Fe-Mn-C alloy interstitial atom potential function construction method based on first principle and machine learning

Abstract

The invention discloses a Fe-Mn-C alloy interstitial atom potential function construction method based on a first principle and machine learning, and belongs to the technical field of material science and computational simulation. The construction method comprises the following steps: firstly, constructing a Fe-Mn-C alloy interstitial element atomic structure model, carrying out structure optimization on the interstitial element atomic structure model by utilizing a first principle, then carrying out first principle molecular dynamics (AIMD) multi-temperature sampling on the model after the structure optimization, and dividing a training set and a verification set; and finally, machine learning is conducted, and the Fe-Mn-C alloy gap potential function is output. According to the construction method, unification of high precision and high efficiency of the potential function is achieved, and the obtained Fe-Mn-C alloy gap potential function can be applied to research of a face-centered cubic (FCC) Fe-Mn-C alloy.

Description

Technical Field

[0001] This invention relates to the fields of materials science and computational simulation technology, specifically to a method for constructing interstitial atomic potential functions of Fe-Mn-C alloys based on first-principles calculations and machine learning. Background Technology

[0002] Fe-Mn-C alloys, as an important system in steel materials, are widely used in structural materials such as high-manganese steel, wear-resistant steel, and advanced high-strength steel due to their excellent strength, wear resistance, and good plasticity. In this type of alloy, manganese (Mn) exists mainly in the α-Fe or γ-Fe lattice through substitutional solid solution, while carbon (C), as a typical interstitial element, usually occupies tetrahedral or octahedral interstitial positions in the lattice, thus significantly affecting the material's mechanical properties, thermal expansion, phase transformation behavior, and diffusion kinetics.

[0003] The presence of interstitial carbon atoms in Fe-Mn-C alloys induces localized lattice distortion and stress field changes, leading to a series of microscopic mechanisms such as dislocation dragging, solid solution strengthening, and altered diffusion activation energy. Therefore, accurately characterizing the potential energy surface distribution of interstitial carbon atoms at different sites and temperatures is of fundamental scientific significance and engineering guiding value for understanding the mechanical response, phase transition mechanism, and diffusion behavior of this system.

[0004] Traditional empirical interatomic potentials, such as the embedded atom method (EAM), the modified embedded atom method (MEAM), and the bond order potential (BOP), rely on predefined functional forms and finite parameter sets to describe inter-element interactions. While these methods offer advantages in computational speed, they often struggle to accurately characterize complex local environmental changes, especially when dealing with substitutional and interstitial elements, particularly over large temperature spans. For instance, in Fe-Mn-C alloys, the potential energy surfaces of carbon atoms at different interstitial sites differ significantly, and the atomic thermal vibration modes and diffusion paths differ markedly between low and high temperatures, making it difficult for empirical potentials to account for these nonlinear characteristics.

[0005] First-principles calculations, especially those based on density functional theory (DFT), can self-consistently solve for electronic structures and accurately obtain interatomic interactions without relying on empirical parameters. These methods offer high accuracy in predicting lattice constants, elastic constants, bond energies, and diffusion barriers. However, the computational cost of DFT calculations increases rapidly with the number of atoms in the system, and it struggles to support long-term and large-scale atomic dynamics simulations, failing to meet the simulation requirements spanning multiple scales from nanometers to micrometers.

[0006] In recent years, machine learning of interatomic potentials has gradually become an important tool for bridging high precision and high efficiency. This type of method utilizes high-precision first-principles data as a training set, and directly fits the potential energy surface to the data-driven model through deep neural networks, Gaussian processes, kernel regression, etc., without pre-setting the function form. It can significantly improve computational efficiency while maintaining near-first-principles accuracy. Typical frameworks such as Deep Potential (DP) and Gaussian Approximation Potential (GAP) have achieved good results in polycrystalline metals, semiconductors, oxides, and liquid systems.

[0007] However, existing research on machine learning-based potentials mostly focuses on single-phase, single-type defect metal systems. For Fe-Mn-C ternary systems involving multiple interactions of interstitial and substitutional atoms, especially studies distinguishing between tetrahedral and octahedral interstitial sites of carbon atoms in potential energy surface fitting over a wide temperature range, there is still a lack of research. Existing methods have the following shortcomings in data acquisition strategies, temperature coverage, interstitial type labeling, and dynamic sampling: the temperature distribution of training data is narrow, usually concentrated around room temperature, leading to decreased prediction accuracy of the potential function in extremely low or high temperature diffusion ranges; the carbon atom interstitial site categories are not distinguished, and direct mixed training causes potential energy surface smoothing distortion, making it difficult to reflect the true local energy valley structure; and the lack of an iterative data supplementation mechanism results in insufficient accuracy of the potential function in rare, unsampled configuration regions.

[0008] Therefore, there is an urgent need for a method that combines the accuracy of first-principles calculations with the efficiency of machine learning modeling to perform high-precision fitting of the potential energy surface of different interstitial sites of carbon atoms in Fe-Mn-C alloys across the entire temperature range. This method would not only ensure the accuracy of the description of microscopic defects and diffusion behavior, but also be able to run efficiently in large-scale simulations such as molecular dynamics, thereby providing a reliable atomic-scale calculation tool for material design, service performance prediction, and process optimization. Summary of the Invention

[0009] To overcome the problems of insufficient differentiation between different interstitial types, narrow temperature coverage, and lack of iterative sampling mechanism in the existing Fe-Mn-C alloy potential function, the present invention aims to provide a method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning. By simultaneously collecting high-precision first-principles data of two types of interstitial sites, tetrahedral and octahedral, and performing systematic sampling across the entire temperature range, and combining a deep neural network architecture to construct an interatomic interaction model, the method achieves a balance between high precision and high efficiency in the potential function, and is particularly suitable for complex multi-element metal systems with interstitial defects.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning is disclosed. This method first constructs an atomic structure model of interstitial elements in the Fe-Mn-C alloy, optimizes the model using first-principles calculations, then performs first-principles molecular dynamics (AIMD) multi-temperature sampling on the optimized model and divides it into training and validation sets. Finally, machine learning is used to output the interstitial potential function of the Fe-Mn-C alloy. The method specifically includes the following steps: (1) A certain proportion of Mn atoms are introduced into the face-centered cubic Fe lattice to form an initial model of Fe-Mn solid solution. The supercell size of the model is not less than 3×3×3, so as to reduce the interference of periodic boundary conditions on interstitial interactions. (2) In the initial model of Fe-Mn solid solution, C atoms are placed in tetrahedral interstitial or octahedral interstitial positions to generate a structural model containing interstitial C atoms (tetrahedral interstitial structural model or octahedral interstitial structural model). (3) The structural optimization of two structural models containing interstitial C atoms was carried out using the VASP first-principles calculation software to obtain the equilibrium lattice constant; (4) Perform AIMD multi-temperature sampling on the optimized structure model containing interstitial C atoms obtained after step (3) and output the training set and validation set; perform machine learning and output the interstitial potential function of the Fe-Mn-C alloy.

[0011] Further, in step (3), the process of optimizing the structure model containing interstitial atoms C is as follows: the plane wave pseudopotential method based on density functional theory (DFT) is used to perform structural relaxation on the structure model containing interstitial atoms C, and the optimized lattice constant (i.e., equilibrium lattice constant), atomic coordinates and total energy are output, thus obtaining the optimized structure model.

[0012] Furthermore, in step (3), during the structural relaxation process, the convergence accuracy parameters are: ENCUT=520 eV, EDIFF=1×10 -5 eV, EDIFFG=-0.02 eV / Å, ISMEAR=0, SIGMA=0.05.

[0013] Furthermore, in step (4), the AIMD multi-temperature sampling and machine learning process includes the following steps (A)-(D): (A) Using the optimized structural model containing interstitial atoms C obtained in step (3) as the initial configuration, de novo molecular dynamics sampling is performed for each type of interstitial site in the temperature range of 4 K to 1400 K, with each temperature range not exceeding 200 K, a time step of 1 fs, and a running time of not less than 10 ps for each temperature range. (B) Divide the training set and validation set proportionally (e.g., 8:2) to ensure that the validation set is independent of the training process; both the training set and the validation set contain energy, force, and stress. (C) Use Deep Potential (DP) and control the training process by setting parameters in xxx.json to obtain the potential function after training; (D) Validate and iteratively optimize the model trained in step (C) until the obtained root mean square error is within the threshold range. The optimized potential function has stable convergence within the threshold range, and the converged potential function is output.

[0014] Further, in step (A), the NPT ensemble (constant number of atoms, pressure, and temperature) is used, and the isothermal algorithm is Nose-Hoover (MDALGO=3) to collect energy, force, and stress information of the low-temperature elastic state, the intermediate-temperature thermal vibration dynamics, and the high-temperature diffusion state.

[0015] Furthermore, in step (A), throughout the sampling process, it is ensured that the near-ground state configuration under low temperature conditions, the thermal vibration configuration under intermediate temperature conditions, and the configuration with significant diffusion at high temperature are covered.

[0016] Furthermore, in step (A), the AIMD output trajectory is denoised and outlier removed, and layered sampling is performed based on energy range, force magnitude and local geometric parameters.

[0017] Further, in step (C), the specific process of controlling the training process by setting parameters in xxx.json includes: in the "descriptor" settings, "type" is set to "se_e2_a" to determine the descriptor type; "rcut" is set to 6.0 Å to balance accuracy and efficiency, and "rcut_smth" is set to 0.5 Å; the "sel" parameter is set to "auto" to automatically select the upper limit of the number of atoms within the cutoff radius; "neuron" is set to [25,50,100], and "resnet_dt": true is enabled; in "fitting_net", it is set to a three-layer network [240,240,240]; the "learning_rate" part is set to "type": "exp", "start_lr": 0.001, "decay_steps": 5000, "decay_rate": 0.95, "stop_lr": 1e-8; "loss"... The initial force term weight was set to 1000, and the energy term weight was set to 0.01. Later, the force and energy weight ratio was gradually adjusted to 1:1.

[0018] Further, in step (D), the potential function trained in step (C) is compared with the corresponding DFT validation set data to obtain the root mean square error; the root mean square error within the threshold range means that the energy error between the training set and the validation set is less than 3 meV / atom, and the force error between the training set and the validation set is less than 0.05 eV / Å.

[0019] Furthermore, in step (D), if the root mean square error obtained after training in step (C) is within the threshold range, no optimization is needed, and the potential function is directly output; if the root mean square error obtained after training in step (C) is not within the threshold range, iterative optimization is required, and the iterative optimization process is carried out according to the following steps (a)-(c): (a) The root mean square error exceeds the threshold range. Analyze the characteristics of the high error configuration (such as temperature range, gap type, local distortion mode, etc.). (b) Specifically, supplement the data by adding AIMD simulations near the high-error configuration, add it to the training set, keep the validation set unchanged, and retrain the potential function; (c) Repeat the “sampling, training, verification” cycle according to steps (A)-(D) until the trained potential function is stable and converges within the threshold range; and derive the converged potential function.

[0020] Furthermore, in step (D), the converged potential function is exported as a calling file adapted to the LAMMPS molecular dynamics platform, while retaining the original TensorFlow / PyTorch format for transfer learning.

[0021] Furthermore, the interstitial potential function of the Fe-Mn-C alloy is applied to the study of face-centered cubic (FCC) Fe-Mn-C alloys, specifically: the diffusion mechanism and energy barrier of C atoms in the interstitial sites of FCC octahedrons and tetrahedrons; the effect of Mn content on the lattice stability and thermal expansion of FCC; and the atomic-scale mechanism of high-temperature phase transformation and dynamic recrystallization processes.

[0022] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: 1. This invention provides independent modeling for the octahedral and tetrahedral gap characteristics of FCC-Fe, ensuring accurate response of the potential energy surface to the local structure. 2. In the process of constructing interstitial atomic potentials in alloys, this invention shares the same training framework from low temperature to near melting point, ensuring the continuity and physical rationality of predictions at different temperatures.

[0023] 3. The construction method of this invention provides a reliable tool for further research on the mechanism of action of Fe-Mn-C in material design and performance improvement.

[0024] 4. The construction method of this invention achieves accuracy close to that of DFT, improves computational efficiency by 2 to 3 orders of magnitude, and can support simulations at the scale of millions of atoms and nanoseconds. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the method for constructing the interatomic potential function of interstitial elements in the Fe-Mn-C alloy according to the present invention.

[0026] Figure 2 This invention utilizes VESTA to construct an atomic model of interstitial elements in Fe-Mn-C alloys.

[0027] Figure 3 This is a truncated portion of the potential function fitted using the method of this invention. Detailed Implementation

[0028] The following description, in conjunction with the accompanying drawings and embodiments, further illustrates the method for constructing the interstitial element potential function of face-centered cubic (FCC) Fe-Mn-C alloy based on first principles and machine learning proposed in this invention. However, those skilled in the art should understand that these embodiments are only used to illustrate the invention and not to limit the scope of protection of the invention.

[0029] The following examples 1-7 illustrate the process of constructing the interstitial potential function of the Fe-Mn-C alloy. Figure 1 As shown. Example 1:

[0030] This embodiment describes the construction of an interstitial element atomic structure model for a Fe-Mn-C alloy. The specific process is as follows: (1) Using face-centered cubic Fe lattice as the initial structure, a supercell with a size not less than 3×3×3 of the original unit cell is constructed by unit cell replication. Under periodic boundary conditions, the initial number of atoms is 108 to reduce the interference of boundary effects on the interaction of interstitial atoms.

[0031] (2) Mn atoms are randomly introduced into the substitution sites of Fe lattice, with a substitution concentration range of 2 at.% to 25 at.%, to form an initial model of Fe-Mn solid solution.

[0032] (3) In the initial model of the Fe-Mn solid solution, C atoms are placed in octahedral interstitial sites or tetrahedral interstitial sites to generate a structural model containing interstitial C atoms (tetrahedral interstitial structure model or octahedral interstitial structure model); wherein: the atomic ratio of C atoms is controlled within the range of 0.5 at.% to 10 at.%.

[0033] (4) To simulate the thermal perturbation effect of the actual lattice, random three-dimensional perturbations of 0.01 Å to 0.1 Å are applied to the initial positions of interstitial atoms to ensure that the training data contains diverse local atomic environments.

[0034] The interstitial element atomic model of the Fe-Mn-C alloy constructed in this embodiment is as follows: Figure 2 As shown. Example 2:

[0035] This embodiment describes the structural optimization of a structural model containing interstitial C atoms using the VASP first-principles calculation software to obtain the equilibrium lattice constant. The specific process is as follows: (1) The structural relaxation and lattice constant optimization of the C-containing interstitial atom structure model described in Example 1 were performed using the plane wave pseudopotential method based on density functional theory (DFT). The equilibrium configuration (i.e., equilibrium lattice constant), atomic coordinates, and total energy were obtained with energy convergence and torque satisfying the set threshold. Among them, VASP was selected as the calculation software. In specific implementation, the convergence accuracy calculation parameters were set as follows: plane wave energy cutoff (ENCUT): 520 Ev; energy convergence threshold (EDIFF): 1×10 -5 eV; Force convergence threshold (EDIFFG): -0.02 eV / Å; Electron filling mode ISMEAR: 0; SIGMA=0.05; Spin polarization is enabled to account for the magnetic contribution of Mn atoms; The output equilibrium configuration includes atomic coordinates, lattice constant (i.e., equilibrium lattice constant) and total energy, and is used as the initial input for subsequent AIMD sampling. Example 3:

[0036] This embodiment involves performing multi-temperature ab initio molecular dynamics (AIMD) sampling on the optimized structural model (equilibrium configuration) containing interstitial C atoms from Example 2. The specific process is as follows: Starting with the equilibrium configuration of Example 2, AIMD simulations were performed in segments within the temperature range of 4 K to 1400 K to ensure coverage of the low-temperature elastic state, the medium-temperature thermal vibration dynamics, and the high-temperature diffusion state.

[0037] In specific implementation, the sampling control parameters include: time step POTIM is 1 fs; temperature span per segment is ≤200 K; running time per segment is ≥10 ps; the kinetic ensemble uses the NPT ensemble (constant number of atoms, pressure and temperature); and the isothermal algorithm is Nose Hoover (MDALGO=3).

[0038] In practice, during the stabilization phase of each temperature range, information on the atomic coordinates, total energy, atomic forces, and stress tensors of the system is collected, and diverse configurations are ensured to cover potential atomic arrangements and distortion modes. Example 4:

[0039] This embodiment describes the construction and processing of the dataset after sampling in Embodiment 3. The specific steps are as follows: (1) Process the AIMD output trajectory, including outlier removal and noise reduction. The removal criteria include: configurations with physically unreasonable energy jumps, divergent force values, or non-convergent calculations.

[0040] (2) The remaining configurations are stratified and sampled according to indicators such as total energy range, force modulus range and local coordination number to ensure that the samples uniformly cover different physical states.

[0041] In practice, the dataset is divided into a training set and a validation set in an 8:2 ratio to ensure that the validation set is statistically independent of the training set. Before training, all features (including inter-atomic distance, energy, force, etc.) are normalized to improve training stability and convergence speed. Example 5:

[0042] This embodiment involves machine learning and potential function training. The specific steps are as follows: (1) Using the dataset in Example 4, the Deep Potential (DP) framework was used to fit the potential function for deep learning. The parameters were configured as follows: "descriptor" type: se_e2_a; cutoff radius rcut: 6.0 Å, smooth cutoff radius rcut_smth: 0.5 Å; atom selection parameter "sel": auto; local environment network neuron: [25, 50, 100], residual connection enabled (resnet_dt: true); fitting network neuron: [240, 240, 240]; learning rate policy: type=exp, start_lr=0.001, stop_lr=1×10^-8, decay_rate=0.95, decay_steps=5000; loss function weights: initially force term 1000, energy term 0.01, gradually adjusted to force:energy=1:1 in the later stage of training.

[0043] Batch normalization and random sample shuffling are enabled during training to improve the model's generalization performance. Example 6:

[0044] This embodiment focuses on model validation and closed-loop iterative optimization. The specific steps are as follows: (1) Test the potential function trained in Example 5 on the LAMMPS validation set, calculate the root mean square error of energy and force, and compare it with the corresponding first-principles results.

[0045] (2) If the energy error is >3~5 meV / atom or the force error is >0.05 eV / Å, the temperature range and local environment type of the configuration with larger analysis error are analyzed. AIMD data is added near this condition and the model is retrained, while the validation set remains unchanged.

[0046] (3) Repeat the “sampling, training, validation” closed loop until the model converges within the set threshold. Example 7:

[0047] This embodiment demonstrates the derivation and application of the potential function. The specific steps are as follows: (1) Export the converged model from Example 6 as a compatible file for the LAMMPS molecular dynamics platform, while retaining the TensorFlow / PyTorch format for subsequent transfer learning or cross-system optimization. The fitted potential function content is truncated as follows: Figure 3 The energy error between the training and validation sets is less than 3 meV / atom, and the force error between the training and validation sets is less than 0.05 eV / Å, indicating a good fitting effect.

[0048] Compared with empirical potentials, the potential function constructed in this invention improves computational efficiency by 2 to 3 orders of magnitude while maintaining near-DFT accuracy. It can support molecular dynamics simulations at the mega-atomic level and nanosecond to microsecond scales, providing a reliable atomic-scale tool for the design and optimization of Fe-Mn-C materials such as high-manganese steel. Example 8:

[0049] This embodiment simulates the diffusion of C atoms in a Fe-Mn-C alloy lattice. The specific operation steps are as follows: (1) Using the Fe-Mn-C deep learning potential function constructed in Example 6, molecular dynamics diffusion simulations were performed on the Fe-Mn-C alloy system containing 24 at.% Mn and 1 at.% C. (2) The simulation model was a 6×6×6 supercell (864 atoms), with an initial condition of 1000 K, an NVT ensemble, a Nose Hoover thermostat, a time step of 1 fs, and a total simulation time of 2 ns.

[0050] The results show that the migration frequency of C atoms from the octahedral to the tetrahedral sites deviates from the first-principles prediction by less than 3%, and the differences in diffusion coefficients at different temperatures can be distinguished. The diffusion activation energy obtained by fitting the Arrhenius curve differs from the DFT data by less than 0.03 eV. This potential function can accurately reflect the influence of Mn concentration on the C diffusion rate, revealing the trapping effect caused by the Mn-C interaction. Example 9:

[0051] This embodiment describes the prediction of high-temperature phase stability and thermal expansion coefficient. The specific operation steps are as follows: (1) Using the potential function constructed in Example 6, the rate of change of equilibrium lattice constant of the Fe-Mn-C system with 15 at.% Mn and 2 at.% C was calculated in the temperature range of 300 K to 1300 K. NPT ensemble simulation was used, and each temperature point was run for 1 ns. (2) The linear thermal expansion coefficient of the system (11.5 × 10⁻⁶) was calculated. -6 K -1 The fitted value obtained from the first-principles multi-temperature static calculation is 11.3 × 10⁻⁶. -6 K -1 The consistency is good, with a deviation of < 2%.

[0052] In addition, it can accurately capture the structural softening characteristics of FCC lattices near the phase transition temperature, providing basic data for high-temperature service prediction.

[0053] Example 10: This embodiment analyzes the interaction between dislocations and interstitial atoms. The specific steps are as follows: (1) Construct a Fe-Mn-C model containing full dislocations, where each atom accounts for 20 at.% Mn and 2 at.% C. (2) Run a MD simulation at 77 K for 5 ns under the potential function constructed in Example 6, and count the residence time and migration path of incomplete dislocations near C atoms.

[0054] The results show that dislocations exhibit significant delayed migration near the C atom stress field, consistent with the solid solution strengthening mechanism observed in the experiment.

[0055] Example 11: This embodiment focuses on the calculation and optimization of a heat treatment process. The specific operation steps are as follows: (1) Based on the potential function constructed in Example 6, the C diffusion behavior of Fe-Mn-C alloy at different annealing temperatures of 800 K, 900 K and 1000 K was simulated in LAMMPS to compare the potential effects of different process parameters on alloy properties. (2) The simulation time was 5 ns, and the NPT ensemble was used.

[0056] Simulation results show that as the annealing temperature increases from 800 K to 1000 K, the average diffusion rate of C atoms increases by approximately two times. However, under high Mn content conditions, the increase in the diffusion coefficient is relatively small, indicating the hindering effect of Mn. Based on these results, a quantitative reference can be provided for shortening heat treatment time and controlling performance, reducing the trial-and-error costs in actual processes.

Claims

1. A method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning, characterized in that: This method first constructs an atomic structure model of interstitial elements in a Fe-Mn-C alloy, optimizes the model using first-principles calculations, then performs first-principles molecular dynamics (AIMD) multi-temperature sampling on the optimized model and divides it into training and validation sets. Finally, machine learning is used to output the interstitial potential function of the Fe-Mn-C alloy. The method specifically includes the following steps: (1) A certain proportion of Mn atoms are introduced into the face-centered cubic Fe lattice to form an initial model of Fe-Mn solid solution. The supercell size of the model is not less than 3×3×3, so as to reduce the interference of periodic boundary conditions on interstitial interactions. (2) In the initial model of Fe-Mn solid solution, C atoms are placed in tetrahedral or octahedral interstitial positions to generate a structural model containing interstitial C atoms (tetrahedral interstitial structure model or octahedral interstitial structure model). (3) The structural model containing interstitial C atoms was optimized using the VASP first-principles calculation software to obtain the equilibrium lattice constant; (4) Perform AIMD multi-temperature sampling on the optimized structure model containing interstitial C atoms obtained after step (3) and output the training set and validation set; perform machine learning and output the interstitial potential function of the Fe-Mn-C alloy.

2. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 1, characterized in that: In step (3), the process of optimizing the structure model containing interstitial atoms C is as follows: the plane wave pseudopotential method based on density functional theory (DFT) is used to relax the structure model containing interstitial atoms C, and the optimized lattice constant (i.e. equilibrium lattice constant), atomic coordinates and total energy are output, thus obtaining the optimized structure model.

3. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 2, characterized in that: In step (3), during the structural relaxation process, the convergence accuracy parameters are: ENCUT=520 eV, EDIFF=1×10 -5 eV, EDIFFG=-0.02 eV / Å, ISMEAR=0, SIGMA=0.

05.

4. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 1, characterized in that: In step (4), the AIMD multi-temperature sampling and machine learning process includes the following steps (A)-(D): (A) Using the optimized structural model containing interstitial atoms C obtained in step (3) as the initial configuration, de novo molecular dynamics sampling is performed for each type of interstitial site in the temperature range of 4 K to 1400 K, with each temperature range not exceeding 200 K, a time step of 1 fs, and a running time of not less than 10 ps for each temperature range. (B) Divide the training set and validation set proportionally (e.g., 8:2) to ensure that the validation set is independent of the training process; both the training set and the validation set contain energy, force, and stress. (C) Use Deep Potential (DP) and control the training process by setting parameters in xxx.json to obtain the potential function after training; (D) Validate and iteratively optimize the model trained in step (C) until the obtained root mean square error is within the threshold range. The optimized potential function has stable convergence within the threshold range, and the converged potential function is output.

5. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 4, characterized in that: In step (A), the NPT ensemble (constant atomic number, pressure, and temperature) is used, and the isothermal algorithm is Nose-Hoover (MDALGO=3) to collect energy, force, and stress information of the low-temperature elastic state, the intermediate-temperature thermal vibration dynamics, and the high-temperature diffusion state.

6. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 4, characterized in that: In step (C), the specific process of controlling the training process by setting parameters in xxx.json includes: in the "descriptor" settings, "type" is set to "se_e2_a" to determine the descriptor type; "rcut" is set to 6.0 Å to balance accuracy and efficiency, and "rcut_smth" is set to 0.5 Å; the "sel" parameter is set to "auto" to automatically select the upper limit of the number of atoms within the cutoff radius; "neuron" is set to [25,50,100], and "resnet_dt": true is enabled; in "fitting_net", it is set to a three-layer network [240,240,240]; the "learning_rate" part is set to "type": "exp", "start_lr": 0.001, "decay_steps": 5000, "decay_rate": 0.95, "stop_lr": 1e-8; "loss"... The initial force term weight was set to 1000, and the energy term weight was set to 0.

01. Later, the force and energy weight ratio was gradually adjusted to 1:

1.

7. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 4, characterized in that: In step (D), the potential function trained in step (C) is compared with the corresponding DFT validation set data to obtain the root mean square error. The root mean square error within the threshold range means that the energy error between the training set and the validation set is less than 3 meV / atom, and the force error between the training set and the validation set is less than 0.05 eV / Å.

8. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 4, characterized in that: In step (D), if the root mean square error obtained after training in step (C) is within the threshold range, no optimization is needed, and the potential function is directly output; if the root mean square error obtained after training in step (C) is not within the threshold range, iterative optimization is required, and the iterative optimization process is carried out according to the following steps (a)-(c): (a) The root mean square error exceeds the threshold range. Analyze the characteristics of the high error configuration (such as temperature range, gap type, local distortion mode, etc.). (b) Specifically, supplement the data by adding AIMD simulations near the high-error configuration, add it to the training set, keep the validation set unchanged, and retrain the potential function; (c) Repeat the “sampling, training, verification” cycle according to steps (A)-(D) until the trained potential function is stable and converges within the threshold range; and derive the converged potential function.

9. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 4, characterized in that: In step (D), the converged potential function is exported as a calling file adapted to the LAMMPS molecular dynamics platform, while retaining the original TensorFlow / PyTorch format for transfer learning.

10. The method for constructing the interstitial potential function of Fe-Mn-C alloy based on first-principles calculations and machine learning according to claim 1, characterized in that: The interstitial potential function of the Fe-Mn-C alloy is applied to the study of face-centered cubic (FCC) Fe-Mn-C alloys, specifically: the diffusion mechanism and energy barrier of C atoms in the interstitial sites of FCC octahedrons and tetrahedrons; the effect of Mn content on the lattice stability and thermal expansion of FCC; and the atomic-scale mechanism of high-temperature phase transformation and dynamic recrystallization processes.

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