Montmorillonite thermal conductivity prediction method based on NEP machine learning potential

Abstract

The invention relates to the technical field of machine learning potential molecular simulation, and provides a montmorillonite thermal conductivity prediction method based on NEP machine learning potential, and the method comprises the following steps: constructing a montmorillonite crystal structure model, carrying out first principle molecular dynamics calculation on the montmorillonite crystal structure model, introducing lattice distortion and atomic disturbance, and generating an initial structure set; performing static single-point DFT calculation on the initial structure set, and constructing a training data set; based on an NEP machine learning framework, utilizing the training data set to train and generate a potential function; optimizing the generation process of the potential function by adopting an active learning strategy; and performing thermal conductivity prediction verification on the potential function, and obtaining a thermal conductivity prediction result of the montmorillonite based on the potential function passing the verification. The defect that a traditional classical potential function depends on an empirical or semi-empirical model and is limited in precision and applicability is overcome, the problem that the dynamic behavior and the heat conduction mechanism of a complex material are difficult to accurately capture is solved, the calculation cost is reduced, and meanwhile the precision is kept.

Description

Technical Field

[0001] This invention relates to the field of machine learning potential molecular simulation technology, and more specifically, to a method for predicting the thermal conductivity of montmorillonite based on NEP machine learning potential. Background Technology

[0002] Montmorillonite is a layered silicate mineral composed of alternating layers of silicon-oxygen tetrahedra and aluminum-oxygen octahedrons. It possesses excellent adsorption and expansion properties, showing broad application potential in environmental remediation, drug delivery systems, catalyst supports, and nanocomposites. However, due to scale limitations, macroscopic experimental methods struggle to fully resolve the complex behavior of its microstructure. Molecular dynamics (MD) simulations, as a precise computational method, can simulate heat transfer processes at the atomic scale, revealing details of phonon behavior and interatomic interactions. Traditional classical potential functions typically rely on empirical or semi-empirical models to describe interatomic interactions; their accuracy and applicability are limited by the range of parameterized data and simplified physical models, making it difficult to accurately capture the dynamic behavior and heat conduction mechanisms of complex materials. Machine learning potentials (MLPs) learn from large amounts of density functional theory (DFT) computational data using machine learning algorithms, enabling accurate prediction of interatomic forces and energies while maintaining near-DFT accuracy and significantly reducing computational costs. Among these, non-atomic potentials (NEPs) have significant advantages in predicting the thermal transport properties of complex material systems. The application of MLPs allows MD simulations to handle larger-scale systems and more accurately simulate the thermal conduction characteristics of materials. Currently, there are no reports on research into methods for constructing machine learning potential-driven models for predicting the thermal conductivity of montmorillonite. Summary of the Invention

[0003] In view of this, the present invention proposes a solution to address the problems existing in the prior art.

[0004] To achieve the above objectives, the present invention provides a method comprising:

[0005] A montmorillonite crystal structure model was constructed, and first-principles molecular dynamics calculations were performed on the montmorillonite crystal structure model. Lattice distortion and atomic perturbation were introduced to generate an initial structure set.

[0006] Perform static single-point DFT calculations on the initial structure set to construct the training dataset;

[0007] Based on the NEP machine learning framework, the potential function is trained using the training dataset.

[0008] An active learning strategy is used to optimize the generation process of the potential function;

[0009] The potential function is used to predict and verify its thermal conductivity. Based on the verified potential function, the predicted thermal conductivity of montmorillonite is obtained.

[0010] Furthermore, the process of constructing the montmorillonite crystal structure model includes:

[0011] The montmorillonite unit cell crystal structure was constructed using Materials Studio software;

[0012] The convergence test and structural optimization of the montmorillonite unit cell crystal structure were performed using VASP to construct the montmorillonite crystal structure model.

[0013] Furthermore, the NEP machine learning framework uses a feedforward neural network with a single hidden layer to represent the total energy of the atom, obtains the potential function, uses descriptors to represent the local environmental characteristics of the atom, and employs a separable natural evolution strategy during network training to optimize the parameters of the feedforward neural network to minimize the loss function.

[0014] Furthermore, the loss function is as follows:

[0015]

[0016] in , These are the 1-norm and 2-norm errors of the training parameters, respectively. , , These are the root mean square errors of energy, force, and virial, respectively. , , , , It is the weight of the corresponding phase.

[0017] Furthermore, the process of optimizing the generation process of the potential function using an active learning strategy includes:

[0018] NEP-MD simulations were performed under NPT or NVT ensembles, and NEP-MD dynamic trajectories were generated by setting different thermodynamic conditions.

[0019] The farthest point sampling method is used as an active learning strategy to select candidate structures from the NEP-MD dynamic trajectory that are different from the existing training dataset.

[0020] The candidate structures are verified by static single-point DFT calculation, and the verified structures are then imported into the training dataset.

[0021] The training and import process is repeated until the energy error of the potential function is less than the set value.

[0022] Furthermore, the process of predicting and verifying the thermal conductivity of the potential function includes:

[0023] The potential function is subjected to lattice scaling experiments and thermal stability verification. If the verification fails, the network training process is re-executed.

[0024] If the validation is successful, thermal conductivity will be calculated using non-equilibrium molecular dynamics, homogeneous non-equilibrium molecular dynamics, and spectroscopic thermal flux decomposition methods for cross-validation.

[0025] Furthermore, if the prediction error of the potential function for the system potential energy in the lattice scaling test result is ≤0.1eV / atom, the verification is deemed successful; the thermal stability verification includes: performing NPT-MD simulation on the potential function at 600 K temperature, and if the potential energy change is within 0.5%, the verification is deemed successful.

[0026] The cross-validation is considered successful if the relative error is within 5%.

[0027] Furthermore, the process of generating the initial structure set includes:

[0028] In the first-principles molecular dynamics calculations, the ensemble was set to NVT, the time step was 2.0 fs, and the simulation time was 10 ps. The temperature was gradually increased from 50 K to 1000 K. During the calculation, the model trajectory was extracted every 100 fs to obtain several dynamic structures.

[0029] By applying random strain of -5.0% to 5.0% to each degree of freedom of the unit cell, and combining it with random perturbation of atomic positions of 0.1 Å, an initial structure set containing perturbed and dynamic structures is constructed.

[0030] Furthermore, the cutoff energy for the convergence test is increased from 300 eV to 600 eV, with a cutoff energy increase gradient of 50 eV. The k-point grid is used for 2×2×1 to 3×3×3 graded tests in the Γ-center grid. The relative energy difference of the potential energy after optimization is less than 0.025 eV.

[0031] Furthermore, the static single-point DFT calculation was performed using the VASP software package with the Perdew-Burke-Ernzerhof function, the plane wave cutoff energy was set to 450 eV, the k-point grid was set to 0.04 Å, and the convergence criterion for the electronic self-consistent loop was 10. -6 eV.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] This invention proposes a method for predicting the thermal conductivity of montmorillonite based on NEP machine learning potentials. By constructing a montmorillonite crystal structure model and introducing lattice distortion and atomic perturbations to generate an initial structure set, a training dataset is constructed using static single-point DFT calculations. The potential function is then trained using the NEP machine learning framework, and an active learning strategy is employed to optimize the potential function generation process. Finally, multiple verification methods are used to ensure the accuracy and reliability of the potential function, achieving high-precision prediction of montmorillonite thermal conductivity. This method overcomes the shortcomings of traditional classical potential functions, which rely on empirical or semi-empirical models and have limited accuracy and applicability. It solves the problem of accurately capturing the dynamic behavior and heat conduction mechanisms of complex materials, significantly reducing computational costs while maintaining near-DFT accuracy. Furthermore, this method provides more precise theoretical support for the study of the thermophysical properties of montmorillonite and its applications, contributing to the research and application of montmorillonite in environmental remediation, drug delivery systems, catalyst supports, and nanocomposite materials. Attached Figure Description

[0034] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings:

[0035] Figure 1 This is a schematic diagram of the process for predicting the thermal conductivity of montmorillonite based on NEP machine learning potential proposed in this invention.

[0036] Figure 2 The diagram shows the convergence test results provided by this invention, where (a) is the cutoff energy convergence test result and (b) is the kpoints grid convergence test result.

[0037] Figure 3 This invention provides a stable structural model of montmorillonite, where (a) to (c) are the atomic configurations of montmorillonite in the directions a, b, and c, and (d) is the three-dimensional atomic configuration of montmorillonite.

[0038] Figure 4 This invention provides the accuracy performance of the potential function model, where (a) represents the evolution of the energy, force, and virial loss functions RMSE relative to the training generations. (bd) Comparison between the NEP model predictions and the DFT reference data for energy (b), force (c), and virial (d).

[0039] Figure 5 The results are the potential function verification results provided by this invention, where (a) is the potential energy fluctuation at 600 K simulated by NEP-MD, and (b) is the comparison of atomic potential energy under different lattice scale factors calculated by NEP model and DFT.

[0040] Figure 6 This is the cross-validation result of the potential function thermal conductivity provided by the present invention. Detailed Implementation

[0041] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0042] refer to Figure 1 The NEP machine learning potential-driven method for predicting the thermal conductivity of montmorillonite in this embodiment may include the following steps:

[0043] Step 1: Construct the montmorillonite unit cell crystal structure using Materials Studio software.

[0044] In this embodiment, the boundary conditions of the montmorillonite unit cell crystal structure are three-dimensional periodic boundary conditions.

[0045] Step 2: Use VASP to perform convergence testing and structural optimization on the montmorillonite crystal structure model to obtain the equilibrium montmorillonite structure model;

[0046] In this embodiment, the convergence test cutoff energy is increased from 300 eV to 600 eV, the stage energy is increased by a gradient of 50 eV, and the k-point grid is used to perform 2×2×1 to 3×3×3 graded tests in the Γ center grid; the relative energy difference of the potential energy after optimization is less than 0.025 eV.

[0047] Step 3: Perform first-principles molecular dynamics (AIMD) calculations on the optimized structure, introducing lattice distortion and atomic perturbations to generate an initial structure set;

[0048] In this embodiment, the AIMD calculation is performed on the optimized structure. The ensemble is NVT, the time step is 2.0 fs, and the simulation time is 10 ps. The temperature gradually increases from 50 K to 1000 K. During the calculation, the model trajectory is extracted every 100 fs, and a total of 100 dynamic structures are obtained.

[0049] By applying random strain of -5.0% to 5.0% to each degree of freedom of the unit cell, and combining it with random perturbation of atomic positions at 0.1 Å, an initial structure set containing 100 perturbation structures and 100 dynamic structures was constructed.

[0050] Step 4: Perform DFT calculation on the initial structure set, and collect energy, force and virial data to construct a training dataset;

[0051] In this embodiment, static single-point DFT calculations are used to compute precise data on the energy, force, and virial of the initial structure set, employing the VASP software package with the Perdew-Burke-Ernzerhof (PBE) function. The plane wave cutoff energy is set to 450 eV, the k-point grid is set to 0.04 Å, and the convergence criterion for the electronic self-consistent loop is 10. -6 eV.

[0052] Step 5: Based on the NEP machine learning framework, train the potential function using the training dataset;

[0053] In this embodiment, the NEP (Neuro-Evolutionary Potential) framework uses a feedforward neural network (NN) with a single hidden layer to represent the total energy U of the atoms as the site energy U. i The sum of the site energy U i The output of the neural network can be represented as:

[0054] (1)

[0055] Where tanh(x) is the activation function in the hidden layer, w (0) w (1) These are the weight parameters from the input to the hidden layer and from the hidden layer to the output, respectively. (0) b (1) It is the bias vector, q v i It is a vector of descriptors used to describe the local environment of an atom.

[0056] In the NEP framework, the descriptor q v i To capture the local environmental characteristics of atoms, two types of descriptors are used: radial descriptors and angular descriptors. Radial descriptors rely solely on the distance between nearest-neighbor atoms and the central atom, while angular descriptors further consider the directionality of neighboring atoms relative to the central atom, involving many-body interactions. The radial descriptor has a cutoff radius of 6 Å, and the angular descriptor has a cutoff radius of 4 Å.

[0057] During training, the NEP model uses a separable natural evolution strategy (SNES) to optimize the neural network's parameter minimization loss function. The loss function consists of the root mean square error (RMSE) of multiple physical quantities (such as energy, force, and virial), incorporating 1-norm and 2-norm terms with respect to the parameters, as shown in the formula:

[0058] (2)

[0059] in , These are the 1-norm and 2-norm errors of the training parameters, respectively. , , These are the root mean square errors of energy, force, and virial, respectively. , , , , It is the weight of the corresponding phase.

[0060] Step 6: Optimize the potential function using an active learning strategy, including the following steps:

[0061] Step 601: Perform NEP-MD simulation under NPT or NVT ensemble to generate dynamic trajectories under various thermodynamic conditions;

[0062] Step 602: Use the farthest point sampling method as an active learning strategy to select candidate structures that are significantly different from the existing training dataset from the NEP-MD trajectory, so as to ensure the diversity and coverage of the dataset;

[0063] Step 603: Perform DFT single-point energy verification on the candidate configuration and import the verified structure into the training set;

[0064] Step 604: Repeat the training 2 to 3 times until the potential function energy error is less than the set value.

[0065] Step 7: Verify the thermal conductivity prediction based on the potential function. The prediction of the thermal conductivity of montmorillonite based on the potential function includes the following steps:

[0066] Step 701, Lattice Scaling Verification: Apply strain within ±5% of the lattice constant to verify that the prediction error of the potential function for the total energy of the system is ≤0.1 eV / ų;

[0067] Step 702, Thermal stability verification: Perform NPT-MD simulation at 600 K to ensure that the potential energy change is within 0.5%;

[0068] Step 703: Potential functions that fail verification return to step 6 for retraining.

[0069] Step 704: Calculate thermal conductivity using non-equilibrium molecular dynamics (NEMD), homogeneous non-equilibrium molecular dynamics (HNEMD), and spectroscopic thermal flux decomposition (SHC), and perform cross-validation. If the relative error of the three methods is ≤5%, the validation is considered successful.

[0070] Figure 2 This is a graph showing the convergence test results provided in this embodiment. The convergence test cutoff energy increases from 300 eV to 600 eV, with a stage energy increase gradient of 50 eV. The k-point grid is used for hierarchical testing from 2×2×1 to 3×3×3 in the Γ-center grid. After optimization, the relative energy difference of the potential energy is less than 0.025 eV. As shown in the graph, the cutoff energy is 550 eV, and the Γ-center grid is 3×3×1.

[0071] See Figure 3 The image shows the steady-state structural model of montmorillonite after structural optimization using the parameters described above.

[0072] See Figure 4 This is the montmorillonite thermal conductivity prediction potential function model in this embodiment. As shown in the figure, the total loss function converges, with root mean square errors of 1.069 meV / atom for energy, 76.031 meV / Å for force, and 15.07 meV / atom for virial.

[0073] See Figure 5 For the potential function lattice scaling test and thermal stability verification of this embodiment, by Figure 5 It can be seen that the calculated results of the potential function almost coincide with the calculated results of the DFT, indicating the accuracy of the potential function. The potential energy change is within 0.5% at 800 K, indicating that the potential function is also relatively stable in describing high temperature conditions.

[0074] See Figure 6 This is the cross-validation result of the potential function in this embodiment. (From...) Figure 6 It can be seen that the thermal conductivity results obtained by the three different methods are almost the same, indicating that the method of constructing a montmorillonite thermal conductivity prediction model based on NEP machine learning potential is feasible.

[0075] This embodiment presents a method for constructing a montmorillonite thermal conductivity prediction model based on NEP machine learning potential. This method achieves high-precision prediction of montmorillonite thermal conductivity, overcomes the limitations of traditional potential functions, and facilitates molecular simulation of montmorillonite. This model can further provide more accurate theoretical support for the study and application of montmorillonite's thermophysical properties.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the thermal conductivity of montmorillonite based on NEP machine learning potential, characterized in that, include: A montmorillonite crystal structure model was constructed, and first-principles molecular dynamics calculations were performed on the montmorillonite crystal structure model. Lattice distortion and atomic perturbation were introduced to generate an initial structure set. Perform static single-point DFT calculations on the initial structure set to construct the training dataset; Based on the NEP machine learning framework, the potential function is trained using the training dataset. An active learning strategy is used to optimize the generation process of the potential function; The potential function is used to predict and verify its thermal conductivity. Based on the verified potential function, the predicted thermal conductivity of montmorillonite is obtained.

2. The method according to claim 1, characterized in that, The process of constructing the montmorillonite crystal structure model includes: The montmorillonite unit cell crystal structure was constructed using Materials Studio software; The convergence test and structural optimization of the montmorillonite unit cell crystal structure were performed using VASP to construct the montmorillonite crystal structure model.

3. The method according to claim 1, characterized in that, The NEP machine learning framework uses a feedforward neural network with a single hidden layer to represent the total energy of an atom, obtains the potential function, uses descriptors to represent the local environmental characteristics of the atom, and employs a separable natural evolution strategy during network training to optimize the parameters of the feedforward neural network and minimize the loss function.

4. The method according to claim 3, characterized in that, The loss function is as follows: in , These are the 1-norm and 2-norm errors of the training parameters, respectively. , , These are the root mean square errors of energy, force, and virial, respectively. , , , , It is the weight of the corresponding phase.

5. The method according to claim 1, characterized in that, The process of optimizing the generation of the potential function using an active learning strategy includes: NEP-MD simulations were performed under NPT or NVT ensembles, and NEP-MD dynamic trajectories were generated by setting different thermodynamic conditions. The farthest point sampling method is used as an active learning strategy to select candidate structures from the NEP-MD dynamic trajectory that are different from the existing training dataset. The candidate structures are verified by static single-point DFT calculation, and the verified structures are then imported into the training dataset. The training and import process is repeated until the energy error of the potential function is less than the set value.

6. The method according to claim 1, characterized in that, The process of performing thermal conductivity prediction and verification on the potential function includes: The potential function is subjected to lattice scaling experiments and thermal stability verification. If the verification fails, the network training process is re-executed. If the validation is successful, thermal conductivity will be calculated using non-equilibrium molecular dynamics, homogeneous non-equilibrium molecular dynamics, and spectroscopic thermal flux decomposition methods for cross-validation.

7. The method according to claim 1, characterized in that, The verification is considered successful if the prediction error of the potential function for the system potential energy in the lattice scaling test result is ≤0.1 eV / atom; the thermal stability verification includes: performing NPT-MD simulation on the potential function at 600 K temperature, and the verification is considered successful if the potential energy change is within 0.5%; The cross-validation is considered successful if the relative error is within 5%.

8. The method according to claim 1, characterized in that, The process of generating the initial structure set includes: In the first-principles molecular dynamics calculations, the ensemble was set to NVT, the time step was 2.0 fs, and the simulation time was 10 ps. The temperature was gradually increased from 50 K to 1000 K. During the calculation, the model trajectory was extracted every 100 fs to obtain several dynamic structures. By applying random strain of -5.0% to 5.0% to each degree of freedom of the unit cell, and combining it with random perturbation of atomic positions of 0.1 Å, an initial structure set containing perturbed and dynamic structures is constructed.

9. The method according to claim 2, characterized in that, The convergence test cutoff energy is increased from 300 eV to 600 eV, with a cutoff energy increase gradient of 50 eV. The k-point grid is used for the 2×2×1 to 3×3×3 graded test in the Γ center grid. The optimized potential energy relative energy difference is less than 0.025 eV.

10. The method according to claim 1, characterized in that, The static single-point DFT calculation was performed using the VASP software package with the Perdew-Burke-Ernzerhof function. The plane wave cutoff energy was set to 450 eV, the k-point grid was set to 0.04 Å, and the convergence criterion for the electronic self-consistent loop was 10. -6 eV.

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