A method for constructing machine learning potential for TiH binary system

Abstract

The present invention discloses a method for constructing a machine learning potential for a TiH binary system, comprising the following steps: constructing a reference electronic structure dataset using the first-principles calculation software VASP; training and testing an artificial neural network potential-ANN potential model on the reference dataset; calculating and comparing dimer curves, lattice constants, elastic moduli, and the like using VASP and the trained ANN potential, respectively, as a performance test; and specifically improving data showing large errors between the ANN model and the DFT results in the model test and performance test results by increasing the relevant configuration weights until an ANN potential model meeting the required accuracy is obtained. The machine learning potential model constructed by the present invention can better fit the interatomic interaction potential energy surface of the TiH binary system, solving the problems of small time and space scales in first-principles calculations and low accuracy of traditional empirical potentials, thereby providing a technical foundation for high-precision, large-scale simulation and research of the TiH binary system.

Description

Technical Field

[0001] The present invention relates to the field of TiH alloys and proposes a method for constructing a machine learning potential for a TiH binary system. Background Art

[0002] Titanium is an excellent hydrogen storage metal with good compatibility with hydrogen. The low hydrogen solubility limit makes α-Ti very easy to form hydrides in a hydrogen-rich environment, and its hydrogen absorption density can reach 9.2×10 22 atom / cm 3 , and its absorption of hydrogen is reversible. Therefore, titanium hydrides are widely used in hydrogen storage, as materials for the preparation of solid deuterium or tritium targets for neutron generators, and in hot hydrogen processing of titanium alloys. Therefore, understanding the structure and physicochemical properties of titanium hydrides in the TiH binary system is of great significance for basic research and engineering applications.

[0003] At present, the research on the physical and chemical phenomena of TiH binary system mainly focuses on the influence of surface oxide and Ti matrix integrity on H adsorption, migration and hydrogenation, as well as the influence of hydride formation on embrittlement and local corrosion resistance. However, due to the limitations of existing characterization and modeling technologies, there are still many knowledge gaps and challenges. For example, although the DFT simulation based on density functional theory has very high computational accuracy, its time complexity is O(N 3 ) That is, the amount of calculation is proportional to the cube of the number of atoms in the structure. Therefore, the time and space scales of the system that can be studied are relatively small, and complex defects in the system, such as dislocation networks, stacking layers, and interfaces / phase boundaries, are usually difficult to solve using DFT alone. Classical molecular dynamics simulation is an alternative method that can study larger time and space scales. However, the calculation results of atomic potential energy and forces using traditional empirical potentials often have large deviations. There has been a phenomenon in which the molecular dynamics simulation based on traditional empirical potentials is inconsistent with the ab initio calculation results for the diffusion of H in titanium hydrides. The lack of a reliable interatomic interaction potential in the TiH binary system affects the prediction of hydrogenation phenomena.

[0004] Molecular dynamics simulations using machine learning potentials achieve high accuracy approaching that of first-principles calculations, while maintaining the high efficiency of traditional semi-empirical potentials. The machine learning algorithm can effectively fit the potential energy surface of the atomic interactions of the TiH binary system, resolving the issues of the small time and space scales of first-principles calculations and the low accuracy of traditional empirical potentials. This provides a technical foundation and theoretical guidance for high-precision, large-scale simulations and experimental development of the TiH binary system. Summary of the Invention

[0005] To address the current problem of a lack of molecular simulation tools that balance accuracy and scale for the TiH binary system, the present invention provides a method for constructing a machine learning potential for the TiH binary system. A reference electronic structure dataset for the TiH binary system is constructed using first-principles calculation software. An artificial neural network is trained on the reference dataset using the AENET software package to obtain an ANN potential model, which is then tested. Performance tests are then conducted using VASP and the trained ANN potential on dimer curves, EV curves, RDF curves, lattice constants, elastic moduli, and defect formation energies. Targeted improvements are made to poorly performing properties until a machine learning potential model for the TiH binary system that meets accuracy requirements is obtained.

[0006] In order to solve the technical problem, the present invention adopts the following technical solution:

[0007] A method for constructing a machine learning potential for a TiH binary system is performed in the following steps:

[0008] Step 1: Use the first-principles software VASP to construct a basic reference electronic structure dataset including dimer structures, stable crystal configurations of Ti and common TiH compounds, random structures, and AIMD trajectory extracted structures. The specific method is as follows:

[0009] 11) Dimer structure: Create a supercell according to the VASP structure file POSCAR format, fix the position of one atom, and move another atom in one direction until the entire dimer curve potential well is covered.

[0010] 12) Stable Crystal Configurations of Ti and Common TiH Compounds: Construct HCP, BCC, FCC, Diamond, SC, A12, A13, and A15 structures of Ti, as well as initial configurations of Ti2H, TiH, and TiH2, using the VASP structure file POSCAR format. Use VASP for high-precision structural optimization. Based on this, apply multiple strains to the corresponding directions of the crystal according to the deformation matrices of different crystal systems to form a large number of perturbation configurations of the stable structure of the crystal system.

[0011] 13) Random structures: The ab initio random structure search program AIRSS was used to search for various possible symmetries and arrangements under different TiH composition ratios, generating a large number of random structures. VASP was used to perform coarse-precision optimization on these random structures, and structures were extracted from the optimization trajectory at regular intervals.

[0012] 14) AIMD trajectory structure extraction: Constant temperature and constant volume AIMD simulations are performed for H2 at different temperatures and pressures, Ti, TiH, and TiH2 perfect crystals at different temperatures and compositions, and different types of defect structures. A structure is extracted from the MD simulation trajectory at a certain number of steps.

[0013] Step 2: Use the AENET software package to train and test the ANN (artificial neural network) potential model on the basic reference electronic structure data set. The specific method is as follows:

[0014] 21) Use the generate.x tool in the AENET software package to compile the structures and energies in the reference electronic structure dataset into a set in a specific format.

[0015] 22) Debug the model parameters, including the cutoff radius, the shortest distance between atoms, the order of the descriptor basis function expansion, the neural network size, and the learning rate, and set the number of iterations and the test set weight. Use the train.x tool to split the dataset into training and test sets, and train the ANN potential model on the training set.

[0016] 23) Use predict.x to test the ANN potential model based on the reference electronic structure data (E DFT ) and ANN potential prediction results (E ANN ), where

[0017] When the RMSE and MAE of the ANN in both the training and test sets converge to below 10 meV, the model is considered to have DFT accuracy.

[0018] Step 3: Use VASP and the trained ANN potential model to calculate and compare the dimer curve, EV curve, RDF curve, equilibrium lattice constant, elastic modulus, and defect formation energy as a performance test;

[0019] 31) For structures with different distances between two atoms, single-point calculations were performed using VASP and ANN potentials, respectively, to extract energy-distance information, and obtain Dimer curves with the horizontal axis of VASP and ANN being the distance between the two atoms and the vertical axis being the total energy of the system.

[0020] 32) The stable crystal configuration of Ti and common TiH compounds was optimized. The volume of the optimized structure was expanded and compressed by changing the normalization coefficient in POSC AR with a continuous fixed step size. The single-point calculations of the structures with different volumes were performed using VASP and ANN potential. The volume of each atom was used as the As the abscissa, the energy volume curve - EV curve is obtained.

[0021] 33) Constant temperature and constant volume AIMD and ANN-MD simulations were performed on the supercell of body-centered cubic Ti. The supercell was heated from room temperature to a temperature above the melting point of Ti to melt the structure. The last frame structure was used as the initial structure and a constant temperature simulation was performed at this temperature. The distance between each particle in the system and other particles was calculated based on the position information of the atoms in the trajectory file XDATCAR generated by AIMD and the trajectory file dump generated by ANN-MD. A suitable distance range and step size were selected. For each distance interval, the number of particle pairs in this interval was counted. The count result was divided by the total number of particle pairs and the volume of the distance interval to obtain the value of the radial distribution function g(r). The RDF curve with the horizontal axis being the distance and the vertical axis being the g(r) was obtained.

[0022] 34) The close-packed hexagonal phase structure of Ti was exported from the Material Studio software structure library as a .cif file format, then converted to POSCAR format using VESTA software. The structure was then optimized with high precision using VASP software to obtain the equilibrium lattice constant.

[0023] 35) Based on the deformation matrices of different crystal systems, quasi-continuous strain was applied to the corresponding directions of the crystal structure after high-precision optimization. Single-point calculations were performed on the structure under different strains using VASP and LAMMPS, respectively. Nonlinear curve fitting was performed based on the relationship between strain and energy to obtain the crystal elastic constants, which were then substituted into the bulk modulus calculation formula to obtain the bulk modulus B.

[0024] For example, the deformation matrix of the hexagonal crystal system is:

[0025]

[0026] Its crystal elastic constant is C 11 、C 12 、C 13 、C 33 and C 44 , the calculation formula of its bulk modulus B is:

[0027]

[0028] 36) The structure after high-precision optimization in step 34) is expanded by VESTA software to obtain a supercell. On the basis of the supercell, a single vacancy, a single tetrahedral interstitial H atom, and a single octahedral interstitial H atom structure are established. Then, considering various permutations and combinations, a double vacancy, a double tetrahedral interstitial H atom, and a double octahedral interstitial H atom structure are constructed. The distances between point defects are sorted to obtain the first neighbor, second neighbor, and third neighbor configurations of the double vacancy, double tetrahedral interstitial H atom, and double octahedral interstitial H atom. VASP and LAMMPS are used to perform single-point calculations on the first to third neighbor supercell structures of perfect crystals, single defects, and double defects, respectively. The energy of the unit cell Ti and H2 molecules is calculated separately, and the energy is divided by the number of atoms to obtain the chemical potential of Ti and H2; according to the defect formation energy calculation formula E f =E d -E p ±nμ, where E d is the total energy of the defective system, E p is the total energy of the perfect crystal, μ is the chemical potential of the missing atom, and n is the number of defect atoms. The first to third neighbor structure formation energies of single defects and double defects are obtained and compared with the results calculated by VASP and LAMMPS.

[0029] Step 4: For data with large errors between the ANN potential model and the DFT results (i.e., VASP calculation results) in the model test and performance test results, targeted improvements are made by increasing the relevant configuration weights until an ANN potential model that meets the accuracy is obtained. The specific method is:

[0030] 41) Set the error limit of VASP and ANN calculation results to δ = |E DFT -E ANN |≤30meV, for data exceeding the error limit, extract and check the configuration, perform optimization or constant temperature and constant volume AIMD and ANN-md simulations, and extract the optimization or simulation trajectory into the data set; for performance with large errors in performance testing, perform targeted constant temperature and constant volume AIMD and ANN-md simulations, and extract the simulation trajectory into the data set;

[0031] 42) Repeat steps 2, 3, and 41) and continue iterating until the error is reduced to an acceptable range, thereby obtaining an ANN potential model that meets the accuracy requirements.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The machine learning potential model trained by the present invention can very accurately describe the high-dimensional interatomic interaction potential energy surface of the TiH binary system with a calculation accuracy close to that of DFT based on reference data of electronic structure calculations;

[0034] 2. Molecular dynamics simulations based on ANN potential models are very efficient, many orders of magnitude faster than DFT calculations and comparable to traditional empirical potentials, which enables them to simulate larger time and space scales;

[0035] 3. The nonlinear functional form of the ANN potential is very general and flexible and does not require any prior knowledge of the physical functional form of atomic interactions in the TiH system;

[0036] 4. The ANN potential model of the present invention provides a simulation tool for the TiH binary system that takes both accuracy and scale into consideration. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of common crystal structures and titanium hydrides of Ti in the present invention, (a) HCP phase structure of Ti, (b) BC C phase structure of Ti, (c) FCC structure of Ti, (d) SC structure of Ti, (e) Diamand structure of Ti, (f) A12 structure of Ti, (g) A13 structure of Ti, (h) A15 structure of Ti, (i) TiH2, (j) TiH, (k) Ti2H;

[0038] Figure 2 This is a graph showing the fitting results of the ANN model of the present invention to the DFT data in the reference data set;

[0039] Figure 3 This is a comparison diagram of the ANN model and DFT calculation of the dimer curve of the present invention;

[0040] Figure 4 : This is a comparison diagram of the EV curve of the present invention using the ANN model and DFT calculation, (a) is the EV curve of a common crystal configuration of Ti, and (b) is the EV curve of a common titanium hydride;

[0041] Figure 5 This is a comparison diagram of the ANN model and DFT calculation of the radial distribution function of the present invention;

[0042] Figure 6 It is a schematic diagram of the iterative convergence of the loss function in the ANN model training process of the present invention;

[0043] Figure 7 This is a schematic diagram of the complete data set of the present invention, with a total of 35,081 structures. DETAILED DESCRIPTION

[0044] To more clearly illustrate the technical solution of the present invention, a preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings. The described embodiment is only one of the preferred embodiments of the present invention, and is not intended to be a complete list of embodiments. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0045] Example 1

[0046] Step 1: Use the first-principles software VASP to construct a basic reference electronic structure dataset including dimer structures, stable crystal configurations of Ti and common TiH compounds, random structures, and AIMD trajectory extracted structures. The specific method is as follows:

[0047] 11) Dimer structure: Create a VASP structure file in POSCAR format The supercell fixes the position of an atom and steps in a certain direction (such as ) and move another atom until the entire dimer curve potential well is covered, resulting in a total of 121 dimer structures.

[0048] 12) Stable crystal structures of Ti and common TiH compounds: Based on the VASP structure file POSCAR format, the HCP, BCC, FCC, Diamond, SC, A12, A13, A15 structures of Ti and the initial structures of Ti2H, TiH, TiH2 are constructed. The stable crystal structures of some Ti and common TiH compounds are as follows: Figure 1 As shown; VASP is used for high-precision structural optimization; on this basis, multiple strains are applied to the corresponding directions of the crystal according to the deformation matrix of different crystal systems to form a large number of perturbation configurations of the stable structure of the crystal system.

[0049] 13) Random structures: The ab initio random structure search program AIRSS was used to search for various possible symmetries and arrangements of TiH with composition ratios of 32:0, 32:1, 16:1, 8:1, 4:1, 2:1, 1:1, and 1:2, generating a large number of random structures. VASP was used to perform coarse-precision optimization on these random structures, and one structure was extracted every 20 steps from the latter part of the optimization trajectory.

[0050] 14) AIMD trajectory extraction structure: for H2 at 0-1GPa and 1-2GPa at 200K, 300K, and 500K, HCP phase of Ti, TiH, TiH2 and other perfect crystals at 300K, 600K, 900K, 1200K, 1500K, 1800K, 2100K, and 2400K, c H= 0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40% of Ti HCP phase, constant temperature and constant volume AIMD simulation was performed, and a structure was extracted every 20 steps from the MD simulation trajectory.

[0051] Step 2: Use the AENET software package to train and test the ANN potential (artificial neural network potential) model on the basic reference electronic structure dataset. The specific method is as follows:

[0052] 21) Use the generate.x tool in the AENET software package to compile the reference electronic structure dataset into a collection in a specific format.

[0053] 22) After debugging the model parameters, set the cutoff radius to The shortest distance between atoms is The descriptor basis function expansion orders are n=5 and l=6, the neural network has two hidden layers: 40×20, the learning rate is 0.001, the number of iterations is set to 20,000, and the test set ratio is 10%; the data set is divided into training set and test set using the train.x tool, and the ANN potential model is trained on the training set.

[0054] 23) Use predict.x to test the ANN potential model. The ANN prediction of the structure formation energy in the entire data set is compared with the DFT results. Figure 2 As shown in Figure 2, the closer the data points are to the y=x line, the more accurate the ANN's prediction of the data is; the more data points are close to the y=x line, the better the ANN fits the configuration space of the reference data set.

[0055] Step 3: Use VASP and the trained ANN potential model to calculate and compare the dimer curve, EV curve, RDF curve, equilibrium lattice constant, elastic modulus, and defect formation energy as a performance test. The specific method is as follows:

[0056] 31) For the dimer structure with different distances between two atoms, VASP and trained ANN potential were used to perform single-point calculations, extract energy-distance information, and obtain dimer curves with the horizontal axis of VASP and ANN as the distance between the two atoms and the vertical axis as the total energy of the system. The results are as follows Figure 3 As shown in Figure 3, the ANN calculation curve basically coincides with the DFT calculation curve, indicating that ANN has DFT accuracy on the Dimer curve.

[0057] 32) The volume expansion and compression of the stable crystal configuration of Ti and common TiH compounds were carried out. The VASP and ANN potential were used to perform single-point calculations on structures with different volumes. The volume of each atom was calculated as As the horizontal axis, the energy volume curve-EV curve is obtained, and the results are as follows Figure 4 As shown in Figure 3, the ANN calculation curve basically coincides with the DFT calculation curve, indicating that ANN has DFT accuracy on the EV curve.

[0058] 33) The constant temperature and constant volume AIMD and ANN-MD simulations were performed on the body-centered cubic Ti supercell. The supercell was heated from room temperature to 2500K to melt the structure. The last frame structure was used as the initial structure and constant temperature simulation was performed at 2500K. According to the atomic position information in the XDATCAR (AIMD) and dump (ANN-MD) files, g(r) was solved and the RDF curve with the horizontal axis as the distance and the vertical axis as the radial distribution function was obtained. The results are shown in Figure 3. Figure 5 As shown in the figure, the ANN basically reproduces the radial distribution function curve of Ti obtained by DFT calculation. The position, peak width and height of the second and third nearest neighbor peaks of each peak are well predicted, indicating that the ANN has DFT accuracy in the radial distribution function.

[0059] 34) The HCP phase structure of Ti was exported from the Material Studio software structure library as a .cif file. This structure was then converted to POSCAR format using VESTA software. High-precision structural optimization was performed using VASP software to determine the equilibrium lattice constants and c / a ratios for the HCP phase of Ti. The results, shown in Table 1, show that the ANN-predicted lattice constants and c / a ratios are very close to those obtained using DFT, with the c / a ratio being consistent with the experimental value.

[0060] 35) According to the deformation matrix of the hexagonal crystal system, quasi-continuous strain is applied to the corresponding directions of the crystal structure after high-precision optimization. Single-point calculations are performed on the structure under different strains using VASP and LAMMPS respectively. Nonlinear curve fitting is performed based on the relationship between strain and energy to obtain the crystal elastic constant C. 11 、C 12 、C 13 、C 33 and C 44 , the bulk modulus B is obtained according to the bulk modulus calculation formula. The results are shown in Table 1, C 13 、C 44 The difference between the experimental value and the DFT calculation result is less than 10 GPa, C 11 、C 12 、C 33 、C 66 The difference is less than 15 GPa, and B is less than 2 GPa. The overall prediction results are close to the experimental values ​​and DFT results.

[0061] 36) The high-precision optimized structure in 34) was expanded using VESTA software to obtain a supercell. Based on the supercell, the first-nearest-neighbor, second-nearest-neighbor, and third-nearest-neighbor configurations of a single vacancy, a single tetrahedral interstitial H atom, a single octahedral interstitial H atom, a divacancy, a double tetrahedral interstitial H atom, and a double octahedral interstitial H atom were established. Single-point calculations were performed on the first- to third-nearest-neighbor supercell structures of the perfect crystal, single defect, and double defect using VASP and LAM MPS, respectively. The first- to third-nearest-neighbor formation energies of the single and double defects were obtained using the formation energy calculation formula. The results are shown in Table 2. The ANN-predicted formation energy of the single vacancy is close to the DFT result; the ANN-predicted formation energy of the single OIS-H is generally consistent with the DFT calculation result; the lower OIS formation energy than the TIS interstitial formation energy is consistent with the DFT and theoretical results; the ANN-predicted values ​​of the divacancy, double TIS-H, and double OIS-H are generally consistent with the DFT calculation result.

[0062] Step 4: For data with large errors between the ANN potential model and the DFT results in the model test and performance test results, targeted improvements are made by increasing the relevant configuration weights until an ANN potential model that meets the accuracy is obtained. The specific method is:

[0063] 41) For data exceeding the error limit, extract and check the configuration, perform optimization or constant temperature and constant volume AIMD and ANN-MD simulations, and extract the optimization or simulation trajectory into the data set; for performance with large errors in performance testing, perform targeted constant temperature and constant volume AIMD and ANN-MD simulations, and extract the simulation trajectory into the data set.

[0064] 42) Repeat steps 2, 3, and 41) and iterate until the error is reduced to an acceptable range. The MAE and RMSE of the final ANN model in the training set and test set are: train-MAE = 0.00361 eV / atom, trian-RMSE = 0.00582 eV / atom, test-MAE = 0.00416 eV / atom, test-RMSE = 0.00824 eV / atom, all converging to below 10 meV. Figure 6 As shown, the model is considered to have DFT accuracy at this time, and the complete data set is as follows Figure 7 shown.

[0065] Table 1: Comparison of lattice constant, c / a, elastic modulus, and bulk modulus of Ti HCP phase using ANN, experimental, and DFT calculations

[0066]

[0067] Note: ANN, Exp, and DFT represent ANN potential model calculation results, experimental values, and VASP calculation results, respectively. DFT (This work) refers to the DFT calculation results in this paper. DFT without (This work) refers to the DFT calculation results of others in the reference literature.

[0068] References:

[0069] [1]Barrett C,Massalski T.Structure of Metals,CrystallographicMethods,Principles and Data[J].Pergamon Press,1966.

[0070] [2]E,S,Fisher,et al.Single-Crystal Elastic Moduli and the hcp→bccTransformation in Ti,Zr,and Hf[J].Physical Review,1964.DOI:10.1103 / physrev.135.a482.

[0071] [3]Gibson JS, Srinivasan SG, Baskes MI, et al.A multi-state modifiedembedded atom potential method for titanium[J].ModellingSimul.mater.sci.eng,2017,25(1):015010.DOI:10.1088 / 1361-651X / 25 / 1 / 015010.

[0072] Table 2: Comparison of ANN and DFT calculation results of vacancy and interstitial H atom defect formation energy in the HCP phase of Ti of the present invention

[0073]

[0074] Note: TIS-H represents hydrogen atoms in tetrahedral interstitial space; OIS-H represents hydrogen atoms in octahedral interstitial space; V represents vacancy defect; 1NN represents first nearest neighbor. f TIS-H,1NN For example, it represents the defect formation energy of two hydrogen atoms in the tetrahedral gap of the Ti-HCP phase that are first-nearest neighbors in distance.

[0075] The above description is merely an exemplary embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A method for constructing a machine learning potential for a TiH binary system, characterized in that: Follow these steps: Step 1: Use the first-principles software VASP to construct a basic reference electronic structure dataset including dimer structures, stable crystal configurations of Ti and common TiH compounds, random structures, and AIMD trajectory extracted structures. The method is as follows: 11) Dimer structure: Create a supercell according to the VASP structure file POSCAR format, fix the position of one atom, and move another atom in one direction until the entire dimer curve potential well is covered; 12) Stable crystal structures of Ti and common TiH compounds: Construct HCP, BCC, FCC, Diamond, SC, A12, A13, A15 structures of Ti and initial structures of Ti2H, TiH, and TiH2 according to the VASP structure file POSCAR format; Use VASP for high-precision structural optimization; on this basis, according to the deformation matrix of different crystal systems, multiple strains are applied to the corresponding directions of the crystal to form a large number of perturbation configurations of the stable structure of the crystal system; 13) Random structures: The ab initio random structure search program AIRSS was used to search for various possible symmetries and arrangements under different TiH composition ratios, generating a large number of random structures. These random structures were then subjected to coarse-grained optimization using VASP, and structures were extracted from the optimization trajectory at regular intervals. 14) AIMD trajectory structure extraction: Constant temperature and constant volume AIMD simulations are performed for H2 at different temperatures and pressures, Ti, TiH, and TiH2 perfect crystals at different temperatures and compositions, and different types of defect structures. A structure is extracted from the MD simulation trajectory at a certain number of steps. Step 2: Using the AENET software package to train and test the ANN potential model on the basic reference electronic structure data set; Step 3: Use VASP and the trained ANN potential model to calculate and compare the dimer curve, EV curve, RDF curve, equilibrium lattice constant, elastic modulus, and defect formation energy as a performance test; Step 4: For data with large errors between the ANN potential model and the DFT results in the model test and performance test results, targeted improvements are made by increasing the relevant configuration weights until an ANN potential model that meets the accuracy is obtained.

2. The method for constructing the TiH binary system machine learning potential according to claim 1, characterized in that: In step 2, the method for training and testing the ANN potential model using the AENET software package is as follows: 21) Use the generate.x tool in the AENET software package to compile the structures and energies in the reference electronic structure dataset into a set in a specific format; 22) Debug model parameters, including cutoff radius, minimum interatomic distance, descriptor basis function expansion order, neural network size, and learning rate, and set the number of iterations and test set weights. Use the train.x tool to split the dataset into training and test sets, and train the ANN potential model on the training set. 23) Use predict.x to test the ANN potential model based on reference electronic structure data and ANN potential prediction results The mean absolute error (MAE) and the root mean square error (RMSE) between , ,When the RMSE and MAE of the ANN in both the training and test sets converge to below 10 meV, the model is considered to have DFT accuracy.

3. The method for constructing the TiH binary system machine learning potential according to claim 1, characterized in that: In step 3, the method for comparing the calculation results of VASP and ANN potential as a performance test is as follows: 31) For structures with different distances between two atoms, single-point calculations were performed using VASP and ANN potentials, respectively, to extract energy-distance information. Dimer curves were obtained, with the horizontal axis of VASP and ANN being the distance between the two atoms and the vertical axis being the total energy of the system. 32) The stable crystal configuration of Ti and common TiH compounds was optimized. The volume of the optimized structure was expanded and compressed by changing the normalization coefficient in POSCAR with a continuous fixed step size. Single-point calculations were performed using VASP and ANN potential for structures with different volumes. The volume of each atom, i.e., Å, was used. 3 / atom as the horizontal axis, and the energy volume curve, that is, the EV curve, is obtained; 33) Perform constant temperature and constant volume AIMD and ANN-MD simulations on the body-centered cubic Ti supercell, respectively. The supercell is heated from room temperature to a temperature above the melting point of Ti to melt the structure. The last frame structure is used as the initial structure and a constant temperature simulation is performed at this temperature. The distance between each particle in the system and other particles is calculated based on the atomic position information in the trajectory file XDATCAR generated by AIMD and the trajectory file dump generated by ANN-MD. A suitable distance range and step size are selected. For each distance interval, the number of particle pairs in this interval is counted. The count result is divided by the total number of particle pairs and the volume of the distance interval to obtain the value of the radial distribution function g(r). The RDF curve with the horizontal axis as distance and the vertical axis as g(r) is obtained; 34) Export the close-packed hexagonal phase structure of Ti from the Material Studio software structure library as a .cif file format, then convert it to POSCAR format using VESTA software. Use VASP software to perform high-precision structural optimization on the structure to obtain the equilibrium lattice constant; 35) Based on the deformation matrices of different crystal systems, quasi-continuous strain was applied to the corresponding directions of the crystal structure after high-precision optimization. Single-point calculations were performed on the structure under different strains using VASP and LAMMPS, respectively. Nonlinear curve fitting was performed based on the relationship between strain and energy to obtain the crystal elastic constants, which were then substituted into the bulk modulus calculation formula to obtain the bulk modulus. 36) The structure after high-precision optimization in step 34) is expanded using VESTA software to obtain a supercell. Based on the supercell, single vacancy, single tetrahedral interstitial H atom, and single octahedral interstitial H atom structures are established. Then, considering various permutations and combinations, divacancy, ditetrahedral interstitial H atom, and dioctahedral interstitial H atom structures are constructed. The distances between point defects are sorted to obtain the first-nearest neighbor, second-nearest neighbor, and third-nearest neighbor configurations of divacancy, ditetrahedral interstitial H atom, and dioctahedral interstitial H atom. Single-point calculations are performed on the first to third-nearest neighbor supercell structures of perfect crystals, single defects, and double defects using VASP and LAMMPS, respectively. The energies of the unit cell Ti and H2 molecules are calculated respectively, and the chemical potentials of Ti and H2 are obtained by dividing the energies by the number of atoms. The defect formation energy is calculated according to the formula ,in is the total energy of the defective system, The total energy of a perfect crystal, Where is the chemical potential of the defect atom and n is the number of defect atoms. The first to third neighbor structure formation energies of single defects and double defects are obtained and compared with the results calculated by VASP and LAMMPS.

4. The method for constructing the TiH binary system machine learning potential according to claim 1, characterized in that: In step 4, the method for targeted improvement of the data with large errors between the ANN potential model and the DFT results in the model test and performance test results is as follows: 41) For data with RMSE > 30 meV in model testing, extract and view the configuration, perform optimization or constant temperature and constant volume AIMD and ANN-MD simulations, and extract the optimization or simulation trajectory into the data set; For performance with large errors in performance testing, conduct targeted constant temperature and constant volume AIMD and ANN-MD simulations, and extract the simulation trajectories into the data set; 42) Repeat steps 2, 3, and 41) until the error is reduced to an acceptable range, and an ANN potential model that meets the accuracy requirements is obtained.

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