Construction method of multicomponent alloy system machine learning potential function

Abstract

The invention discloses a multi-element alloy system machine learning potential function construction method, and relates to the technical field of material science, and the method comprises the following steps: S1, carrying out the modeling of a needed multi-element alloy system through employing a first principle, completing the calculation of the first principle, and taking a result as a data source; s2, extracting structure and force information from the data source, vectorizing the collected information, and forming a data set for training a neural network model; and S3, training the processed data set based on a deep learning model of machine learning, and generating a potential function model of machine learning. The potential function constructed by the method provided by the invention is high in precision and low in calculation cost.

Description

Technical Field

[0001] The present invention belongs to the field of material science and technology, and in particular relates to a method for constructing a machine learning potential function for a multi-element alloy system. Background Art

[0002] With the advancement of materials science, multi-element systems have attracted much attention in recent years due to their diverse element combinations and excellent performance. However, the complex interactions between atoms in multi-element systems make traditional potential function models face huge challenges in dealing with these systems. Traditional potential function models such as embedded atom method (EAM) or modified embedded atom method (MEAM) perform well in describing simple systems, but their prediction accuracy and applicability are significantly reduced when facing complex multi-element systems. This is mainly because there are more types of atoms and combinations in multi-element systems, making the construction of potential functions extremely complicated. In practical applications, such as the research on metal nuclear fuels, it is crucial to accurately describe the forces on atoms in complex multi-element alloy systems.

[0003] In recent years, machine learning technology has shown great potential in the field of materials science. Through machine learning methods, the problems of large computational complexity and low precision in traditional methods can be effectively solved. In particular, deep learning models such as neural networks can perform well in processing complex data sets due to their powerful fitting ability and nonlinear characteristics. Therefore, constructing the potential function of multi-element alloy systems based on machine learning methods has become a promising research direction. Summary of the invention

[0004] In view of the defects existing in the prior art, the purpose of the present invention is to provide a method for constructing a machine learning potential function for a multi-element alloy system. The potential function constructed by this method has high accuracy and low computational cost.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for constructing a machine learning potential function for a multi-element alloy system comprises the following steps:

[0007] S1. Model the required multi-element alloy system using first principles and complete first principles calculations, using the results as the data source;

[0008] S2, extracting structure and force information from the data source, vectorizing the collected information, and forming a data set for training a neural network model;

[0009] S3. Train the processed data set based on a deep learning model for machine learning to generate a potential function model for machine learning.

[0010] Furthermore, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, step S1 is specifically as follows:

[0011] S11. Establish a lattice model with a reasonable structure for a specific multi-element alloy system;

[0012] S12, performing structural relaxation on the lattice model using an atomic scale material simulation tool;

[0013] S13, performing electronic self-consistent calculations on the relaxed lattice, thereby obtaining sufficient lattice structure and mechanical information as a data source;

[0014] S14. Repeat steps S11-S13 multiple times to obtain sufficiently diverse model results under the system to enrich the data source.

[0015] Furthermore, in the method for constructing a machine learning potential function for a multi-element alloy system as described above, in step S11, during the modeling process, the atomic species at the lattice positions are distributed according to a specified ratio or a random ratio, and defects are added so that the model can simulate various atomic distribution conditions to the greatest extent.

[0016] Further, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, step S13 is specifically as follows:

[0017] S131, applying a specified random distribution to the position of each atom in the relaxed lattice, so that the atomic positions in the lattice fluctuate within a small range;

[0018] S132, using a computer program package for atomic-scale material simulation to perform electronic self-consistency on the lattice model, and storing the calculation results as a data source;

[0019] S133, repeat steps S131 and S132 multiple times until sufficient results are obtained for the model as a data source.

[0020] Furthermore, in the method for constructing a machine learning potential function for a multi-element alloy system as described above, the step of extracting structure and force information from a data source in step S2 is specifically as follows: extracting the type, position coordinates, and resultant force of each atom in each calculation result from the data source obtained in step S1.

[0021] Furthermore, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, the vectorization of the collected information in step S2 is specifically as follows:

[0022] S21, defining a training space, where the training space is a region within a certain radius centered on the target atom, gridding the training space, and then vectorizing it;

[0023] S22, vectorizing the element types of atoms;

[0024] S23, for an atom in the extracted information, set it as the central atom, and map the type vectors of other atoms in the training space centered on it to the space vectors corresponding to their positions, as the input of the training set;

[0025] S24, normalizing the resultant force vector on the central atom and using it as the output of the training set;

[0026] S25. Repeat steps S23 to S24 until all atoms in the extracted information are traversed, thereby obtaining the entire training set.

[0027] Furthermore, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, in step S21, the training space is gridded, i.e., the three-dimensional space is divided into a plurality of small grids, and the space is vectorized, i.e., a three-dimensional coordinate is assigned to each grid.

[0028] Further, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, the definition and setting principles of the training space in step S21 include:

[0029] 1) For each sample in the training set, its information source is the environment and force information within a certain radius around the central atom corresponding to the sample, and the space within the radius is the training space;

[0030] 2) Set the training space according to the accuracy requirements. The larger the space, the more accurate the trained machine learning potential function, but the higher the training computational cost, and vice versa.

[0031] 3) The training space should not be smaller than the cutoff radius of large-scale atomic / molecular parallel simulation tools, or larger than the size of the lattice model of computer programs for atomic-scale material simulations;

[0032] 4) Grid the training space according to the accuracy requirements, and the grid size should be much smaller than the lattice constant;

[0033] 5) The grid is based on a three-dimensional rectangular coordinate system or other coordinate systems;

[0034] 6) The grid is uniform or non-uniform, with a denser grid closer to the central atom to improve accuracy.

[0035] Further, in the method for constructing the machine learning potential function of the multi-element alloy system as described above, step S3 is specifically as follows:

[0036] S31. Use the deep learning framework to build a neural network model, select a multilayer perceptron or convolutional neural network as the basic model, and optimize the model's fitting ability and generalization performance by adjusting the network structure and hyperparameters;

[0037] S32, inputting the processed training set into the neural network model for training, thereby generating a potential function model for machine learning.

[0038] Furthermore, in the method for constructing a machine learning potential function for a multi-element alloy system as described above, in step S32, during the training process, the model performance is evaluated through a validation set and a test set, and the model parameters are adjusted to improve the accuracy.

[0039] Compared with the prior art, the method for constructing a machine learning potential function for a multi-element alloy system provided by the present invention has the following beneficial effects:

[0040] The present invention uses a neural network model to accurately predict the forces acting on atoms in a multi-element alloy system. The core idea of ​​this method is to grid and vectorize complex three-dimensional spatial information, vectorize the element types of atoms in the multi-element system, and thus vectorize the three-dimensional spatial environment around the central atom under investigation, and obtain a data structure similar to a three-channel image after vectorization, which is used as the input of the neural network. The resultant force acting on the central atom is used as the output of the neural network, and the atoms in the training set are traversed to train the neural network. The trained neural network can directly give the resultant force acting on an atom in the environment according to the environment around it, without having to traverse and sum the interaction forces with each neighboring atom within its truncation radius, thereby achieving the generation of a high-precision potential function model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of a method for constructing a machine learning potential function for a multi-element alloy system provided in an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the neural network training set data structure. DETAILED DESCRIPTION

[0043] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0044] Figure 1 A flow chart of a method for constructing a machine learning potential function of a multi-element alloy system provided in an embodiment of the present invention is shown, and the method comprises the following steps:

[0045] S1. Use first principles to model the required multi-element alloy system and complete first principles calculations, using the results as the data source.

[0046] First-principles calculations (such as density functional theory, DFT) can provide high-precision atomic structure and mechanical information, but their computational cost is high and suitable for small-scale systems. In order to obtain enough data for training neural network models, it is necessary to perform as many first-principles calculations as possible within a reasonable computing resource range. The specific steps include:

[0047] S11. For a specific multi-element alloy system, a lattice model with a reasonable structure, i.e., a POSCAR file, is established. During the modeling process, the atomic species on the lattice positions are distributed according to a specified ratio or a random ratio, and defects such as vacancies and gaps can be added so that the model can simulate various atomic distribution conditions to the greatest extent.

[0048] S12, structurally relax the lattice model. Specifically, atomic-scale material simulation tools such as Vienna Ab initio Simulation Package (VASP) can be used to structurally relax the crystal model, and the calculation results are stored as a data source.

[0049] S13, perform multiple electronic self-consistent calculations on the relaxed lattice to obtain sufficient lattice structure and mechanical information as a data source. Specifically:

[0050] S131, applying a specified random distribution to the position of each atom in the relaxed lattice, so that the atomic positions in the lattice fluctuate within a small range;

[0051] S132, using a computer program package for atomic-scale material simulation (VASP) to perform electronic self-consistency on the lattice model, and storing the calculation results as a data source;

[0052] S133, repeat steps S131 and S132 multiple times until sufficient results are obtained for the model as a data source.

[0053] S14. Repeat steps S11-S13 multiple times to obtain sufficiently diverse model results under the system to enrich the data source.

[0054] S2. Extract structure and force information from the data source, vectorize the collected information, and form a data set for training the neural network model.

[0055] The type, position coordinates and resultant force of each atom in each VASP calculation result are extracted from the data source obtained in step S1.

[0056] In order to train the data using the neural network model, the original three-dimensional spatial information needs to be vectorized. This process is similar to the idea of ​​pixel-wise vectorization of a two-dimensional image in image processing. Specifically, for a multi-element alloy system, it is necessary to describe each atom in the lattice and its surrounding environment, which includes the following steps:

[0057] S21, define a training space, grid the training space, and then vectorize it. The training space is an area within a certain radius centered on the target atom. The training space is gridded, that is, the three-dimensional space is divided into multiple small grids, and the vectorization of the space is to give each grid a three-dimensional coordinate, such as [157,420,301].

[0058] The definition and setting principles of the training space are as follows:

[0059] 1) For each sample in the training set, its information source is the environment and force information within a certain radius around the central atom corresponding to the sample, and the space within this radius is the training space;

[0060] 2) Set the training space according to the accuracy requirements. The larger the space, the more accurate the trained machine learning potential function, but the higher the training computational cost, and vice versa.

[0061] 3) The training space should not be smaller than the cutoff radius of the LAMMPS calculation or larger than the size of the lattice model of the VASP calculation;

[0062] 4) Grid the training space according to the accuracy requirements. The grid size should be much smaller than the lattice constant. The denser the grid, the more accurate the trained machine learning potential function, but the higher the computational cost of training, and vice versa.

[0063] 5) The grid can be based on a three-dimensional rectangular coordinate system or other coordinate systems, such as spherical polar coordinates;

[0064] 6) The grid can be uniform or non-uniform, for example, the grid is denser near the central atom to improve accuracy.

[0065] S22. Vectorize the element types of atoms. For example, in a ternary system, [0,0,0] represents no atom here, [1,0,0] represents the atom of element A, [0,1,0] represents the atom of element B, and [0,0,1] represents the atom of element C.

[0066] S23, for an atom in the extracted information, set it as the central atom, and map the type vectors of other atoms in the training space centered on it to the space vectors corresponding to their positions, as the input of the training set;

[0067] S24, normalizing the resultant force vector on the central atom as the output of the training set;

[0068] S25, repeat steps S23 to S24 until all atoms in the extracted information are traversed, thereby obtaining the entire training set. The data structure diagram of the training set is as follows Figure 2 shown.

[0069] It should be noted that Figure 2 This is only a simplified illustration to help more intuitively understand the concept of the present invention. The grid division and atomic positions in actual applications should be based on specific needs.

[0070] S3. Based on the deep learning model of machine learning, the processed data set is trained to generate a potential function model of machine learning. Specifically, it includes:

[0071] S31. After data preparation is completed, use a deep learning framework (such as TensorFlow or PyTorch) to build a neural network model. The design of the neural network model needs to take into account the complexity and nonlinear characteristics of the multi-element alloy system. Usually, a multilayer perceptron (MLP) or convolutional neural network (CNN) is selected as the basic model, and the model's fitting ability and generalization performance are optimized by adjusting the network structure and hyperparameters.

[0072] S32, input the processed training set into the neural network model for training. During the training process, the model performance is evaluated through the validation set and the test set, and the model parameters are adjusted to improve the accuracy.

[0073] After the training is completed, the generated machine learning potential function model (neural network) can accurately predict the forces acting on atoms in a multi-component system based on the input atomic type and surrounding environment information, and can be directly applied to large-scale atomic / molecular parallel simulation tools (such as LAMMPS) for molecular dynamics simulation. During the simulation process, for each atom, the atomic position and type within its truncation radius are vectorized according to the training method, and input into the neural network model for calculation to obtain the predicted force. In this way, the forces and movements of atoms in a multi-component system can be effectively simulated, and the problem of fitting high-complexity potential functions can be solved.

[0074] The method for constructing the multivariate system machine learning potential function provided by the present invention can be applied to the molecular dynamics simulation study of the behavior of metal nuclear fuels. The metal nuclear fuels can be uranium-zirconium (U-Zr) metal nuclear fuels, uranium-plutonium-zirconium (U-Pu-Zr) metal nuclear fuels, etc.

[0075] Example 1

[0076] In this embodiment, for a new type of Mo-Re / SiC metal-ceramic composite material for a space reactor, the present invention provides a machine learning potential function suitable for the Mo-Re-Si-C multi-component system. In the Mo-Re / SiC composite material, especially at the metal / ceramic interface, the formation of metal carbides, silicides and eutectics is caused by diffusion and other factors. Therefore, in order to use molecular dynamics to accurately simulate and predict the properties and evolution of materials during preparation and use, a potential function that can describe this complex multi-component system is indispensable.

[0077] Example 2

[0078] In this embodiment, for a molecular dynamics simulation of a high entropy alloy as a plasma-facing material, the main elements of which are Ti, V, Cr, Zr, Nb, Mo and W, the present invention provides a machine learning potential function applicable to the Ti-V-Cr-Zr-Nb-Mo-W multi-element system. The construction process of the machine learning potential function applicable to the Ti-V-Cr-Zr-Nb-Mo-W multi-element system is as follows:

[0079] 1. Establish a cubic crystal system model of Ti-V-Cr-Zr-Nb-Mo-W as a POSCAR file, with 96 atoms, in which the atomic types on the lattice sites are randomly assigned according to random proportions;

[0080] 2. Use VASP to perform structural relaxation on the created model and store the calculation results as a data source;

[0081] 3. For the relaxed lattice, a specified random distribution is applied to the position of each atom, so that its position fluctuates within a certain range;

[0082] 4. Use VASP to perform electronic self-consistency on the crystal model and store the calculation results as a data source;

[0083] 5. Repeat steps 3 and 4 1000 times.

[0084] 6. Repeat steps 1 to 5 100 times.

[0085] 7. Extract the type, position coordinates and resultant force of each atom in each VASP calculation result from the data source obtained in step 6;

[0086] 8. Set the cutoff radius to The training space is large enough to ensure that sufficient interaction information is included;

[0087] 9. Grid the training space finely, and set the size of each grid to The training space is divided into 100×100×100 three-dimensional grids (similar to the two-dimensional pixels of an image);

[0088] 10. Vectorize the element types of atoms, [0,0,0,0,0,0,0] represents no atom here, [1,0,0,0,0,0,0] represents the atom of Ti element, [0,1,0,0,0,0,0] represents the atom of V element, [0,0,1,0,0,0,0] represents the atom of Cr element, [0,0,0,1,0,0,0] represents the atom of Zr element, [0,0,0,0,1,0,0] represents the atom of Nb element, [0,0,0,0,0,1,0] represents the atom of Mo element, [0,0,0,0,0,0,1] represents the atom of W element;

[0089] For each atom extracted from the results, set it as the central atom, map the species vector of each other atom in the training space centered on it to the space vector corresponding to its position (the species vector corresponding to the grid without atoms is [0,0,0,0,0,0,0]), and then flatten it into a one-dimensional vector as the input of the training set;

[0090] 11. The resultant force vector on the central atom is normalized and used as the output of the training set;

[0091] 12. Repeat steps 11 and 12 until all atoms in the extracted information are traversed to obtain the entire training set;

[0092] 13. Use TensorFlow to build a neural network model and input the processed training set into the neural network model for training;

[0093] 14. After training, the generated machine learning potential function model can accurately predict the combined force on atoms in a multi-element system based on the input atomic type and surrounding environment information;

[0094] 15. In LAMMPS calculations, the positions and types of atoms within the cutoff radius are vectorized according to the method used to train machine learning potential functions and used as the input of the neural network. The output resultant force is then inverse-processed to normalize the output and directly applied to the corresponding atoms to calculate the atomic velocity and position.

[0095] Example 3

[0096] The redistribution behavior of U-Pu-Zr metal fuel components under working conditions is an important multi-physics, multi-scale complex problem. The method for constructing the machine learning potential function of the multi-element system as described above is used to construct the machine learning potential function of the U-Pu-Zr ternary alloy, and the molecular dynamics simulation of the component redistribution behavior of U-Pu-Zr metal nuclear fuel under working conditions is realized to study its behavior mechanism.

[0097] Example 4

[0098] The diffusion and migration of lanthanide fission products in metal nuclear fuels will cause erosion of the cladding material, thereby reducing the mechanical properties of the cladding or even causing damage. The above-mentioned method for constructing the machine learning potential function of the multi-element system is used to construct the "U-Pu-Zr-lanthanide" multi-element alloy machine learning potential function, and the molecular dynamics study of the diffusion behavior of lanthanide elements in U-Pu-Zr metal nuclear fuel is realized.

[0099] Example 5

[0100] The method for constructing the potential function of multivariate system machine learning as mentioned above is applied to the study of the mechanism of Cr coating protecting the anti-corrosion of zirconium-based nuclear fuel cladding materials, and the molecular dynamics simulation of the diffusion behavior of atoms of each element in the Cr coating on the Zr matrix under a high-temperature water coolant environment is realized.

[0101] The present invention provides a method for constructing a machine learning potential function for a multi-element alloy system, which accurately predicts the forces on atoms in the multi-element alloy system through a neural network model. The core idea of ​​the method is to grid and vectorize complex three-dimensional spatial information, vectorize the element types of atoms in the multi-element system, and thus vectorize the three-dimensional spatial environment around the central atom under investigation, and obtain a data structure similar to that after vectorization of a three-channel image, which is used as the input of the neural network, and the resultant force on the central atom is used as the output of the neural network, and the atoms in the training set are traversed to train the neural network. The trained neural network can directly give the resultant force on an atom in the environment according to the environment around it, without having to traverse and sum the interaction forces with each neighboring atom within its truncation radius, thereby achieving the generation of a high-precision potential function model.

[0102] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for constructing a machine learning potential function for a multi-element alloy system, comprising the following steps: S1. Use the first principles to model the required multi-element alloy system and complete the first principles calculation, using the results as the data source; S2, extracting structure and force information from the data source, vectorizing the collected information, and forming a data set for training a neural network model; S3. Train the processed data set based on a deep learning model for machine learning to generate a potential function model for machine learning.

2. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 1, characterized in that: Step S1 is specifically as follows: S11. Establish a lattice model with a reasonable structure for a specific multi-element alloy system; S12, performing structural relaxation on the lattice model using an atomic scale material simulation tool; S13, performing electronic self-consistent calculations on the relaxed lattice, thereby obtaining sufficient lattice structure and mechanical information as a data source; S14. Repeat steps S11-S13 multiple times to obtain sufficiently diverse model results under the system to enrich the data source.

3. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 2, characterized in that: In step S11, during the modeling process, the atomic species on the lattice positions are distributed according to a specified ratio or a random ratio, and defects are added so that the model can simulate various atomic distribution conditions to the greatest extent.

4. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 3, characterized in that: Step S13 is specifically as follows: S131, applying a specified random distribution to the position of each atom in the relaxed lattice, so that the atomic positions in the lattice fluctuate within a small range; S132, using a computer program package for atomic-scale material simulation to perform electronic self-consistency on the lattice model, and storing the calculation results as a data source; S133, repeat steps S131 and S132 multiple times until sufficient results are obtained for the model as a data source.

5. The method for constructing a machine learning potential function for a multi-element alloy system according to any one of claims 1 to 4, characterized in that: The step of extracting the structure and force information from the data source in step S2 specifically includes extracting the type, position coordinates and resultant force of each atom in each calculation result from the data source obtained in step S1.

6. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 5, characterized in that: The step S2 of vectorizing the collected information is as follows: S21, defining a training space, where the training space is a region within a certain radius centered on the target atom, gridding the training space, and then vectorizing it; S22, vectorizing the element types of atoms; S23, for an atom in the extracted information, set it as the central atom, and map the type vectors of other atoms in the training space centered on it to the space vectors corresponding to their positions, as the input of the training set; S24, normalizing the resultant force vector on the central atom and using it as the output of the training set; S25. Repeat steps S23 to S24 until all atoms in the extracted information are traversed, thereby obtaining the entire training set.

7. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 6, characterized in that: In step S21, the training space is gridded, i.e. the three-dimensional space is divided into a plurality of small grids, and the vectorization of the space is to assign a three-dimensional coordinate to each grid.

8. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 7, characterized in that: The definition and setting principles of the training space in step S21 include: 1) For each sample in the training set, its information source is the environment and force information within a certain radius around the central atom corresponding to the sample, and the space within the radius is the training space; 2) Set the training space according to the accuracy requirements. The larger the space, the more accurate the trained machine learning potential function, but the higher the training computational cost, and vice versa. 3) The training space should not be smaller than the cutoff radius of large-scale atomic / molecular parallel simulation tools, or larger than the size of the lattice model of computer programs for atomic-scale material simulations; 4) Grid the training space according to the accuracy requirements, and the grid size should be much smaller than the lattice constant; 5) The grid is based on a three-dimensional rectangular coordinate system or other coordinate systems; 6) The grid is uniform or non-uniform, with a denser grid closer to the central atom to improve accuracy.

9. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 6, characterized in that: Step S3 is specifically as follows: S31. Use the deep learning framework to build a neural network model, select a multilayer perceptron or convolutional neural network as the basic model, and optimize the model's fitting ability and generalization performance by adjusting the network structure and hyperparameters; S32, inputting the processed training set into the neural network model for training, thereby generating a potential function model for machine learning.

10. The method for constructing a machine learning potential function for a multi-element alloy system according to claim 9, characterized in that: In step S32, during the training process, the model performance is evaluated through the validation set and the test set, and the model parameters are adjusted to improve the accuracy.

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