A machine learning approach for rapidly predicting the electrical conductivity of metal compounds with high precision

Abstract

A machine learning method for rapidly predicting the high-precision conductive properties of metal compounds uses a graph neural network to collect PBE band gaps from semiconductor materials such as binary metal oxides, nitrides, and sulfides to generate training samples. A structure-bandgap prediction model for semiconductor materials is initially trained using the training samples to obtain a prediction model for rapidly predicting PBE band gaps. The HSE06 band gaps of a subset of semiconductor materials in the training samples are then calculated to generate secondary training samples. This prediction model is then retrained using transfer learning to obtain a high-precision bandgap prediction model for semiconductor materials, which can be used to predict energy gaps at the HSE06 level. This method significantly reduces the computational cost of bandgap prediction, effectively avoiding tedious experimental operations and design costs. It can be extended to other material systems and has guiding significance for the discovery of materials with functional properties.

Description

Technical Field

[0001] The present invention relates to a technology in the field of chemistry, specifically a machine learning method for rapidly predicting the high-precision conductive properties of metal compounds. Background Art

[0002] The band gap is the energy difference between the lowest point of the conduction band and the highest point of the valence band in a material's band structure, also known as the energy gap. Existing methods for measuring band gaps require synthesizing the crystalline material and then measuring it using experimental methods such as diffuse reflectance, resistivity, surface photovoltage, photoconductivity, or UV–vis. Improved techniques often use density generalization theory calculations to roughly estimate the band gap of a crystal. The mainstream method is based on the Perdew-Berke-Ernzerhof (PBE) exchange-correlation functional calculation method within the generalized gradient approximation (GGA). Although this method is relatively inexpensive compared to experimental methods, the calculated band gap often deviates significantly from the experimental value. The hybrid functional Heyd-Scuseria-Ernzerhof (HSE06) calculation method calculates band gaps with minimal deviation from experimental values, but the computational cost is very high, approximately 5-10 times that of PBE calculations. Summary of the Invention

[0003] In response to the above-mentioned shortcomings of the existing technology, the present invention proposes a machine learning method for rapidly predicting the high-precision conductive properties of metal compounds. This method can significantly reduce the computational cost of band gap prediction, effectively avoid the tedious experimental operation and design costs, and can be extended to other material systems. It has guiding significance for the discovery of materials with functional properties.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a machine learning method for rapidly predicting the high-precision conductive properties of metal compounds. The method collects PBE band gaps of semiconductor materials such as binary metal oxides, nitrides, and sulfides to generate training samples, and uses a graph neural network to establish a structure-band gap prediction model for the semiconductor materials. The training samples are used for initial training to obtain a prediction model for rapidly predicting the PBE band gap. The HSE06 band gaps of some semiconductor materials in the training samples are then calculated to generate secondary training samples. The prediction model is trained secondary through transfer learning to obtain a high-precision band gap prediction model for the semiconductor materials for energy gap prediction at the HSE06 level.

[0006] The collection refers to: collecting element information, atomic coordinates, lattice constants and corresponding PBE band gap values of atoms in the crystal structures of binary metal oxides, nitrides and sulfides with PBE band gap values greater than 0 from public databases.

[0007] The structure-bandgap prediction model adopts but is not limited to ordinary conventional convolutional neural networks.

[0008] The initial training and the secondary training are performed, but not limited to, at least once, until the error is within 0.4 eV.

[0009] The present invention relates to a system for implementing the above method, comprising: a data unit, a PBE bandgap prediction unit, and an HSE06 bandgap prediction unit, wherein: the data unit is connected to the PBE bandgap prediction unit and transmits information, and the PBE bandgap prediction unit is connected to the HSE06 bandgap prediction unit and transmits information.

[0010] Technical Effects

[0011] The present invention comprehensively solves the problems of the prior art in which the experimental preparation of metal compound materials and the measurement of band gaps require expensive chemical material and instrument costs, the detection process requires tedious steps such as pre-preparation, synthesis, and measurement, and generally requires precision instruments for operation, resulting in long experimental cycles and low detection accuracy.

[0012] Compared to existing technologies, this invention utilizes machine learning to establish a highly accurate and efficient bandgap prediction model, avoiding tedious and expensive experimental steps and reducing reliance on first-principles calculations. Using transfer learning techniques, it accurately predicts material band gaps at the HSE06 level while minimizing computational costs. This method is also highly scalable and can be extended to encompass the entire material database, yielding comprehensive, high-precision band gap predictions. This method converts all low-precision PBE band gaps of a material into high-precision HSE06 band gaps, facilitating further research and application of these materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Schematic diagram of PBE band gap for graph neural network training;

[0014] Figure 2 Schematic diagram of transfer learning. DETAILED DESCRIPTION

[0015] This embodiment relates to a machine learning method for rapidly predicting the high-precision conductive properties of metal compounds, comprising the following steps:

[0016] Step 1) Data Collection: We collected all binary metal oxide, nitride, and sulfide crystal structures from the Materials Project database. These crystal structures contain elemental information, atomic coordinates, lattice constants, and corresponding PBE band gap values. We selected crystal structures with band gaps greater than 0, i.e., semiconductor structures. A total of 1,503 semiconductor structures were collected: 979 oxides, 356 sulfides, and 168 nitrides.

[0017] Step 2) Establish a graph neural network, specifically including:

[0018] 2.1) Calculate the interatomic distances d of the crystal structures of 1503 semiconductor materials to identify neighboring atoms. This information, along with bond lengths, is used as a descriptor for the semiconductor material to uniquely characterize its crystal structure.

[0019] The interatomic distance is: Where: (x i ,y i ,z i ) is the spatial xyz coordinate of the i-th atom, (x j ,y j ,z j ) is the spatial xyz coordinate of the jth atom.

[0020] The judgment means that when the distance between atoms is less than 10 angstroms, they are judged as neighboring atoms, otherwise they are not counted as neighboring atoms.

[0021] The descriptors correspond one-to-one to their PBE band gap values.

[0022] 2.2) Use the descriptor obtained in step 2.1 as the input of the convolutional neural network and the PBE band gap value as the output (i.e., label) to train the entire network.

[0023] The convolutional neural network is composed of neurons, and there are connection parameters between the neurons, also known as weights. The structure of the neural network is 3 to 5 hidden layers, with 10 to 50 neurons in each layer. During the training process, the Adam optimizer (an optimization algorithm used to solve optimization problems) is used for iteration, and 32 to 128 units are selected as batch training units. The initial learning rate during training is 0.002 to 0.003, that is, the step size of each update of the connection parameters. Before training, the connection parameters between the neurons in the neural network are randomly initialized, and then the parameters of the neurons are adjusted according to the corresponding relationship between output and input, that is, the training process.

[0024] The error function of the training is Where: M is the number of input structures, E NN,i is the band gap of the i-th structure predicted by the neural network, i.e., the i-th predicted band gap. E DFT,i is the band gap of the ith structure calculated using PBE, i.e., the ith band gap, E RMSE is the root mean square error between the two.

[0025] 2.3) After training is complete (RMSE < 0.4 eV), a prediction model from crystal structure to PBE band gap is obtained. When the atomic information of the crystal structure is input and the descriptors are calculated, the PBE band gap value can be quickly calculated by performing four arithmetic operations using the weight parameters between neurons.

[0026] Step 3) HSE06 band gap calculation: 150 structures were randomly selected from 1503 semiconductor structures and subjected to HSE06 high-precision band gap calculation to obtain 150 HSE06 band gaps.

[0027] Step 4) Transfer learning: The crystal descriptors of the 150 structures obtained in step 3) are used as the input of the prediction model trained in step 2), and the corresponding HSE06 band gap is used as the output for secondary training.

[0028] The connection parameters between neurons in the prediction model are initialized using the parameters obtained in Step 2. A learning rate of ~0.001 is set to fine-tune the parameters. After training is complete (RMSD < 0.4 eV), a model for predicting the HSE06 band gap from structure is obtained. Using only ~150 structures, high HSE06 band gap prediction accuracy is achieved, thanks to the fact that the model's initial parameters are derived from a pre-trained PBE band gap prediction model.

[0029] Step 5) Repeat steps 2) to 4) until the error reaches the required level, and then obtain the optimized prediction model, which is then used to predict the band gap of all crystal structures based on the HSE06 level.

[0030] By searching by band gap using the above method, we can obtain semiconductor materials that can be used in the fields of sensors, solar cells, etc. as candidates and promote their further application.

[0031] The present invention runs in the Python 3.X environment. By inputting the crystal file of the semiconductor material in CIF format and using the transfer learning technology to call the model, the PBE band gap prediction model is migrated to the HSE06 band gap prediction model, which makes the required training data set very small and greatly reduces the calculation cost.

[0032] In summary, the present invention can predict 1503 HSE06 band gap values using only 150 HSE06 band gap values, and provides material candidates in different fields based on the size of the band gap values, greatly shortening the material research and development cycle.

[0033] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principles and purpose of the present invention. The scope of protection of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. All implementation schemes within its scope shall be subject to the constraints of the present invention.

Claims

1. A machine learning method for rapidly predicting the high-precision conductive properties of metal compounds, characterized in that: By collecting the PBE band gaps of semiconductor materials such as binary metal oxides, nitrides, and sulfides to generate training samples, a graph neural network is used to establish a structure-band gap prediction model for semiconductor materials. The training samples are used for initial training to obtain a prediction model for quickly predicting the PBE band gap. The HSE06 band gaps of some semiconductor materials in the training samples are then calculated to generate secondary training samples. The prediction model is then trained again through transfer learning to obtain a high-precision band gap prediction model for semiconductor materials for energy gap prediction at the HSE06 level. Specifically, this includes: Step 1) Data collection: All binary metal oxide, nitride, and sulfide crystal structures were collected from the Materials Project database. These crystal structures contain atomic element information, atomic coordinates, lattice constants, and corresponding PBE band gap values. Crystal structures with band gap values greater than 0 were selected, i.e., semiconductor structures. A total of 1503 semiconductor structures were selected: 979 oxides, 356 sulfides, and 168 nitrides. Step 2) Establish a graph neural network, which includes: 2.1) Calculate the interatomic distances d of the crystal structures of 1503 semiconductor materials to identify neighboring atoms. This information, along with bond lengths, is used as a descriptor for the semiconductor material to uniquely characterize its crystal structure. 2.2) Use the descriptor obtained in step 2.1 as the input of the convolutional neural network and the PBE band gap value as the output, and train the entire network; 2.3) After training, a prediction model from crystal structure to PBE band gap is obtained. When the atomic information of the crystal structure is input and the descriptors are calculated, the PBE band gap value can be quickly calculated by performing four arithmetic operations using the weight parameters between neurons; Step 3) HSE06 band gap calculation: 150 structures are randomly selected from 1503 semiconductor structures and the HSE06 high-precision band gap calculation is performed to obtain 150 HSE06 band gaps; Step 4) Transfer learning: The crystal descriptors of the 150 structures obtained in step 3) are used as the input of the prediction model trained in step 2), and the corresponding HSE06 band gap is used as the output for secondary training; Step 5) Repeat steps 2) to 4) until the error reaches 0.4 eV, and obtain the optimized prediction model, which is then used to predict the band gap of all crystal structures based on the HSE06 level.

2. The machine learning method for rapidly predicting the high-precision conductive properties of metal compounds according to claim 1, characterized in that: The interatomic distance is: Where: (x i ,y i ,z i ) is the spatial xyz coordinate of the i-th atom, (x j ,y j ,z j ) is the spatial xyz coordinate of the jth atom; The judgment means that when the distance between atoms is less than 10 angstroms, they are judged as neighboring atoms, otherwise they are not counted as neighboring atoms; The descriptors correspond one-to-one to their PBE band gap values.

3. The machine learning method for rapidly predicting the high-precision conductive properties of metal compounds according to claim 1, characterized in that: The error function of the training is Where: M is the number of input structures, E NN,i is the band gap of the i-th structure predicted by the neural network, i.e., the i-th predicted band gap, E DFT,i is the band gap of the ith structure calculated using PBE, i.e., the ith band gap, E RMSE is the root mean square error between the two.

4. The machine learning method for rapidly predicting the high-precision conductive properties of metal compounds according to claim 1, characterized in that: The connection parameters between neurons in the prediction model are based on the parameters obtained in step 2 as the initial point of this step. The learning rate is set to 0.001 to fine-tune the parameters. After the training is completed, a model for predicting the band gap of HSE06 from the structure is obtained.

5. A system for implementing the method according to any one of claims 1 to 4, characterized in that: include: Data unit, PBE bandgap prediction unit, HSE06 bandgap prediction unit, wherein: the data unit is connected to the PBE bandgap prediction unit and transmits information, and the PBE bandgap prediction unit is connected to the HSE06 bandgap prediction unit and transmits information.

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