering algorithm in machine learning includes:

setting the clustering number, converting each structure into a characteristic vector as the input of clustering in the clustering process, and converting the crystal structure into the characteristic vector by adopting an atom central symmetry function ACSFs; the atom central symmetry function comprises a radial function and an angular function, and the radial symmetry function G2 describing the radial environment of the atom i is

The function G2 is a sum of a gaussian function multiplied by a cutoff function. The width of the Gaussian function is defined by a parameter eta, and the center of the Gaussian function is defined by a parameter R_sMoving to a certain radial distance, the G2 function of the movement is suitable for describing the spherical shell around the reference atom, and the truncation function takes the form:

wherein R is_ijIs the distance of atom i from atom j, if R_ijGreater than the cutoff radius R_cThe truncation function and its derivative value are zero; the angular function of the central atom i is angle

Is given by the expression:

where λ has a value of +1 or 1, the angular resolution being provided by the parameter ζ; the larger the zeta value, the narrower the range of non-zero symmetric function values, so a set of angular functions with different zeta values is used to obtain a distribution of angles centered around each reference atom; the angular distribution is determined by selecting appropriate η and R_cDetermining, for controlling the radial portion; by setting upDifferent parameter values, namely a series of functions G2 and G4 can be used for converting the local environment of the central atom into a feature vector; the atomic feature vectors of the same element are added to obtain the feature vector of the same element, the feature vectors of different elements are spliced in sequence, and the similarity of the two structures can be quantitatively described by calculating the distance between the feature vectors of the two structures.

Further, in the third step, the strategy for optimizing the structure clusters the structure set in a clustering manner, predicts the energy of the structure in each cluster according to the machine learning potential model trained in the sixth step, ranks the structures according to the energy from low to high, and considers the principle of energy priority and diversity when selecting the structure to be optimized.

Further, in the fifth step, the training set is derived from each frame structure in each structure optimization process in the fourth step, and meanwhile, the energy difference of the front frame structure and the rear frame structure during selection is considered, and when the energy difference is smaller than a set value, the training set is not added to the current frame structure.

Further, in step six, the training of the machine learning potential model includes:

simultaneously training a plurality of machine learning potential models in an integrated mode, taking the average value of all model predictions as a prediction result, and simultaneously training energy and force corresponding to a structure in the training process of each machine learning potential model; the machine learning potential model adopts a Back Propagation Neural Network (BPNN), and other machine learning potential models are also applicable to the method.

Further, in the seventh step, a trained machine learning potential model is adopted to optimize a structure without relaxation; the optimized and converged structure is stored into the optimized and converged structure of the machine learning potential model for the ninth step; and (4) taking the structure without convergence after optimization as a source of the secondary clustering structure.

Further, in the ninth step, after a termination condition is met, sorting the structure set which is converged after the machine learning potential model is optimized according to energy, and recommending the first K structures to be verified by adopting a more reliable density functional theory method in the fourth step; and adding the verified K structures into a structure set optimized by adopting a density functional theory, and finally sequencing the structures in the structure set optimized by adopting the density functional theory according to the energy from low to high, and selecting the first N structures as recommended thermodynamically stable structure sets.

Another object of the present invention is to provide a system for predicting and recommending a thermodynamically stable structure of a disordered material, which applies the method for predicting and recommending a thermodynamically stable structure of a disordered material, the system for predicting and recommending a thermodynamically stable structure of a disordered material comprising:

the non-redundant structure determining module is used for generating all possible non-redundant structures in a specified replacement/defect/co-occupation state by adopting an existing program (such as a supercell program);

the structure clustering module is used for clustering the structures by adopting a clustering algorithm in machine learning;

the structure to be optimized acquisition module is used for recommending and obtaining a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, and the recommendation principle follows energy priority and diversity priority;

the recommended structure optimization module is used for optimizing the recommended structure by adopting a density functional theory method;

the training set acquisition module is used for preparing a training set from the track of the optimized structure;

the model training module is used for training a machine learning situation model;

the unrelaxed structure optimization module is used for optimizing an unrelaxed structure by adopting a trained machine learning potential model;

the multi-generation operation module is used for judging whether the set termination condition is reached or not in a multi-generation operation mode;

and the structure set recommending module is used for recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition.

It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:

(1) generating all possible non-redundant structures in the designated replacement/defect/co-occupation state by using an existing program (such as a supercell program);

(2) clustering the structure by adopting a clustering algorithm in machine learning;

(3) recommending and obtaining a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, wherein the recommending principle follows energy priority and diversity priority;

(4) optimizing the recommended structure by adopting a density functional theory method;

(5) preparing a training set from the trajectory of the optimized structure;

(6) training a machine learning potential model;

(7) optimizing a structure without relaxation by adopting a trained machine learning potential model;

(8) judging whether a set termination condition is reached or not by adopting a multi-generation operation mode, and if not, repeating the steps (2) to (8) until the termination condition is met;

(9) and after the termination condition is met, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization.

Another object of the present invention is to provide an information data processing terminal, which is used for implementing the system for predicting and recommending the thermodynamically stable structure of the disordered material.

By combining all the technical schemes, the invention has the advantages and positive effects that: the prediction recommendation method of the disordered material thermodynamically stable structure provided by the invention takes a disordered structure material as a research object, adopts the existing program (such as a supercell program) to obtain all non-redundant structures in a designated substitution/defect/co-occupation state, recommends a thermodynamically stable structure set in the non-redundant structures with very low calculation cost and time cost based on machine learning, and provides a reliable theoretical model for experiments, wherein the recommended thermodynamically stable structure set not only comprises a thermodynamically most stable structure, but also comprises a plurality of structures with energy close to that of the thermodynamically most stable structure. Therefore, the method provided by the invention overcomes the defects of the existing disordered structure program (SOD, enumlib, supercell, dissorder), and fills the blank of the field of disordered materials; the method breaks through the traditional method of computing all non-redundant structures by enumeration, changes the view point of needing to carry out a large amount of density functional theory computation, can find the most thermodynamically stable structure with very low computation cost and time cost, and can predict and recommend a plurality of structures with energy similar to the most thermodynamically stable structure; the invention can be used as a theoretical characterization instrument to cooperate with an experimental characterization instrument to quickly provide candidate structures for experiments on line and help structural characterization, can also be suitable for discovering materials with excellent functions based on framework template modification, and has wide and valuable commercial application scenes. Meanwhile, the method is not only suitable for predicting and recommending disordered structure materials, but also suitable for predicting the crystal structure in a wider range by combining with a sampling technology, and is used for discovering new materials.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

Fig. 1 is a flow chart of a method for predicting and recommending a thermodynamically stable structure of a disordered material according to an embodiment of the invention.

Fig. 2 is a schematic diagram of a method for predicting and recommending a thermodynamically stable structure of a disordered material according to an embodiment of the invention.

FIG. 3 is a schematic structural diagram of a system for predicting and recommending a thermodynamically stable structure of a disordered material according to an embodiment of the invention;

in the figure: 1. a non-redundant structure determination module; 2. a structure clustering module; 3. a module for acquiring a structure to be optimized; 4. a recommendation structure optimization module; 5. a training set acquisition module; 6. a model training module; 7. an unrelaxed structure optimization module; 8. a multi-generation operation module; 9. and a structure set recommendation module.

FIG. 4 is a graph showing the correspondence between the marker names and energies of 2664 non-redundant structures optimized by VASP after 2X 2 cell expansion of BaScO2F (ICSD:150171) provided by the embodiment of the invention.

Fig. 5 is a graph of a relationship between a running algebra and energy of an optimized structure adopting a density functional theory per generation according to an embodiment of the present invention.

FIG. 6 is a schematic diagram of the total energy and the most stable structure of 10496 non-redundant structures in the example E-Fe 2C 2X 3 supercell structure optimized by VASP.

Fig. 7 is a graph of a relationship between a running algebra and energy of an optimized structure adopting a density functional theory per generation according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Aiming at the problems in the prior art, the invention provides a prediction and recommendation method, equipment and a terminal for a thermodynamically stable structure of a disordered material, and the invention is described in detail below by combining the attached drawings.

As shown in fig. 1, the method for predicting and recommending the thermodynamically stable structure of the disordered material provided by the embodiment of the invention comprises the following steps:

s101, generating all possible non-redundant structures in a designated substitution/defect/co-occupation state by adopting an existing program (such as a supercell program);

s102, clustering the structure by adopting a clustering algorithm in machine learning;

s103, recommending a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, wherein the recommending principle follows energy priority and diversity priority;

s104, optimizing the recommended structure by adopting a density functional theory method;

s105, preparing a training set from the track of the optimized structure;

s106, training a machine learning potential model;

s107, optimizing a structure without relaxation by adopting a trained machine learning potential model;

s108, judging whether a set termination condition is reached or not by adopting a multi-generation operation mode, and if not, repeating S102 to S108 until the termination condition is met;

and S109, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition.

The schematic diagram of the prediction and recommendation method for the thermodynamically stable structure of the disordered material provided by the embodiment of the invention is shown in fig. 2.

As shown in fig. 3, the system for predicting and recommending the thermodynamically stable structure of the disordered material provided by the embodiment of the invention comprises:

the non-redundant structure determining module 1 is used for generating all possible non-redundant structures in a specified substitution/defect/co-occupation state by adopting the existing program supercell;

the structure clustering module 2 is used for clustering the structures by adopting a clustering algorithm in machine learning;

the structure to be optimized acquisition module 3 is used for recommending and obtaining a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, and the recommending principle follows energy priority and diversity priority;

the recommended structure optimization module 4 is used for optimizing the recommended structure by adopting a density functional theory method;

a training set obtaining module 5, configured to prepare a training set from the trajectory of the optimized structure;

the model training module 6 is used for training a machine learning potential model;

an unrelaxed structure optimization module 7, configured to optimize an unrelaxed structure using a trained machine learning potential model;

the multi-generation operation module 8 is used for judging whether the set termination condition is reached in a multi-generation operation mode;

and the structure set recommending module 9 is used for recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition.

The technical solution of the present invention is further described below with reference to specific examples.

Example 1

The prediction recommendation method for the thermodynamic stable structure of the disordered material, provided by the embodiment of the invention, comprises the following steps:

the method comprises the following steps: generating all possible non-redundant structures in the designated replacement/defect/co-occupation state by using an existing program (such as a supercell program);

step two: clustering the structure by adopting a clustering algorithm in machine learning;

step three: recommending a structure needing to be optimized by adopting a density functional theory in the next step from each clustering result, wherein the recommending principle follows energy priority and diversity priority;

step four: optimizing the recommended structure by using a density functional theory method;

step five: preparing a training set from the trajectory of the optimized structure;

step six: training a machine learning potential model;

step seven: optimizing a structure without relaxation by adopting a trained machine learning potential model;

step eight: judging whether a set termination condition is reached, if not, repeating the second step to the eighth step until the termination condition is met;

step nine: and after the termination condition is met, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization.

According to the strategy for recommending the structure to be optimized in the step four described in the step two and the step three, provided by the embodiment of the invention, the structure set is clustered by adopting a clustering mode, the energy of the structure in each cluster is predicted according to the machine learning potential model trained in the step six, the structure is ranked according to the energy from low to high, and the principle of energy priority and diversity is taken into consideration when the structure to be optimized is selected, so that the structure recommended to be optimized in the step four can be guaranteed to have a higher probability to become a thermodynamically stable structure.

The fourth step provided by the embodiment of the invention optimizes the structure recommended by the third step by adopting a reliable method of optimizing the density functional theory.

The training set in the fifth step provided by the embodiment of the invention is derived from each frame structure in each structure optimization process in the fourth step, and meanwhile, the energy difference of the front frame structure and the rear frame structure during selection is considered, and when the energy difference is smaller than a set value, the training set is not added to the current frame structure.

Step six provided by the embodiment of the invention adopts an integrated mode to train a plurality of machine learning potential models simultaneously, the average value predicted by all models is adopted as a prediction result, and the energy and the force corresponding to the structure are trained simultaneously in the training process of each machine learning potential model. In this example, the invention uses BPNN (back propagation neural network) as the machine-learned potential model, but is not limited to BPNN, and other machine-learned potential models are also suitable for the method.

The seventh step provided by the embodiment of the invention adopts a trained machine learning potential model to optimize the structure without relaxation. The optimized converged structure can be stored into the optimized converged structure of the machine learning potential model for centralized use in the step nine; and (4) taking the structure without convergence after optimization as a source of the secondary clustering structure.

The prediction recommendation method for the thermodynamic stable structure of the disordered material provided by the embodiment of the invention adopts a multi-generation operation mode, and repeats the operations from the second step to the eighth step when the termination condition in the eighth step is not met. By means of multi-generation operation, on one hand, training samples can be increased, model training is more reliable, and the structure to be optimized recommended to the step four is more likely to become a thermodynamically stable structure; on the other hand, the number of structures converged in the relaxation structure optimized by the machine learning potential model is continuously increased, and the probability of finding a thermodynamically stable structure is greatly improved.

According to the prediction recommendation method for the thermodynamically stable structure of the disordered material, provided by the embodiment of the invention, the energy ordering is carried out on the structure set which is converged after the machine learning potential model is optimized after the ninth step meets the termination condition, the first K structures are recommended to be verified by adopting a density functional theory method which is more reliable than the fourth step, then the verified K structures are added into the structure set which is optimized by adopting the density functional theory, finally the structures in the structure set which is optimized by adopting the density functional theory are ordered from low to high according to the energy, and the first N structures are selected as the recommended thermodynamically stable structure set. By adopting the recommendation method, not only the most thermodynamically stable structure can be found, but also a plurality of structures with energy close to that of the most thermodynamically stable structure can be found.

Example 2

The prediction recommendation method for the thermodynamic stable structure of the disordered material is realized by adopting the following specific technical scheme:

step one, a used program such as a supercell program is used to generate all possible non-redundant structures in a specified replacement/defect/co-occupied state, wherein the supercell size is required to be specified.

And step two, clustering the structures by adopting a clustering algorithm (such as K-means) in machine learning, wherein the structures needing clustering refer to the non-redundant structure generated in the step one for the first generation and refer to the structure without convergence after the optimization of the machine learning potential model of the previous generation for the second generation and later. The clustering number is generally set to be small (the recommended value is 3 or 5), each structure needs to be converted into a feature vector as an input of clustering in the clustering process, and the crystal structure is converted into the feature vector by adopting Atom Central Symmetry Functions (ACSFs). The atom central symmetry function comprises a radial function and an angular function, and the radial symmetry function G2 describing the radial environment of the atom i is

The function G2 is a sum of a gaussian function multiplied by a cutoff function. The width of the Gaussian function is defined by a parameter eta, and the center of the Gaussian function can be defined by a parameter R_sMoving to a certain radial distance, the G2 function of these movements is suitable for describing the spherical shell around the reference atom, the truncation function taking the form:

wherein R is_ijIs the distance of atom i from atom j, if R_ijGreater than the cutoff radius R_cThe truncation function and its derivative value are zero. The angular function of the central atom i is angle

Is given by the expression:

the values of λ may be +1 and 1, the angular resolution being provided by the parameter ζ. The larger the zeta value, the narrower the range of non-zero symmetric function values. Thus, a set of angle functions with different zeta values can be used to obtain the distribution of angles centered around each reference atom. Furthermore, the angular distribution can be adjusted by selecting appropriate η and R_cThey control the radial component. By setting different parameter values, the local environment of the central atom can be converted into a feature vector by a series of functions G2 and G4. Further, if the feature vectors of the whole structure are needed, the atom feature vectors of the same elements can be added to obtain the feature vectors of the same elements, the feature vectors of different elements are further spliced in sequence, and the similarity of the two structures can be quantitatively described by calculating the distance between the feature vectors of the two structures.

And step three, recommending a structure from each clustering result in the step two for next optimization by adopting a density functional theory. And (4) giving consideration to energy priority and diversity priority according to a recommendation principle, wherein a random strategy is adopted for randomly selecting a structure from each clustering result in the first generation due to the fact that the learning potential of a training machine is not available. And starting the second generation, sequencing the structures in each cluster from low to high according to the energy by adopting the existing machine learning potential, selecting the structure with the lowest energy, simultaneously considering the similarity between the selected structure and the structure which is optimized by adopting the density functional theory at present, calculating the similarity by adopting the method explained in the second step, selecting the structure when the similarity is greater than a set value, otherwise, selecting the structure with the second energy sequencing for similarity judgment, and according to the step, until the structure meeting the requirements is selected.

And step four, optimizing the structure selected in the step three by adopting a density functional theory method, and storing the optimized structure into a structure set optimized by adopting the density functional theory.

And step five, preparing a training set, extracting each frame structure (including corresponding energy and force) in each structure optimization process in the step four, and taking the energy difference principle into consideration when extracting each frame structure, namely adding the frame structure into the training set when the energy of the frame structure is larger than a set value. The optimized tracks of each generation of optimized structures are extracted according to the method and then added into the training set, the number of the training sets is increased continuously along with the increase of the number of the optimized structures, the maximum training set value T can be set, when the number of the training sets is larger than the set value T, the training sets are sorted from low to high according to energy, and the front T structure is selected for training. Meanwhile, each generation of optimized structure is stored, so that the third step and the analysis result can be conveniently used.

And step six, training a machine learning situation model. And converting the structure space into the feature space by adopting Atom Central Symmetry Functions (ACSFs) described in the step two, wherein a machine learning potential model adopts BPNN (back propagation neural network), the BPNN is trained by adopting a pytorch library, the energy and the force of the structure are trained simultaneously in the training process, in order to ensure the reliability of the prediction model, the invention adopts an integrated BPNN mode to train a plurality of BPNN models simultaneously, and the average result of the prediction of the plurality of models is used as the final prediction result.

And step seven, optimizing the structure without relaxation by adopting the machine learning potential model trained in the step six. The first generation of non-relaxed structure refers to the structure generated in the step one after the structure removal is optimized by adopting a density functional theory, and the second generation of non-relaxed structure refers to the structure generated after the previous generation of machine learning potential model is optimized and not converged after the structure removal is optimized by adopting the current generation of the structure by adopting the density functional theory. And the machine learning potential model adopts BFGS to optimize the atomic position, and the convergence condition is that when the stress of the structure is less than a stress set value or the energy error predicted by the integrated BPNN model is greater than a set value. And after the optimization is finished, extracting the last frame structure in the optimization process, and respectively storing the last frame structure in the structure set of machine learning potential optimization convergence and the structure of the current generation machine learning potential model optimization non-convergence. And the machine learning potential model optimizes the converged structure for further verification and use by adopting a density functional theory at the end of the step nine, and optimizes the unconverged structure for use by two classes in the step two.

And step eight, judging whether the set termination condition is reached, wherein the termination condition can adopt two modes. The first is to judge whether the set algebra is reached, if the set algebra is reached, the program is terminated, and if the set algebra is not reached, the step two is skipped to the reciprocating circulation until the termination condition is met. And the second method is to judge the survival algebra of the best individual in the history, if the survival algebra of the best individual in the history reaches the set survival algebra, the program is terminated, and if the survival algebra of the best individual in the history does not reach the set survival algebra, the step two is repeated until the termination condition is met.

And step nine, after a termination condition is met, sorting the structures in the structure set converged after the machine learning potential optimization according to the energy from low to high, recommending the first K structures to be verified by adopting a density functional theory method which is more reliable in the step four, then adding the verified K structures into the structure set optimized by adopting the density functional theory, finally sorting the structures in the structure set optimized by adopting the density functional theory according to the energy from low to high, and selecting the first N structures as the recommended thermodynamically stable structure set.

Example 3

In the BaScO2F (ICSD:150171) structure, O atoms and F atoms belong to the same sites to occupy together, the O/F occupancy is 0.667/0.333 respectively, the number of atoms in unit cells is 5, the number of atoms in 2 x 2 super cells is 40, and the number of corresponding non-redundant structures reaches 2664 structures. This example recommends a thermodynamically stable set of structures from 2664 structures based on machine learning potentials.

Step one, adopting a supercell program to designate a 2 × 2 × 2 cell expansion mode to generate 735471 structures of all possible combined structures of BaScO2F, and then removing symmetrical equivalent structures to obtain 2664 non-redundant structures.

And step two, clustering the structures by adopting a K-means algorithm in scimit-lean, wherein the structures needing clustering in the first generation are 2664 structures in the step one, and the structures needing clustering after the second generation refer to structures which do not converge after the previous generation of machine learning potential optimization. The number of clusters is 3, where each structure is converted to a feature vector using ACSFs as the K-means input. The parameters G2 and G4 corresponding to ACSFs are set as follows: g2_ etas ═ 1, g2_ Rses ═ 1, 2, 3, g4_ etas ═ 1, g4_ zetas ═ 1, 2, g4_ lambdas ═ 1, -1.

And step three, selecting a structure from each clustering result, and recommending the structure to the next step for optimization by adopting a density functional theory. For the first generation, the invention adopts a random mode to select two structures as the next to-be-optimized structure, and the randomly selected structure in the embodiment is the structure with the reference number of 34, 259; for the second generation and later, one of the clustering results is selected according to the principle of energy priority and diversity priority, three structures to be optimized are selected, the structures of the clustering results are ranked from low to high according to the energy predicted by the machine learning potential model of the previous generation, the structures with the lowest energy are selected during selection, meanwhile, the similarity between the structures and m structures with the lowest energy optimized by adopting the density functional theory of the previous generation is judged for comparison, in the embodiment, the m value is set to be 1, the similarity is set to be 0.5, the method described in the step two is adopted for similarity calculation, and when the similarity is smaller than 0.5, the structure with the second energy ranking is considered until a candidate structure meeting the conditions is selected.

And step four, optimizing the structure selected in the step three by adopting VASP software, and storing the optimized structure into a structure set optimized by adopting a density functional theory.

And step five, preparing a training set from an optimization track of the optimized structure, wherein a 128-frame structure (including energy and force of a corresponding structure) is shared in the optimization processes of the first two optimized structures, the energy difference value is set to be 0.01eV, the training set is added when the energy difference between the front structure and the rear structure is greater than a set value, the number of the training sets is 40, and T is set to be 20000 in the training process.

And step six, training 10 groups of BPNN models in an integrated mode, and taking the average value of the 10 groups of training as a prediction result. Wherein the parameters corresponding to the ACSFs are set as follows: g2_ etas ═ 0.05, 4, 20], g2_ Rses ═ 0, g4_ etas ═ 0.005, g4_ zetas ═ 1, 4, g4_ lambdas [ -1, 1 ]. The neural network adopts two hidden layers, each layer has forty nodes, the corresponding activation function is a tanh function, and the trained model parameters are stored after the training meets the set energy convergence standard and the set force convergence standard.

And step seven, optimizing the structure without relaxation by adopting the machine learning potential model trained in the step six. The first generation of non-relaxed structure refers to 2664 non-redundant structure removal steps generated in the first step, and the third step adopts 2 structures optimized by the density functional theory, 2662 structures in total, and the second generation of non-relaxed structure refers to the structure which is not converged after the optimization of the previous generation of machine learning potential model and is removed by adopting the structure optimized by the density functional theory in the current generation. And optimizing the atomic position by adopting a BFGS algorithm, when the stress is less than 0.05, the structure converges, the last frame structure (comprising corresponding energy and force) of the converged structure is stored into a structure set of machine learning potential optimization convergence, and the last frame structure (comprising corresponding energy and force) of the unconverged structure is stored into a structure which does not converge after the machine learning potential optimization. In this example, the first generation machine learning potential model has 13 optimized converged structures, the non-converged structures have 2649 optimized converged structures, and the 2649 optimized structures are provided for clustering in the second step of the next generation.

And step eight, judging whether a set termination condition is reached, wherein the termination condition sets that the invention adopts a first mode, namely a set running algebra, in the example, the algebra set by the invention is 6, and repeating the steps two to eight until the termination condition is met.

And step nine, after a termination condition is met, sorting the converged structure set after the machine learning potential optimization according to the energy from low to high, selecting the first 12 structures to recommend to a density functional theory for optimization, storing the optimized structures into the structure set optimized by the density functional theory, and finally sorting the structures in the structure set optimized by the density functional theory according to the energy from low to high, and selecting the first 20 structures as a finally recommended thermodynamically stable structure set.

FIG. 4 is a graph showing the correspondence between the marker names and energies of 2664 non-redundant structures after 2X 2 cell expansion of example BaScO2F (ICSD:150171) and after optimization by VASP. The purpose of optimizing 2664 structures by adopting a density functional theory is to obtain a complete test set, so that whether the method of the invention recommends a reliable thermodynamically stable structure set by using smaller calculation cost can be evaluated.

FIG. 5 is a graph of the running algebra versus the energy of the structure optimized using density functional theory per generation. The black hollow sphere represents the total energy of the structure optimized by adopting the density functional theory in each generation, and the gray solid sphere represents the energy of the structure with the lowest energy in the history (in all the generations operated at present) optimized by adopting the density functional theory. In this example, a total of six generations were run, with the lowest energy structure appearing in the fourth generation remaining the lowest energy structure in the history in the fifth and sixth generations. The structure is the lowest energy structure of the 2664 structures calculated by an exhaustive method in fig. 4, and the corresponding energy value is-298.1296 eV.

Table 1 shows the marker names and corresponding energies of the top 20 ranked structures obtained from low to high in energy after the 2664 non-redundant structures were expanded 2X 2 of example BaScO2F (ICSD:150171) using VASP optimization.

TABLE 1

Table 2 shows the tag names and corresponding energies of the top 20 recommended structures after the 6 th generation operation of the method of the present invention is terminated and whether the recommended structures appear in the corresponding structures in table 1. From table 2, it can be shown that 16 of the 20 structures recommended by the method appear in table 1, indicating that the method can recommend a reliable prediction recommendation set of thermodynamically stable structures of disordered materials with very little computational resources and time penalty. The exhaustive method needs to optimize all 2664 structures by adopting a density functional theory to find the most thermodynamically stable structure, the method can find the most thermodynamically stable structure by only optimizing 29 structures by adopting the density functional theory, and meanwhile, a batch of structures with energy similar to that of the most thermodynamically stable structure are provided.

TABLE 2

Recommending	Structure tag name	Total energy (eV)	Whether or not it is in Table 1
				1	000029	-298.1296	Is that
2	001840	-298.1036	Is that
				3	000791	-298.0732	Is that
4	000210	-298.0698	Is that
				5	001873	-298.0495	Is that
6	001789	-298.0490	Is that
				7	000098	-298.0484	Is that
8	000095	-298.0477	Is that
				9	000537	-298.0450	Is that
10	000444	-298.0438	Is that
				11	001827	-298.0433	Is that
12	000794	-298.0429	Is that
				13	001818	-298.0409	Is that
14	000046	-298.0408	Is that
				15	000373	-298.0388	Is that
16	000211	-298.0379	Is that
				17	000479	-298.0335	Whether or not
18	000475	-298.0324	Whether or not
				19	001791	-298.0310	Whether or not
20	000230	-298.0305	Whether or not

Example 4

In order to obtain a thermodynamically stable epsilon-Fe 2C structure, the epsilon-Fe 2C structure was created by making defects (removing half of the C atoms in the system, defect ratio 0.5) starting from the epsilon-FeC structure. The number of atoms in the epsilon-FeC unit cell is 4, the number of atoms in the supercell is 48(24 Fe and 24C), and the number of corresponding non-redundant structures reaches 10496 structures after 12C atoms are removed. This example is a set of structures that recommend thermodynamic stability from 10496 structures based on machine learning potential. Case source article j.phys.chem.c 2017, 121, 39, 21390-.

Step one, adopting a supercell program to designate a 2 x 3 cell expansion mode to generate all possible combination structures of epsilon-Fe 2C, wherein the number of the possible combination structures is 2704156, and then removing symmetrical equivalent structures to obtain non-redundant structures, and the number of the non-redundant structures is 10496.

And step two, clustering the structures by adopting a K-means algorithm in scimit-lean, wherein the structures needing clustering in the first generation are 10496 structures in the step one, and the structures needing clustering after the second generation refer to structures which do not converge after the previous generation machine learning potential is optimized. The number of clusters is 3, where each structure is converted to a feature vector using ACSFs as the K-means input. The parameters G2 and G4 corresponding to ACSFs are set as follows: g2_ etas ═ 1, g2_ Rses ═ 1, 2, 3, g4_ etas ═ 1, g4_ zetas ═ 1, 2, g4_ lambdas ═ 1, -1.

And step three, selecting a structure from each clustering result, and recommending the structure to the next step for optimization by adopting a density functional theory. For the first generation, the invention adopts a random mode to select two structures as the next to-be-optimized structure, and the randomly selected structure in the embodiment is the structure with the label number of 0 and 52; for the second generation and later, one of the clustering results is selected according to the principle of energy priority and diversity priority, three structures to be optimized are selected, the structures of the clustering results are ranked from low to high according to the energy predicted by the machine learning potential model of the previous generation, the structures with the lowest energy are selected during selection, meanwhile, the similarity between the structures and m structures with the lowest energy optimized by adopting the density functional theory of the previous generation is judged for comparison, in the embodiment, the m value is set to be 1, the similarity is set to be 0.5, the method described in the step two is adopted for similarity calculation, and when the similarity is smaller than 0.5, the structure with the second energy ranking is considered until a candidate structure meeting the conditions is selected.

And step five, preparing a training set from an optimization track of the optimized structure, wherein 74 frame structures (including energy and force of corresponding structures) coexist in the optimization processes of the first two optimized structures, the energy difference value is set to be 0.01eV, the training set is added when the energy difference between the front structure and the rear structure is larger than a set value, the number of the training sets is 18, and T is set to be 20000 in the training process.

And step seven, optimizing the structure without relaxation by adopting the machine learning potential model trained in the step six. The first generation of non-relaxed structures refers to 10496 non-redundant structure removal steps generated in the first step, and adopts 2 structures optimized by the density functional theory, wherein 10494 structures are used in total, and the second generation of non-relaxed structures refers to the structures which are not converged after the optimization of the previous generation of machine learning potential model and adopt the structures optimized by the density functional theory in the current generation. And optimizing the atomic position by adopting a BFGS algorithm, when the stress is less than 0.05, the structure converges, the last frame structure (comprising corresponding energy and force) of the converged structure is stored into a structure set of machine learning potential optimization convergence, and the last frame structure (comprising corresponding energy and force) of the unconverged structure is stored into a structure which does not converge after the machine learning potential optimization. In the example, the first generation machine learning potential model optimizes 0 converged structures, 10494 structures without convergence, and 10494 structures are provided for clustering in the next generation step two.

And step eight, judging whether a set termination condition is reached, wherein the termination condition sets that the invention adopts a first mode, namely a set running algebra, in the example, the algebra set by the invention is 10, and repeating the steps two to eight until the termination condition is met.

And step nine, after a termination condition is met, sorting the converged structure set after the machine learning potential optimization according to the energy from low to high, selecting the first 21 structures to recommend to a density functional theory for optimization, storing the optimized structures into the structure set optimized by the density functional theory, and finally sorting the structures in the structure set optimized by the density functional theory according to the energy from low to high, and selecting the first 16 structures as a finally recommended thermodynamically stable structure set.

FIG. 6 shows the total energy and most stable structure of 10496 non-redundant structures in the example e-Fe 2C 2X 3 supercell structure after VASP optimization. The pictures are derived from the articles J.Phys.chem.C 2017, 121, 39, 21390 and 21396, the authors in the article adopt a density functional theory to optimize 10496 structures to obtain the most thermodynamically stable structure, and by using the example, whether the method of the invention recommends a reliable thermodynamically stable structure set with a small calculation cost can be evaluated. It should be noted that the 10496 non-redundant structures are not optimized by the VASP in the present invention, but are directly compared by using the original text results. The VASP optimized structures used in the present invention are not completely consistent with the parameters of the authors, and the most thermodynamically stable structure shown in fig. 5 has an energy of-312.4113 eV, which is lower than the energy calculated using the parameters of the present invention, but this has no effect on the conclusion of the present invention.

FIG. 7 is a graph of the running algebra versus the energy of the structure optimized using density functional theory per generation. The black hollow sphere represents the total energy of the structure optimized by adopting the density functional theory in each generation, and the gray solid sphere represents the energy of the structure with the lowest energy in the history (in all the generations operated at present) optimized by adopting the density functional theory. In this example, a total of ten generations were run, with the energy of the lowest energy configuration occurring in the eighth generation being-310.7659 eV, a 1.64eV difference from the target configuration energy of-312.4113 eV, and this configuration was maintained in the ninth and tenth generations.

Table 3 shows the structure tag names and corresponding energies of the first 16 recommended after the 10-generation operation of the method of the present invention is terminated. From table 3, it can be shown that the energy corresponding to the 16 proposed structures in the method is all in the low energy region in fig. 5, and the energy corresponding to the first proposed structure is-312.4113 eV, which is the most stable structure in the 10496 non-redundant structures. The method is shown to be capable of recommending a reliable prediction recommendation set of the thermodynamically stable structure of the disordered material by using very few computing resources and time cost. The exhaustion method needs to optimize all 10496 structures by adopting a density functional theory to find the most thermodynamically stable structure, the method can find the most thermodynamically stable structure by only optimizing 50 structures by adopting the density functional theory, and meanwhile, a batch of structures with energy similar to that of the most thermodynamically stable structure are provided.

TABLE 3

In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.

The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims

1. The method for predicting and recommending the thermodynamically stable structure of the disordered material is characterized by comprising the following steps of:

step one, generating all possible non-redundant structures in a specified substitution/defect/co-occupation state by adopting an existing program supercell;

secondly, clustering the structure by adopting a clustering algorithm in machine learning;

recommending and obtaining a structure to be optimized which needs to be optimized by adopting a density functional theory from each clustering result, wherein the recommending principle follows energy priority and diversity priority;

fourthly, optimizing the recommended structure by adopting a density functional theory method;

step five, preparing a training set from the track of the optimized structure;

step six, training a machine learning situation model;

step seven, optimizing a structure without relaxation by adopting a trained machine learning potential model;

step eight, judging whether a set termination condition is reached or not by adopting a multi-generation operation mode, and if not, repeating the step two to the step eight until the termination condition is met;

and step nine, recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition.

2. The method for predicting and recommending the thermodynamically stable structure of a disordered material according to claim 1, wherein in the second step, the clustering of the structure by using a clustering algorithm in machine learning comprises: setting the clustering number, converting each structure into a characteristic vector as the input of clustering in the clustering process, and converting the crystal structure into the characteristic vector by adopting an atom central symmetry function ACSFs; the atom central symmetry function comprises a radial function and an angular function, and the radial symmetry function G2 describing the radial environment of the atom i is

The function G2 is the sum of a gaussian function multiplied by a cutoff function; the width of the Gaussian function is defined by a parameter eta, and the center of the Gaussian function is defined by a parameter R_sMoving to a certain radial distance, the G2 function of the movement is suitable for describing the spherical shell around the reference atom, and the truncation function takes the form:

wherein R is_ijIs the distance of atom i from atom j, if R_ijGreater than the cutoff radius R_cThe truncation function and its derivative value are zero; angular function of the central atom iIs a corner

Is given by the expression:

where λ has a value of +1 or 1, the angular resolution being provided by the parameter ζ; the larger the zeta value, the narrower the range of non-zero symmetric function values, so a set of angular functions with different zeta values is used to obtain a distribution of angles centered around each reference atom; the angular distribution is determined by selecting appropriate η and R_cDetermining, for controlling the radial portion; converting the local environment of the central atom into a feature vector by setting different parameter values through a series of functions G2 and G4; the atomic feature vectors of the same element are added to obtain the feature vector of the same element, the feature vectors of different elements are spliced in sequence, and the similarity of the two structures can be quantitatively described by calculating the distance between the feature vectors of the two structures.

3. The method for predicting and recommending the thermodynamically stable structure of the disordered material according to claim 1, wherein in the third step, the strategy for optimizing the structure clusters the structure set in a clustering manner, predicts the energy of the structure in each cluster according to the machine learning potential model trained in the sixth step, sorts the energy according to the energy from low to high, and considers the energy priority and diversity principle when selecting the structure to be optimized.

4. The method for predicting and recommending the thermodynamically stable structure of a disordered material according to claim 1, wherein in step five, the training set is derived from each frame structure in each structure optimization process in step four, and the energy difference between the front frame structure and the rear frame structure during selection is considered, and when the energy difference is smaller than a set value, the training set is not added to the current frame structure.

5. The method for predicting and recommending a thermodynamically stable structure of a disordered material according to claim 1, wherein in step six, the training of the machine learning potential model comprises: simultaneously training a plurality of machine learning potential models in an integrated mode, taking the average value of all model predictions as a prediction result, and simultaneously training energy and force corresponding to a structure in the training process of each machine learning potential model; the machine learning potential model adopts a Back Propagation Neural Network (BPNN), and other machine learning potential models are also suitable for a prediction recommendation method of a disordered material thermodynamic stable structure.

6. The method for predicting and recommending the thermodynamically stable structure of the disordered material according to claim 1, wherein in the seventh step, a trained machine learning potential model is used to optimize the structure without relaxation; the optimized and converged structure is stored into the optimized and converged structure of the machine learning potential model for the ninth step; and (4) taking the structure without convergence after optimization as a source of the secondary clustering structure.

7. The prediction recommendation method for the thermodynamically stable structure of the disordered material according to claim 1, wherein in the ninth step, after a termination condition is met, the structure set converged after the machine learning potential model is optimized is sorted according to energy, and the first K structures are recommended to be verified by a more reliable density functional theory method in the fourth step; and adding the verified K structures into a structure set optimized by adopting a density functional theory, and finally sequencing the structures in the structure set optimized by adopting the density functional theory according to the energy from low to high, and selecting the first N structures as recommended thermodynamically stable structure sets.

8. A system for implementing the method for predicting and recommending the thermodynamically stable structure of the disordered material, which is described in any one of claims 1 to 7, wherein the system for predicting and recommending the thermodynamically stable structure of the disordered material comprises:

the non-redundant structure determining module is used for generating all possible non-redundant structures in a specified substitution/defect/co-occupation state by adopting a used program supercell;

and the structure set recommendation module is used for predicting and recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization after meeting the termination condition.

9. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:

(1) generating all possible non-redundant structures in the specified replacement/defect/co-occupation state by using the used program supercell;

(5) preparing a training set from the trajectory of the optimized structure;

(6) training a machine learning potential model;

(9) and after the termination condition is met, predicting and recommending a thermodynamically stable structure set based on the structure set optimized by the density functional theory and the structure set converged after the machine learning potential optimization.

10. An information data processing terminal, characterized in that the information data processing terminal is used for implementing a predictive recommendation system for thermodynamically stable structures of disordered materials according to claim 8.