Van der waals heterostructure potential field simulation method and apparatus

Abstract

The application discloses a Van der Waals heterostructure potential field simulation method and device, and belongs to the technical field of quantum and molecular simulation. The method comprises the following steps: obtaining a first data set and a first parameter set corresponding to the first data set; training an MLP based on the first data set and the first parameter set, wherein the MLP is used for simulating the in-layer potential energy of the Van der Waals heterostructure; obtaining a second data set and a second parameter set corresponding to the second data set; fitting an anisotropic interlayer potential energy function ILP based on the second data set and the second parameter set, wherein the ILP is used for simulating the interlayer potential energy of the Van der Waals heterostructure; fitting the ILP based on the many-body effect to obtain a transition state ILP; and obtaining a first function based on the MLP and the transition state ILP, wherein the first function is used for simulating the transition state mixed potential energy of the in-layer-to-interlayer interaction of the Van der Waals heterostructure. The method can realize the simulation of the mixed force field of the Van der Waals interface while taking into account the calculation accuracy and efficiency.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of quantum and molecular simulation, and particularly relates to a van der Waals heterostructure potential field simulation method and device. BACKGROUND

[0002] The van der Waals heterostructure is a material structure vertically stacked by two-dimensional materials. The van der Waals heterostructure presents a "structural super-slip" state due to its unique anisotropic physical and mechanical properties. Unlike the traditional definition of super lubrication (friction coefficient is less than 0.001), the structural super-slip is defined as a state in which the wear is zero and the friction coefficient is close to zero when the two solid surfaces are in direct contact and slip without lubricant.

[0003] To develop practical and usable intelligent MEMS (Micro-Electro-Mechanical System) devices based on the structural super-slip system, a complex process flow such as material growth, transfer and structure preparation needs to be gone through. Research shows that under this actual working condition, the friction and wear behavior of the structural super-slip device will be affected by many factors, resulting in the disappearance of its super-slip performance, and the factors that play a leading role include interface deformation, boundary effect, material defects and surface adsorbates.

[0004] The experimental tools and means in the related art are difficult to quantitatively study and distinguish the influence of the above factors on the super-slip, and the existing friction theory model and calculation method cannot effectively describe the friction and wear behavior of the structural super-slip system under multiple physical fields and extreme environments, and a van der Waals heterostructure mixed force field simulation method is needed to accurately simulate the structural super-slip system. SUMMARY

[0005] The present disclosure provides a van der Waals heterostructure potential field simulation method and device, which can realize the simulation of the mixed force field of the van der Waals interface while taking into account the calculation accuracy and efficiency. The technical solution at least includes the following solutions:

[0006] In a first aspect, a method for simulating potential field of van der Waals heterostructure is provided, including: obtaining a first data set and a first parameter set corresponding to the first data set, the first data set including a plurality of different single-layer van der Waals heterostructures, the first parameter set including intra-layer potential energy of each single-layer van der Waals heterostructure, force on each atom in each single-layer van der Waals heterostructure, and virial stress tensor of each atom in each single-layer van der Waals heterostructure; training a machine learning potential function MLP based on the first data set and the first parameter set, the MLP being used to simulate intra-layer potential energy of van der Waals heterostructure; obtaining a second data set and a second parameter set corresponding to the second data set, the second data set including a plurality of different double-layer van der Waals heterostructures, the second parameter set including inter-layer potential energy of each double-layer van der Waals heterostructure in the second data set; fitting an anisotropic inter-layer potential function ILP based on the second data set and the second parameter set, the ILP being used to simulate inter-layer potential energy of van der Waals heterostructure; fitting the ILP based on many-body effect to obtain a transition state ILP; and obtaining a first function based on the MLP and the transition state ILP, the first function being used to simulate transition state mixed potential energy of intra-layer to inter-layer interaction of van der Waals heterostructure.

[0007] Optionally, the training of the machine learning potential function MLP based on the first data set and the first parameter set includes: obtaining a first predicted parameter set corresponding to the first parameter set, the first predicted parameter set including intra-layer potential energy of each single-layer van der Waals heterostructure predicted by the MLP, force on each atom in each single-layer van der Waals heterostructure predicted by the MLP, and virial stress tensor of each atom in each single-layer van der Waals heterostructure predicted by the MLP; constructing a loss function of the MLP based on the first parameter set and the first predicted parameter set; and minimizing the loss function of the MLP by using a separable natural evolution strategy to train the MLP.

[0008] Optionally, the MLP is a neural network potential function NEP, and the obtaining of the first predicted parameter set includes: processing the first data set by using a single-hidden-layer feedforward neural network to obtain a feature descriptor of atomic coordinates of each atom in each single-layer van der Waals heterostructure in the first data set; and obtaining the first predicted parameter set based on the feature descriptor.

[0009] Optionally, a first single-layer van der Waals heterostructure is any single-layer van der Waals heterostructure in the first data set, and intra-layer potential energy of the first single-layer van der Waals heterostructure predicted by the MLP is represented by the following formula in the first predicted parameter set:

[0010]

[0011] wherein, a first intra-layer potential energy of the first monolayer van der Waals heterostructure predicted by the MLP, is an energy of a first atom in the first monolayer van der Waals heterostructure, the single hidden layer feedforward neural network comprises a number of neurons, is a connection weight matrix corresponding to the first neuron, a value range of the connection weight matrix is 1 to , each of the monolayer van der Waals heterostructures comprises a number of feature descriptors, is a connection weight vector corresponding to the first neuron and the first feature descriptor, a value range of the connection weight vector is 1 to , is a bias vector corresponding to the first neuron, is a bias term, is a feature descriptor of atomic coordinates of the first atom, tanh is a hyperbolic tangent activation function, a value range of the bias vector is 1 to , is a total number of atoms in the first monolayer van der Waals heterostructure, , , are all integers; in the first prediction parameter set, a resultant force borne by a first atom of the first monolayer van der Waals heterostructure predicted by the MLP is expressed by the following formula: wherein, is the resultant force borne by the first atom of the first monolayer van der Waals heterostructure,

[0012] is a force of a first atom in the first monolayer van der Waals heterostructure on a second atom, is an energy of the second atom, is a position vector of the second atom relative to the first atom,

[0013]

[0014] wherein, is the resultant force borne by the first atom of the first monolayer van der Waals heterostructure, is the force of the first atom in the first monolayer van der Waals heterostructure on the second atom, is the energy of the second atom, is the position vector of the second atom relative to the first atom, is the resultant force borne by the first atom of the first monolayer van der Waals heterostructure, is the energy of the second atom, is the position vector of the second atom relative to the first atom, is the resultant force borne by the first atom of the first monolayer van der Waals heterostructure, is the energy of the second atom, is the position vector of the second atom relative to the first atom, is the resultant force borne by the first atom of the first monolayer van der Waals heterostructure, ​​The atom relative to the first Position vectors of atoms, It is an integer. The value range is 1 to and Not equal to ;

[0015] In the first set of prediction parameters, the MLP predicts the first monolayer van der Waals heterostructure's first... The virial stress tensor of an atom is expressed by the following formula:

[0016]

[0017] in, For the first monolayer van der Waals heterostructure The virial stress tensor of an atom.

[0018] Optionally, the loss function of the MLP is expressed by the following formula:

[0019]

[0020] in, Let MLP be the loss function. For the first dataset, the first Intralayer potential of a single-layer van der Waals heterostructure For the parameters in the first parameter set, and Correspondingly, it represents the first data set obtained by density functional theory (DFT) calculation. Intralayer potential of a single-layer van der Waals heterostructure For the parameters in the first parameter set, and Correspondingly, it represents the first monolayer van der Waals heterostructure obtained by DFT calculation. The net force on each atom For the parameters in the first parameter set, and correspond, This indicates the first data set obtained by DFT computation. The first single-layer van der Waals heterostructure The dimensional force stress tensor of an atom This represents the total number of single-layer van der Waals heterostructures in the first dataset. The value range is 1 to , The parameter vector includes the first... The connection weight matrix corresponding to each neuron , the first neuron, the first feature descriptor corresponds to a connection weight vector , the first neuron corresponds to a bias vector , the bias and the to-be-fitted parameters in each of the feature descriptors, is the dimension of the parameter vector , is an integer, , the value range of , , , , and is a neural network hyperparameter.

[0021] Optionally, based on the second data set and the second parameter set, fitting the anisotropic interlayer potential function ILP includes: obtaining a second prediction parameter set, the second prediction parameter set corresponds to the second parameter set, the second prediction parameter set includes the interlayer potential of each of the double-layer van der Waals heterostructure predicted by the MLP; based on the second prediction parameter set and the second parameter set, constructing an ILP objective function; based on the ILP objective function, fitting the parameters of the ILP using a least squares method algorithm.

[0022] Optionally, the first double-layer van der Waals heterostructure is any one of the double-layer van der Waals heterostructures in the second data set, the first double-layer van der Waals heterostructure includes a second single-layer van der Waals heterostructure and a third single-layer van der Waals heterostructure,

[0023] The ILP is expressed by the following formula:

[0024]

[0025] wherein, is the ILP, the ILP is used to predict the interlayer potential of the first double-layer van der Waals heterostructure, represents the interlayer potential between the i-th atom and the j-th atom predicted by the ILP, wherein the i-th atom is an atom in the second single-layer van der Waals heterostructure, and the j-th atom is an atom in the third single-layer van der Waals heterostructure, , is an integer, , the value range of , , ​​​The value range is 1 to , This represents the total number of atoms in the second monolayer van der Waals heterostructure. The total number of atoms in the third monolayer van der Waals heterostructure;

[0026] The ILP prediction of the first The atom and the first The interlayer potential energy between atoms is calculated using the following formula:

[0027]

[0028] in, For the first The atom and the first Position vectors between atoms For the first The normal vector of each atom, For the first The normal vector of each atom, Indicates the first The atom and the first Long-range van der Waals attraction terms between atoms Indicates the first The atom and the first Pauli repulsion terms between atoms This is a smooth cutoff function used to smoothly reduce the potential function and its derivative (up to the third order) to zero when the interatomic spacing exceeds the cutoff distance.

[0029] Optionally, the second dataset includes a first subset and a second subset, wherein the first subset includes multiple two-layer van der Waals heterostructures with different interlayer spacings, and the second subset includes multiple two-layer van der Waals heterostructures with different horizontal slips at a balanced interlayer spacing.

[0030] The objective function of ILP is expressed by the following formula:

[0031]

[0032] in, Let be the objective function of the ILP. The number of bilayer van der Waals heterostructures in the first subset of data. For the first subset of data The weights corresponding to each two-layer van der Waals heterostructure. It is an integer. The first subset of the dataset predicted by the ILP. Interlayer potential of a double-layer van der Waals heterostructure These are the parameters in the second parameter set. and correspond, This represents the first subset of data obtained by density functional theory (DFT) calculation. Interlayer potential of a double-layer van der Waals heterostructure The number of bilayer van der Waals heterostructures in the second subset of data. For the second subset of data The weights corresponding to each two-layer van der Waals heterostructure. The second subset of the dataset predicted by the ILP. Interlayer potential of a double-layer van der Waals heterostructure These are the parameters in the second parameter set. and Correspondingly, it represents the second subset of data obtained by DFT computation. Interlayer potential of a double-layer van der Waals heterostructure This indicates the calculation of the L2 norm.

[0033] Optionally, the transition state ILP is represented by the following formula:

[0034]

[0035] in, For the transition state ILP, Indicates the first The atom and the first Transition potential energy between atoms;

[0036] The first The atom and the first The transition state energy between atoms can be represented by the following formula:

[0037]

[0038] in, For transition function, For the first The atom and the first Many-body effect when the distance between atoms is minimized This is the key weight function.

[0039] In a second aspect, a van der Waals heterostructure potential field simulation apparatus is provided, comprising: a first obtaining module configured to obtain a first dataset and a first parameter set corresponding to the first dataset, the first dataset comprising a plurality of different single-layer van der Waals heterostructures, and the first parameter set comprising an in-plane potential energy of each single-layer van der Waals heterostructure, a force on each atom in each single-layer van der Waals heterostructure, and a virial stress tensor of each atom in each single-layer van der Waals heterostructure; a training module configured to train a machine learning potential (MLP) based on the first dataset and the first parameter set, the MLP being configured to simulate the in-plane potential energy of a van der Waals heterostructure; a second obtaining module configured to obtain a second dataset and a second parameter set corresponding to the second dataset, the second dataset comprising a plurality of different double-layer van der Waals heterostructures, and the second parameter set comprising an interlayer potential energy of each double-layer van der Waals heterostructure in the second dataset; a first fitting module configured to fit an anisotropic interlayer potential (ILP) based on the second dataset and the second parameter set, the ILP being configured to simulate the interlayer potential energy of a van der Waals heterostructure; a second fitting module configured to fit the ILP based on a many-body effect to obtain a transition state ILP; and a simulation module configured to obtain a first function based on the MLP and the transition state ILP, the first function being configured to simulate a transition state mixed potential energy of an in-plane-to-interlayer interaction of a van der Waals heterostructure.

[0040] Optionally, the training module is further configured to obtain a first predicted parameter set corresponding to the first parameter set, the first predicted parameter set comprising an in-plane potential energy of each single-layer van der Waals heterostructure predicted by the MLP, a force on each atom in each single-layer van der Waals heterostructure predicted by the MLP, and a virial stress tensor of each atom in each single-layer van der Waals heterostructure predicted by the MLP; construct a loss function of the MLP based on the first parameter set and the first predicted parameter set; and minimize the loss function of the MLP using a separable natural evolution strategy to train the MLP.

[0041] Optionally, the MLP is a neural network potential (NEP), and the training module is further configured to: process the first dataset using a single-hidden-layer feedforward neural network to obtain a feature descriptor of atomic coordinates of each atom in each single-layer van der Waals heterostructure in the first dataset; and obtain the first predicted parameter set based on the feature descriptor.

[0042] Optionally, the first fitting module is further configured to obtain a second prediction parameter set corresponding to the second parameter set, the second prediction parameter set comprising interlayer potential energy of each of the bilayer van der Waals heterostructure predicted by the MLP; construct an ILP objective function based on the second prediction parameter set and the second parameter set; and fit parameters of the ILP based on the ILP objective function using a least square method algorithm.

[0043] In a third aspect, a computer device is provided, comprising a memory and a processor, at least one computer program is stored in the memory, and the at least one computer program is loaded and executed by the processor, so as to execute the van der Waals heterostructure potential field simulation method described in the above embodiments.

[0044] In a fourth aspect, a computer readable storage medium is provided, at least one computer program is stored in the computer readable storage medium, and the at least one computer program is loaded and executed by a processor, so as to execute the van der Waals heterostructure potential field simulation method described in the above embodiments.

[0045] In a fifth aspect, a computer program product is provided, comprising computer programs / instructions, which, when executed by a processor, implement the method of the first aspect.

[0046] The technical solutions provided by the embodiments of the present disclosure have at least the following beneficial effects:

[0047] The MLP is more accurate than the ILP in describing the layer-in mechanical and physical properties of the van der Waals layered material, but cannot well describe the interlayer long-range interaction, and the ILP is just the opposite of the MLP, which can accurately describe the interlayer van der Waals interaction, but cannot describe the layer-in mechanical and physical properties. Therefore, in the embodiments of the present disclosure, the MLP is used to simulate the layer-in potential energy, and the ILP is used to simulate the interlayer potential energy, so that the simulated layer-in potential energy and interlayer potential energy are relatively accurate. In addition, by introducing the many-body effect to the ILP, a transition state ILP is obtained, which can accurately simulate the interlayer potential energy under the transition state. Then, based on the MLP and the transition state ILP, a first function is obtained, which is equivalent to organically combining the MLP under the transition state and the transition state ILP, so as to accurately simulate the transition state mixed potential energy of the layer-in to layer-in interaction. In this way, the potential field of the entire van der Waals heterostructure is accurately simulated, that is, the layer-in potential energy, the interlayer potential energy, and the transition state mixed potential energy of the layer-in to layer-in interaction can be accurately simulated.

[0048] The MLP only considers the intra-layer potential energy, and a faster speed can be obtained under the condition of ensuring the accuracy due to a smaller truncation radius; the ILP only considers the weak van der Wauls interlayer interaction (i.e. interlayer potential energy), and a small number of parameters ensures that the interlayer interaction calculation can be efficiently calculated even at a larger truncation radius. Therefore, the calculation framework of MLP+ILP in the present application considers both the calculation efficiency and the calculation accuracy.

[0049] Generally, the portability of MLP is poor, and the force field developed for a certain material and configuration cannot be used for another configuration. For complex multi-layer van der Wauls heterostructures, such as double-layer graphene / double-layer boron nitride heterojunction and four-layer graphene homojunction, the machine learning potential function describing graphene needs to be trained separately for the two systems, and cannot be universal. However, the calculation scheme proposed in the embodiments of the present disclosure can perfectly overcome this problem, because the machine learning potential function only needs to describe the properties of a single-layer van der Wauls material, and the interlayer interaction is directly superimposed by the anisotropic potential function. Therefore, after the development of the force field, it can be applied to the above two different systems, and has strong portability. Under this scheme, even for the simulation of structures with dozens of van der Wauls materials, only the intra-layer machine learning of each material and the anisotropic interlayer force field between each two materials need to be trained.

[0050] Since MLP is fitted to the training set using a neural network and the energy and force of the required calculation structure are obtained by interpolation, the quality of the training set is important, and it needs to be widely included in the content to be studied. Direct use of pure MLP needs to consider complex training sets, such as blocks, single-layer, double-layer, three-layer, four-layer, and various material heterostructures in different arrangement modes, etc. With the increase of the complexity of the structure, the training set required by pure MLP increases exponentially, causing a dimension disaster. However, in the scheme proposed in the embodiments of the present disclosure, only the structure of a single-layer van der Wauls material needs to be considered when training MLP, and only a double-layer structure needs to be considered when fitting ILP. The structure configuration considered by the training set is much smaller than that of a single machine learning potential function. At the same time, considering that obtaining an accurate training set usually requires a huge amount of first-principle calculation, therefore, in the present application, the training set construction speed is much faster than that of only using a single machine learning potential function, and the development cycle of the calculation method is greatly shortened.

[0051] The calculation framework of the mixed machine learning and anisotropic force field proposed in the embodiments of the present disclosure can not only be used to accurately describe the physical and mechanical properties of van der Wauls layered material systems, such as interface mechanics, heat transport, force-electric coupling, interface chemical bond-breaking, friction and wear, and other complex processes far from equilibrium. At the same time, this scheme can also be extended to material systems in which strong and weak interactions both play an important role, and has important reference significance for the development of calculation methods in the fields of materials, physics, and chemistry. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present disclosure, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0053] Figure 1 A flow chart of a van der Waals heterostructure potential field simulation method provided by an example embodiment of the present disclosure is shown;

[0054] Figure 2 A flow chart of a van der Waals heterostructure potential field simulation method provided by another example embodiment of the present disclosure is shown;

[0055] Figure 3 is a comparison chart of the calculation consumption of the machine learning potential and the empirical potential at the same time;

[0056] Figure 4 is a schematic diagram of the phonon spectrum of graphite fitted by different methods;

[0057] Figure 5 A structural schematic diagram of a van der Waals heterostructure potential field simulation device provided by an example embodiment of the present disclosure is shown;

[0058] Figure 6 is a structural schematic diagram of a computer device provided by an embodiment of the present disclosure. DETAILED DESCRIPTION

[0059] Unless otherwise defined, the technical terms or scientific terms used herein should be understood as the general meaning understood by those skilled in the art to which the present disclosure belongs. The "first", "second", "third" and similar words used in the patent application description and claims of the present disclosure do not represent any order, quantity or importance, but are only used to distinguish different components. Similarly, "one" or "a" and similar words do not represent a quantity limit, but represent the existence of at least one. "Including" or "containing" and similar words mean that the elements or objects appearing before "including" or "containing" cover the elements or objects listed after "including" or "containing" and their equivalents, and do not exclude other elements or objects.

[0060] In order to make the purposes, technical solutions and advantages of the present disclosure clearer, the embodiments of the present disclosure will be further described in detail below with reference to the drawings.

[0061] In the related art, two types of calculation methods are mainly used to simulate the physical and mechanical behaviors of van der Waals heterostructures (the simulated physical and mechanical behaviors can be converted into potential fields by first principles, that is, the physical and mechanical behaviors and the potential fields belong to similar concepts): quantum mechanics calculation and classical molecular dynamics simulation.

[0062] Quantum mechanics calculation (such as density functional theory) can provide high accuracy in describing van der Waals forces (especially after introducing dispersion correction), and is a commonly used method for current research on the physical properties of systems with hundreds of atoms. However, it is computationally expensive to handle large-scale van der Waals layered material systems (>10 3 atoms).

[0063] In this case, MD (Molecular Dynamics) simulation based on classical molecular dynamics simulation can find a good balance between computational efficiency and accuracy. MD simulation can be applied to larger scale systems containing 10 4 -10 8 atoms. However, the accuracy and computational efficiency of classical molecular dynamics simulation are closely related to the force field used. Therefore, selecting a suitable force field is crucial for obtaining reliable calculation results.

[0064] The force fields commonly used to describe the interactions within van der Waals layered materials include various empirical potential functions, such as REBO (Reactive Empirical Bond Order Potential), Tersoff potential function, and SW potential function (Stillinger-Weber Potential Function). The interlayer interactions are usually simulated by LJ potential function (Lennard-Jones Potential Function). Research has found that the LJ potential function cannot accurately simulate the interfacial mechanics, friction, and thermal transport properties of two-dimensional materials. In addition, using the above force fields to simulate the interfacial mechanical properties of van der Waals layered material systems with boundaries also faces great challenges, because these force fields cannot effectively describe the interfacial bond-breaking and bond-forming processes of edge dangling bonds and the influence of oxygen-containing edge chemical groups on interfacial friction behavior.

[0065] In this context, machine learned potentials (MLP) have emerged as a new tool for studying van der Waals interfaces. MLPs can learn the potential energy surface of a complex system from high-precision quantum mechanical data, combining the accuracy of quantum mechanical calculations with the efficiency of classical force fields. For single-layer two-dimensional layered van der Waals materials, MLPs can simulate various properties with higher accuracy than traditional empirical potential functions. However, MLPs cannot accurately describe long-range van der Waals interactions, and thus cannot accurately simulate multi-layer van der Waals material systems.

[0066] Figure 1 A flowchart of a method for simulating a potential field of a van der Waals heterostructure is shown, which can be performed by a computer device. Referring to Figure 1 The method includes:

[0067] In step 101, a first data set is obtained, and a first parameter set corresponding to the first data set.

[0068] The first data set includes a plurality of different single-layer van der Waals heterostructures.

[0069] Optionally, the first data set includes single-layer van der Waals heterostructures in the following three cases.

[0070] In the first case, a plurality of single-layer van der Waals heterostructures with different strains.

[0071] In the second case, a plurality of single-layer van der Waals heterostructures with different temperatures.

[0072] In the third case, a plurality of single-layer van der Waals heterostructures with different structural perturbations. The structural perturbations include, but are not limited to, mechanical perturbations such as bending, surface undulation, dislocations, vacancy and interstitial atoms, grain boundaries, chemical perturbations such as functional group modification, external atom adsorption, and physical perturbations such as polarization and carrier doping.

[0073] For the above three cases, a plurality of single-layer van der Waals heterostructures can be obtained for each case, thereby constructing the first data set.

[0074] The first parameter set includes the energy of each single-layer van der Waals heterostructure, the total force on each atom in each single-layer van der Waals heterostructure, and the virial stress tensor of each atom in each single-layer van der Waals heterostructure.

[0075] Optionally, the first-principles calculation software is used to calculate the parameters in the first parameter set. For example, the density functional theory (DFT) is used to calculate the parameters in the first parameter set based on the first-principles calculation software. In the embodiments of the present disclosure, the energy accuracy of the first-principles calculation software is required to be at least , force accuracy at least requirement to ensure the accuracy of the calculated parameters in the first parameter set.

[0076] In step 102, a machine learning potential function is trained based on the first data set and the first parameter set.

[0077] The machine learning potential function (MLP) is used to simulate the interlayer potential energy of the van der Waals heterostructure.

[0078] Optionally, the MLP includes but is not limited to: Neuro Evolution Potential (NEP), Gaussian Approximation Potential (GAP), DeepPotential (DP), etc.

[0079] In step 103, a second data set and a second parameter set corresponding to the second data set are obtained.

[0080] The second data set includes a plurality of different double-layer van der Waals heterostructures, and the second parameter set includes the interlayer potential energy of each double-layer van der Waals heterostructure in the second data set.

[0081] Optionally, the second data set includes double-layer van der Waals heterostructures in the following two cases.

[0082] The first case is a plurality of double-layer van der Waals heterostructures with different layer spacings.

[0083] The second case is a plurality of double-layer van der Waals heterostructures with different horizontal shifts at the equilibrium layer spacing.

[0084] In the above-mentioned second data set, the plurality of double-layer van der Waals heterostructures in the first case can be referred to as a first data subset, and the plurality of double-layer van der Waals heterostructures in the second case can be referred to as a second data subset.

[0085] Before calculating the second parameter set, the total energy of the first double-layer van der Waals heterostructure in vacuum, the energy of the second single-layer van der Waals heterostructure and the energy of the third single-layer van der Waals heterostructure are first calculated using the first principle (such as DFT). The first double-layer van der Waals heterostructure is any double-layer van der Waals heterostructure in the second data set, the first double-layer van der Waals heterostructure includes the second single-layer van der Waals heterostructure and the third single-layer van der Waals heterostructure, and the second single-layer van der Waals heterostructure and the third single-layer van der Waals heterostructure have interlayer potential energy.

[0086] After the three parameters are calculated, the interlayer potential of each double-layer van der Waals heterostructure can be calculated by formula (1) to obtain the second parameter set.

[0087] (1)

[0088] In formula (1), is the calculated interlayer potential of the double-layer van der Waals heterostructure, is the total energy of the first double-layer van der Waals heterostructure in vacuum, is the total energy of the second single-layer van der Waals heterostructure, is the energy of the third single-layer van der Waals heterostructure. is the total number of system atoms of the first double-layer van der Waals heterostructure.

[0089] In step 104, based on the second data set and the second parameter set, an anisotropic interlayer potential function is fitted.

[0090] The anisotropic interlayer potential function (ILP) is used to simulate the interlayer potential of the van der Waals heterostructure.

[0091] Here, the interlayer potential of the double-layer van der Waals heterostructure in the second data set includes different cases, and by fitting ILP using the second data set and the second parameter set, the fitted ILP can accurately simulate the interlayer potential of the van der Waals heterostructure.

[0092] In step 105, the ILP is fitted based on the many-body effect to obtain the transition state ILP.

[0093] For most application scenarios, such as describing the boundary local deformation of van der Waals layered materials, edge chemical groups and pinning effects, etc., the MLP in step 102 and the ILP in step 104 can be directly combined together, and the "layer" descriptor is used to distinguish MLP and ILP, so that they respectively describe the intra-layer and inter-layer interactions of the van der Waals heterostructure.

[0094] However, if the simulation process needs to consider the bond-breaking and bond-forming process of edge dangling bonds or the case of oxygen-containing edge chemical groups, this direct combination of MLP and ILP is no longer applicable, and at this time the transition state of intra-layer to inter-layer interaction needs to be considered.

[0095] When considering the transition state, for MLP, only the training and validation set containing the transition state structure data needs to be ensured when calculating the first parameter set, without modifying the training process. For ILP, the many-body effect needs to be introduced to realize the simulation of continuous transition, so as to obtain the transition state ILP.

[0096] In step 106, a first function is obtained based on the MLP and the transition state ILP.

[0097] The first function is used to simulate the transition state mixed potential energy of the interlayer interaction of the van der Waals heterostructure.

[0098] The MLP here is the MLP in step 105 that ensures that the structure data containing the transition state in the training and validation sets is ensured when calculating the first parameter set.

[0099] The first function is equivalent to organically combining the MLP at the transition state and the transition state ILP, so as to accurately simulate the transition state mixed potential energy of the interlayer interaction.

[0100] As can be seen from the above steps 101 to 106, in the embodiment of the present disclosure, the potential field of the van der Waals heterostructure includes: the interlayer potential energy, the interlayer potential energy and the transition state mixed potential energy of the interlayer interaction. Through the interlayer potential energy, the interlayer potential energy and the transition state mixed potential energy of the interlayer interaction, the potential field of the multi-layer van der Waals heterostructure can be accurately described.

[0101] The MLP is more accurate than the ILP in describing the interlayer mechanical physical properties of the van der Waals layered material, but cannot well describe the long-range interlayer interaction, and the ILP is just the opposite of the MLP, which can accurately describe the interlayer van der Waals interaction, but cannot describe the interlayer mechanical physical properties. Therefore, in the embodiment of the present disclosure, the interlayer potential energy and the interlayer potential energy are simulated by using the MLP and the ILP, so that the simulated interlayer potential energy and the interlayer potential energy are more accurate. In addition, the transition state ILP is obtained by introducing the many-body effect to the ILP, which can accurately simulate the interlayer potential energy at the transition state; and based on the MLP and the transition state ILP, a first function is obtained, which is equivalent to organically combining the MLP at the transition state and the transition state ILP, so as to accurately simulate the transition state mixed potential energy of the interlayer interaction. In this way, the potential field of the entire van der Waals heterostructure is accurately simulated, that is, the interlayer potential energy, the interlayer potential energy and the transition state mixed potential energy of the interlayer interaction can be accurately simulated.

[0102] The MLP only considers the interlayer potential energy, and can obtain faster speed under the condition of ensuring accuracy due to smaller truncation radius; the ILP only considers the weak van der Waals interaction between layers (i.e. interlayer potential energy), and a small number of parameters ensure that the interlayer interaction calculation can be calculated efficiently even at a larger truncation radius. Therefore, the calculation framework of MLP+ILP in the present application considers both calculation efficiency and calculation accuracy.

[0103] Generally, the portability of MLP is poor, and the force field developed for a certain material and configuration cannot be used for another configuration. For complex multi-layer van der Waals heterostructures, such as double-layer graphene / double-layer boron nitride heterojunction and four-layer graphene homojunction, the machine learning potential function describing graphene needs to be trained separately for the two systems, and cannot be universal. However, the calculation scheme proposed in the embodiments of the present disclosure can perfectly overcome this problem, because the machine learning potential function only needs to describe the properties of a single-layer van der Waals material, and the interlayer interaction is directly superimposed by the anisotropic potential function. Therefore, after the development of the force field, it can be applied to the above two different systems, and has strong portability. Under this scheme, even for structures with tens of van der Waals materials, only the in-layer machine learning of each material and the anisotropic interlayer force field between each two materials need to be trained.

[0104] Since MLP is fitted to the training set using a neural network and the energy and force of the required calculation structure are obtained by interpolation, the quality of the training set is important and needs to be widely included in the required research. Direct use of pure MLP needs to consider complex training sets, such as blocks, single layers, double layers, three layers, four layers, and different arrangement modes of various material heterostructures. With the increase of the complexity of the structure, the training set required by pure MLP increases exponentially, causing a dimension disaster. However, in the scheme proposed in the embodiments of the present disclosure, only the structure of a single-layer van der Waals material needs to be considered when training MLP, and only a double-layer structure needs to be considered when fitting ILP. The structure configuration considered by the training set is much smaller than that of a single machine learning potential function. At the same time, considering that obtaining an accurate training set usually requires first-principle calculations with huge computational consumption, therefore, in the present disclosure, the training set construction speed is much greater than that of only using a single machine learning potential function, and the development cycle of the calculation method is greatly shortened.

[0105] The calculation framework of mixed machine learning and anisotropic force field proposed in the embodiments of the present disclosure can not only be used to accurately describe the physical and mechanical properties of van der Waals layered material systems, such as interface mechanics, heat transport, force-electric coupling, interface chemical bond-breaking, friction and wear, and other complex processes far from equilibrium. At the same time, this scheme can also be extended to material systems in which strong and weak interactions both play an important role, and has important reference significance for the development of calculation methods in the fields of materials, physics, and chemistry.

[0106] Figure 2 A flowchart of a van der Waals heterostructure potential field simulation method provided by another example embodiment of the present disclosure is shown, which can be executed by a computer device.

[0107] In step 201, a first data set is obtained, and a first parameter set corresponding to the first data set.

[0108] The details of step 201 can refer to the aforementioned step 101, and details are omitted here.

[0109] In step 202, a machine learning potential function MLP is trained based on the first data set and the first parameter set.

[0110] The MLP is used to simulate the intra-layer potential energy of the van der Waals heterostructure.

[0111] Optionally, step 202 includes steps a-c as follows.

[0112] Step a, obtaining a first predicted parameter set.

[0113] The first predicted parameter set corresponds to the first parameter set. The first predicted parameter set includes the intra-layer potential energy of each monolayer van der Waals heterostructure predicted by the MLP, the total force on each atom in each monolayer van der Waals heterostructure predicted by the MLP, and the virial stress tensor of each atom in each monolayer van der Waals heterostructure predicted by the MLP.

[0114] Here, the first predicted parameter set is actually the parameters predicted by the MLP. For each monolayer van der Waals heterostructure in the first data set, the MLP will give a predicted value, and these predicted values constitute the first predicted parameter set.

[0115] With the iterative training of the MLP, the parameters in the first predicted parameter set are also updated accordingly.

[0116] When the selected MLP is different, the way of obtaining the first predicted parameter set in step a is different, and the MLP loss function constructed in step b is also different.

[0117] In the embodiments of the present disclosure, the selected MLP is a neural network potential function NEP, and step 202 will be described below taking NEP as an example. In this case, step a includes the following two steps.

[0118] First, a single hidden layer feedforward neural network is used to process the first data set to obtain a feature descriptor of the atomic coordinates of each atom of each monolayer van der Waals heterostructure in the first data set.

[0119] The feature descriptor is used to obtain the first predicted parameter set.

[0120] Optionally, the first step includes: based on a neural network method, a single hidden layer feedforward neural network is used to convert the atomic coordinates of each atom into a feature descriptor through Chebyshev polynomials. There are to-be-trained parameters in the feature descriptor (all to-be-trained parameters have an initial value in the initial case, which is used to calculate the first parameter set, and these initial values are continuously optimized with the iterative training of the MLP), and the final values of these to-be-trained coefficients can be obtained after the subsequent MLP training is completed.

[0121] The second step is to obtain the first set of prediction parameters based on the feature descriptors.

[0122] The following sections explain how each parameter in the first prediction parameter set in the second step is obtained.

[0123] Optionally, in the first set of prediction parameters, the intralayer potential of the first monolayer van der Waals heterostructure predicted by MLP (i.e. NEP) is expressed by formula (2), and the first monolayer van der Waals heterostructure is any monolayer van der Waals heterostructure in the first dataset.

[0124] (2)

[0125] In formula (2), Used to describe the intralayer potential of the first monolayer van der Waals heterostructure predicted by MLP. For the first single-layer van der Waals heterostructure The energy of an atom The value range is 1 to , This represents the total number of atoms in the first single-layer van der Waals heterostructure. A single-hidden-layer feedforward neural network includes... One neuron, For the first The connection weight matrix corresponding to each neuron. The value range is 1 to Each monolayer van der Waals heterostructure includes Each feature descriptor For the first The _th neuron, the _th The connection weight vector corresponding to each feature descriptor The value range is 1 to . For the first The bias vector corresponding to each neuron. For bias terms, For the first The feature descriptor of the atomic coordinates of each atom, where tanh is the hyperbolic tangent activation function. , , All are integers.

[0126] No. For an individual atom, this is achieved by relating energy to the atom's position vector. The partial derivative can be used to obtain the first... The force of the first atom (part of the force) The atom pair of the first The force of each atom), will all non Atom pairs the force sum of the partial forces of the first atom of the first monolayer van der Waals heterostructure the force sum of the first atom of the first monolayer van der Waals heterostructure In this case, optionally, in the first prediction parameter set, the force sum of the first atom of the first monolayer van der Waals heterostructure predicted by the MLP is represented by formula (3).

[0127] (3)

[0128] In formula (3), is the force sum of the first atom of the first monolayer van der Waals heterostructure, is the force sum of the first atom of the first monolayer van der Waals heterostructure, is the force of the first atom on the first atom of the first monolayer van der Waals heterostructure, is the energy of the first atom, is the position vector of the first atom relative to the first atom, is the position vector of the first atom relative to the first atom, is an integer, the value range of i is 1 to N-1, and i is not equal to j. The meanings of other parameters in formula (3) are the same as in formula (2), and details are omitted here. Here, the first atom is any atom in the first monolayer van der Waals heterostructure except the first atom. Virial stress tensor can be obtained by taking the tensor product of the position vector between atoms and the partial force . Optionally, in the first prediction parameter set, the Virial stress tensor of the first atom of the first monolayer van der Waals heterostructure predicted by the MLP is represented by formula (4).

[0129] Virial stress tensor

[0130] can be obtained by taking the tensor product of the position vector between atoms and the partial force .

[0131] Optionally, in the first prediction parameter set, the Virial stress tensor of the first atom of the first monolayer van der Waals heterostructure predicted by the MLP is represented by formula (4).

[0132] (4)

[0133] In formula (4), is the Virial stress tensor of the first atom of the first monolayer van der Waals heterostructure, ​​​​​​​​The virial stress tensor of each atom. The meanings of the other parameters in formula (4) are the same as those in formulas (2) and (3), and are omitted here.

[0134] By processing each parameter in the first dataset using the first and second steps described above, it is possible to obtain each parameter in the first prediction parameter set.

[0135] Step b: Construct the loss function of the MLP based on the first parameter set and the first prediction parameter set.

[0136] Optionally, the loss function of MLP is expressed by formula (5).

[0137] (5)

[0138] In formula (5), The loss function for MLP. For the first dataset, the first Intralayer potential of a single-layer van der Waals heterostructure The parameters are in the first parameter set. and correspond, This represents the first data point obtained by density functional theory (DFT) calculation. Intralayer potential of a single-layer van der Waals heterostructure. The parameters are in the first parameter set. and correspond, This indicates the first monolayer van der Waals heterostructure obtained using DFT calculations. The net force acting on each atom. The parameters are in the first parameter set. and correspond, This represents the first data point in the dataset obtained by DFT computation. The first single-layer van der Waals heterostructure The force stress tensor of an atom. This represents the total number of single-layer van der Waals heterostructures in the first dataset. The value range is 1 to . Let be a parameter vector, the parameter vector includes the first parameter. The connection weight matrix corresponding to each neuron , No. The _th neuron, the _th The connection weight vector corresponding to each feature descriptor , No. The bias vector corresponding to each neuron Bias And the parameters to be fitted in each feature descriptor. parameter vector Dimensions It is an integer. The value range is 1 to , , , , and For the neural network hyperparameters. The meanings of the other parameters in formula (5) are the same as in formula (2), and are omitted here.

[0139] The MLP loss function is constructed by calculating the root mean square error between the predicted value and the corresponding DFT value; then, using various... , , , and The hyperparameters of a neural network are weighted sums and the absolute value of the parameter vector is introduced. Summation is performed to make some less important parameters tend to 0, thereby achieving feature selection and the sum of squares of the parameter vector. Summing down the values ​​of all parameters makes them smaller and more balanced, preventing some parameters from having too large an impact on the model.

[0140] During training, if only the intra-layer potential is trained, overfitting is likely to occur, resulting in an inaccurate simulation of intra-layer potential by the trained MLP. By introducing a third layer into the MLP training process (including the input and loss function), [the following approach can be adopted]. The net force on the first atom and the first The two parameters, the virial stress tensor of each atom, are equivalent to introducing a regularization term, which can reduce overfitting of the MLP and improve the accuracy of the predicted potential energy within the training MLP. After the MLP training is completed, the various parameters to be fitted in formula (2) (including...) , , , The values ​​of the parameters to be fitted in each feature descriptor are definite. At this time, the formula (2) can be used to predict the in-layer potential energy of the van der Waals heterostructure.

[0141] Step c: Use a separable natural evolution strategy to minimize the loss function of the MLP in order to train the MLP.

[0142] Separable Natural Evolution Strategies (SNES) is a high-efficiency optimization algorithm based on natural evolution strategies. By assuming the separability of the parameter space, the updating process of the covariance matrix is simplified, and it is particularly suitable for high-dimensional optimization problems.

[0143] After using SNES to minimize the loss function to optimize the parameters to be fitted in the neural network, the expected MLP can be obtained by setting the expected energy and force accuracy.

[0144] When training the MLP using the first data set and the first parameter set, the first data set can be divided into a training set and a test set, and the ratio of the training set to the test set is, for example, 9 to 1. Then only the data in the training set and the parameters in the first parameter set are used for training, and the remaining data is used to test and verify the performance of the MLP.

[0145] It should be noted that the MLP in the embodiments of the present disclosure selects NEP, but it is not limited thereto. In other embodiments, other types of MLPs can also be selected. When using other types of MLPs, only step 202 needs to be modified in a similar manner, that is, other types of MLPs are different from NEP only in the training process.

[0146] In step 203, a second data set and a second parameter set corresponding to the second data set are obtained.

[0147] The related content of step 203 is described above with reference to step 103, and the detailed description is omitted here.

[0148] In step 204, the anisotropic interlayer potential function is fitted based on the second data set and the second parameter set.

[0149] Optionally, step 204 includes steps d-f as follows.

[0150] Step d: obtaining a second predicted parameter set.

[0151] The second predicted parameter set corresponds to the second parameter set.

[0152] The second predicted parameter set includes the interlayer potential of each bilayer van der Waals heterostructure predicted by the MLP.

[0153] Here, the second predicted parameter set is actually the parameter predicted by the ILP. For each bilayer van der Waals heterostructure in the second data set, the ILP will give a predicted value, and these predicted values constitute the second predicted parameter set.

[0154] With the iterative training of the ILP, the parameters in the second predicted parameter set will also be updated accordingly.

[0155] Optionally, in the second set of predicted parameters, the interlayer potential energy of the first bilayer van der Waals heterostructure is represented by Equation (6). Here, Equation (6) is the ILP that needs to be fitted.

[0156] (6)

[0157] In formula (6), ILP is used to predict the interlayer potential energy of the first bilayer van der Waals heterostructure. Represents the ILP prediction of the first The atom and the first The interlayer potential energy between atoms, where the first... The atom is an atom in the second monolayer van der Waals heterostructure, the... The atoms are atoms in the third monolayer van der Waals heterostructure. This indicates the number of atoms in the second monolayer van der Waals heterostructure (or the third monolayer van der Waals heterostructure). , It is an integer. The value range is 1 to , The value range is 1 to , This represents the total number of atoms in the second monolayer van der Waals heterostructure. This represents the total number of atoms in the third monolayer van der Waals heterostructure.

[0158] Optionally, the ILP prediction of the first The atom and the first Interlayer potential energy between atoms Calculated using formula (7)

[0159] (7)

[0160] In formula (7), For the first The atom and the first Position vectors between atoms For the first The normal vector of each atom, For the first The normal vector of each atom. Indicates the first The atom and the first The long-range van der Waals attraction terms between atoms are calculated using formula (8). Indicates the first The atom and the first The Pauli repulsion term between atoms is calculated using formula (9). This is a smooth cutoff function used to smoothly reduce the potential function and its derivative (up to the third order) to zero when the interatomic spacing exceeds the cutoff distance. For example, the cutoff distance is... ; The result is obtained using formula (12). The meanings of the other parameters in formula (7) are the same as those in formula (6), and are omitted here.

[0161] (8)

[0162] In formula (8), and , is the dimensionless number used to determine the steepness and starting position of the short-range Fermi-Dirac damping function; The van der Waals attraction coefficient. It is the sum of the effective balance van der Waals atomic radii. These four parameters are all the fitting parameters in ILP. The meanings of the other parameters in formula (8) are the same as in formula (7), and are omitted here.

[0163] (9)

[0164] In formula (9), It is a parameter that sets the steepness of the isotropic repulsion function. and An interaction range was defined. and These are constants used to define the repulsion of isotropic and anisotropic energy scales. These five parameters are all parameters to be fitted in ILP. For the first From the atom to the first The lateral distance of the normal vectors of each atom is calculated using formula (10). For the first From the atom to the first The lateral distance of the normal vectors of each atom is calculated using formula (11). The meanings of the other parameters in formula (9) are the same as those in formula (7), and are omitted here.

[0165] (10)

[0166] (11)

[0167] The meanings of the parameters in formulas (10) and (11) are the same as those in formulas (7) and (9), and will not be elaborated here.

[0168] (12)

[0169] In formula (12), is the cut-off distance. The meanings of other parameters in equation (12) are the same as those in equation (6) and equation (7), and are omitted here.

[0170] Step e, constructing an ILP objective function based on the second prediction parameter set and the second parameter set.

[0171] It can be seen from the above equations (6) to (12) that there are 9 parameters to be fitted in total in the ILP, which are uniformly represented as That is, the ILP can be a function with as the independent variable.

[0172] In this case, the ILP objective function is represented by equation (13).

[0173] (13)

[0174] In equation (13), is the ILP objective function, is the number of double-layer van der Waals heterostructures in the first sub-data set, is the weight corresponding to the th double-layer van der Waals heterostructure in the first sub-data set, is the interlayer potential of the th double-layer van der Waals heterostructure in the first sub-data set predicted by the ILP. is a parameter in the second parameter set, corresponds to , and represents the interlayer potential of the th double-layer van der Waals heterostructure in the first sub-data set calculated by the density functional theory (DFT). is the number of double-layer van der Waals heterostructures in the second sub-data set, is the weight corresponding to the th double-layer van der Waals heterostructure in the second sub-data set, is the interlayer potential of the th double-layer van der Waals heterostructure in the second sub-data set predicted by the ILP. is a parameter in the second parameter set, corresponds to , and represents the interlayer potential of the th double-layer van der Waals heterostructure in the second sub-data set calculated by DFT, represents the calculation of the L2 norm. Wherein, is an integer.

[0175] Wherein, the The equilibrium interlayer spacing of a bilayer van der Waals heterostructure can be represented as When the interlayer spacing of the bilayer van der Waals heterostructure is less than When the interlayer spacing of the bilayer van der Waals heterostructure is greater than or equal to , the bilayer van der Waals heterostructure is in a stable state. When the interlayer spacing of the bilayer van der Waals heterostructure is less than , the bilayer van der Waals heterostructure is in a metastable state. When the interlayer spacing of the bilayer van der Waals heterostructure is greater than or equal to , the bilayer van der Waals heterostructure is in a stable state. By setting the weight value in this way, the difference between the balanced binding energy curve (especially the large energy change in the sub-equilibrium region) and the relatively low energy fluctuation of the sliding potential energy surface can be reflected. Here, the binding energy change from 2 to 16 angstroms needs to be determined for each bilayer van der Waals heterostructure in the first sub-data set, so as to construct the corresponding binding energy curve (which is the interlayer potential energy). The interlayer potential energy of any bilayer van der Waals heterostructure in the second sub-data set is the sliding potential energy surface.

[0176] Step f, based on the ILP objective function, the parameters of ILP are fitted by least square method algorithm.

[0177] By least square method algorithm to minimize ILP objective function, can realize nonlinear fitting calibration ILP in 9 parameters to be fitted, thus obtains ILP.

[0178] After the ILP fitting is completed, the ILP can be used to simulate the interlayer potential energy of the van der Waals heterostructure.

[0179] After the ILP fitting is completed, the ILP can be used to simulate the interlayer potential energy of the van der Waals heterostructure.

[0180] In step 205, the ILP is fitted based on the many-body effect to obtain the transition state ILP.

[0181] For most application scenarios, such as describing the boundary local deformation of van der Waals layered materials, edge chemical groups and pinning effect, etc., the MLP in step 103 and the ILP in step 105 can be directly combined together, and the "layer" descriptor is used to distinguish the MLP and the ILP, so that they respectively describe the intralayer and interlayer interaction of the van der Waals heterostructure.

[0182] However, if the simulation process needs to consider the bond-breaking process of edge dangling bonds or the case of oxygen-containing edge chemical groups, the direct combination of MLP and ILP is no longer applicable, and the transition state of the intralayer to interlayer interaction needs to be considered.

[0183] ​When considering transition states, for MLP, it is only necessary to ensure that the training and validation sets contain structural data of the transition states when calculating the first parameter set, without modifying the training process. For ILP, however, it is necessary to introduce multibody effects to simulate the continuous transition situation, thereby obtaining the transition state ILP.

[0184] Optionally, the transition state ILP is represented by formula (14).

[0185] (14)

[0186] In formula (14), For the transition state ILP, Indicates the first The atom and the first The transition potential energy between atoms is calculated using formula (15). The meanings of the other parameters in formula (14) are the same as those in formulas (6) and (7), and are omitted here in detail.

[0187] (15)

[0188] In formula (15), The transition function is represented by formula (16). For the first The atom and the first The many-body effect under the condition of minimum distance between atoms is expressed by formula (20). Let the key weight function be the key weight function, which guarantees the first key weight function. The atom and the first When atoms are directly adjacent and bonded, the contribution of ILP is 0. The meanings of other parameters in formula (15) are the same as those in formulas (7) and (14), and are omitted here.

[0189] (16)

[0190] In formula (16), As the independent variable, it can be replaced by the one in formula (15) above. and . The step function is represented by formula (17). The meanings of the other parameters in formula (16) are the same as those in formula (15), and are omitted here.

[0191] (17)

[0192] In formula (17), It is a step function. As the independent variable, It can be replaced with the formula (16) above. .

[0193] Furthermore, all parameters input into the transition function in formula (15) need to be normalized, that is... and Normalization is required. The normalization process is represented by formula (18). The normalization process is represented by formula (19).

[0194] (18)

[0195] (19)

[0196] In formula (18), After normalization , To switch regions, and The boundary value for the switching region. In formula (19), After normalization , for The minimum value, for The maximum value of . The meanings of the other parameters in formulas (18) and (19) are the same as those in formula (15), and are omitted here.

[0197] The switching region is defined as the portion considered to be the interlayer distance, and it needs to be determined in conjunction with the potential energy curve. When determining the switching region, the following conditions must be met: the minimum value of the ILP potential well is not disturbed by the unswitched region, and when ILP interactions are turned off, no artificial reaction barrier is generated within a short distance due to ILP repulsion.

[0198] (20)

[0199] In formula (20), For the first The atom and the first The many-body effect between atoms is calculated using formula (21). Indicates the first The atom and the first The case where the distance between atoms is minimized. The meanings of the other parameters in formula (20) are the same as in formula (15), and are omitted here in detail.

[0200] (twenty one)

[0201] The many-body effect can be described by bond order, which is given by formula (21) In formula (21), and is a covalent bond interaction term, is a contribution of radical and conjugation effect, is a contribution of torsion potential.

[0202] where the covalent bond interaction term takes into account the influence of local coordination number and bond angle by introducing a bond weight function and a bond angle penalty function. The bond weight function is used to smoothly transition between bonding and non-bonding interactions, and the bond angle penalty function avoids local energy being too large due to too small bond angle.

[0203] The calculation method of the many-body effect is more in the related art, which is omitted here. For the many-body effect between any group of the i-th atom and the j-th atom, it can be directly calculated.

[0204] In this way, the expression of the transition state ILP can be obtained by combining the above formula (14) to formula (21). By fitting the expression of the transition state ILP in the same way as in step 204, the values of each to-be-fitted parameter in the transition state ILP can be determined.

[0205] In step 206, a first function is obtained based on the MLP and the transition state ILP.

[0206] The first function is used to simulate the transition state mixed potential of the in-plane to interlayer interaction of the van der Waals heterostructure.

[0207] The MLP here is the MLP that ensures that the structure data containing the transition state in the training and validation sets in the calculation of the first parameter set.

[0208] Optionally, the first function is expressed by formula (22).

[0209] (22)

[0210] In formula (22), is the first function, is the MLP, is the transition state ILP. The meanings of the parameters in formula (22) are the same as those in formula (2) and formula (14), which are omitted here.

[0211] The first function is equivalent to organically combining the MLP and the transition state ILP under the transition state, so as to accurately simulate the transition state mixed potential of the in-plane to interlayer interaction.

[0212] ​​Figure 3 is a comparison chart of the calculation consumption of machine learning potential and empirical potential at the same time. Among them, SW, REBO are empirical potential, NEP, DP, GAP are machine learning potential, REBO+LJ is the way of simulating potential field in the related art, and NEP+ILP is the way of simulating potential field in the embodiment of the present disclosure. Here, the calculation consumption of SW is taken as the benchmark, it can be seen that the calculation consumption of NEP is the least among the three machine learning potentials, that is, the calculation efficiency of NEP is the highest.

[0213] Figure 4 is a schematic diagram of the phonon spectrum of graphite fitted by different methods. The phonon spectrum is the relationship between the energy and momentum of the crystal phonon, that is, the dispersion relationship of lattice vibration. The phonon spectrum gives the vibration characteristics of the crystal, and if the vibration characteristics of the crystal are to be accurately described, the interlayer potential and intralayer potential must be accurately described. That is, the more accurate the simulated intralayer potential and interlayer potential, the more accurate the fitted phonon spectrum of graphite, and the accuracy of the phonon spectrum of graphite can indirectly reflect the accuracy of the simulated intralayer potential and interlayer potential. As shown in Figure 4 , the hollow circle part is the measured value (the experimental data is derived from inelastic X-ray scattering measurement), the solid line part is the phonon spectrum of graphite fitted by the NEP+ILP framework in the embodiment of the present disclosure, and the dotted line part is the phonon spectrum of graphite fitted by the REBO+LJ way in the related art. By comparison, it is found that the phonon spectrum simulated by the scheme proposed in the embodiment of the present disclosure is highly consistent with the experimental data in the low frequency and high frequency regions of the phonon spectrum, especially in the description of the interlayer vibration mode. In contrast, the prediction of REBO+LJ potential in the low frequency and high frequency regions has a large deviation from the experimental data, indicating that it has limitations in describing the interlayer and intralayer interaction.

[0214] In combination with Figure 3 and Figure 4 It can be seen that the calculation consumption required by the NEP+ILP framework in the embodiment of the present disclosure is only more than that of the REBO+LJ in the related art by a part (this part of calculation consumption is acceptable), but the accuracy of the fitted potential field in the embodiment of the present disclosure is higher, so the calculation framework proposed in the present disclosure takes into account the efficiency and accuracy.

[0215] The following is a device embodiment of the present application. For details not described in detail in the device embodiment, please refer to the above method embodiment.

[0216] Figure 5 shows a structure schematic diagram of a van der Waals heterostructure potential field simulation device provided by one example embodiment of the present disclosure. Referring to Figure 5The Van der Waals heterostructure potential field simulation device 500 comprises a first acquisition module 501, a training module 502, a second acquisition module 503, a first fitting module 504, a second fitting module 505, and a simulation module 506.

[0217] The first acquisition module 501 is configured to acquire a first data set and a first parameter set corresponding to the first data set, the first data set comprising a plurality of different single-layer Van der Waals heterostructures, and the first parameter set comprising an intra-layer potential energy of each single-layer Van der Waals heterostructure, a resultant force of each atom in each single-layer Van der Waals heterostructure, and a virial stress tensor of each atom in each single-layer Van der Waals heterostructure.

[0218] The training module 502 is configured to train a machine learning potential function MLP based on the first data set and the first parameter set, the MLP being used to simulate the intra-layer potential energy of the Van der Waals heterostructure.

[0219] The second acquisition module 503 is configured to acquire a second data set and a second parameter set corresponding to the second data set, the second data set comprising a plurality of different double-layer Van der Waals heterostructures, and the second parameter set comprising an inter-layer potential energy of each double-layer Van der Waals heterostructure in the second data set.

[0220] The first fitting module 504 is configured to fit an anisotropic inter-layer potential function ILP based on the second data set and the second parameter set, the ILP being used to simulate the inter-layer potential energy of the Van der Waals heterostructure.

[0221] The second fitting module 505 is configured to fit the ILP based on a many-body effect to obtain a transition state ILP.

[0222] The simulation module 506 is configured to obtain a first function based on the MLP and the transition state ILP, the first function being used to simulate a transition state mixed potential energy of the intra-layer to inter-layer interaction of the Van der Waals heterostructure.

[0223] Optionally, the training module 502 is further configured to acquire a first predicted parameter set, the first predicted parameter set corresponding to the first parameter set, the first predicted parameter set comprising an intra-layer potential energy of each single-layer Van der Waals heterostructure predicted by the MLP, a resultant force of each atom in each single-layer Van der Waals heterostructure predicted by the MLP, and a virial stress tensor of each atom in each single-layer Van der Waals heterostructure predicted by the MLP; construct a loss function of the MLP based on the first parameter set and the first predicted parameter set; and minimize the loss function of the MLP by using a separable natural evolution strategy to train the MLP.

[0224] Optionally, the MLP is a neural network potential function NEP, and the training module 502 is further configured to: process the first data set by using a single-hidden-layer feedforward neural network to obtain a feature descriptor of atomic coordinates of each atom of each single-layer van der Waals heterostructure in the first data set; and obtain the first prediction parameter set based on the feature descriptor.

[0225] Optionally, the first fitting module 504 is further configured to: obtain a second prediction parameter set, the second prediction parameter set corresponding to the second parameter set, the second prediction parameter set including an interlayer potential energy of each double-layer van der Waals heterostructure predicted by the MLP; construct an ILP objective function based on the second prediction parameter set and the second parameter set; and fit parameters of the ILP by using a least square method algorithm based on the ILP objective function.

[0226] It should be noted that: when the van der Waals heterostructure potential field simulation device provided in the above embodiments performs van der Waals heterostructure potential field simulation, only the division of the above functional modules is exemplified, and in actual application, the above functions can be distributed to different functional modules to complete all or part of the functions described above, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the van der Waals heterostructure potential field simulation device and the van der Waals heterostructure potential field simulation method provided in the above embodiments belong to the same concept, and the specific implementation process is detailed in the method embodiments, which will not be repeated here.

[0227] The division of the modules in the embodiments of the present disclosure is illustrative, and is only a logical function division. In actual implementation, another division mode can also be used. In addition, each functional module in each embodiment of the present disclosure can be integrated in one processor, or can be physically separated, or two or more modules can be integrated into one module. The integrated module can be realized in the form of hardware or in the form of a software functional module.

[0228] When the integrated module is realized in the form of a software functional module and sold or used as an independent product, it can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present disclosure essentially or the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing an end device (which can be a personal computer, a mobile phone, or a communication device, etc.) or a processor to execute all or part of the steps of the method of each embodiment of the present disclosure. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0229] Figure 6 is a structural schematic diagram of a computer device provided by an embodiment of the present disclosure. As shown in the figure, the computer device 600 includes a processor 601 and a memory 602. Figure 6

[0230] The processor 601 can include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor 601 can be implemented in at least one of a hardware form of a DSP (Digital Signal Processing), an FPGA (Field-Programmable Gate Array), a PLA (Programmable Logic Array). The processor 601 can also include a main processor and a coprocessor, the main processor is a processor for processing data in an awake state, also known as a CPU (Central Processing Unit), and the coprocessor is a low-power processor for processing data in a standby state. In some embodiments, the processor 601 can be integrated with a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content required to be displayed by the display screen. In some embodiments, the processor 601 can also include an AI (Artificial Intelligence) processor, which is used to process machine learning-related computing operations.

[0231] The memory 602 can include one or more computer-readable storage media, which can be non-transitory. The memory 602 can also include a high-speed random access memory, and a non-volatile memory such as one or more disk storage devices, flash storage devices. In some embodiments, the non-transitory computer-readable storage medium in the memory 602 is used to store at least one instruction for being executed by the processor 601 to implement the van der Waals heterostructure potential field simulation method provided in the embodiments of the present disclosure.

[0232] Those skilled in the art can understand that the structure shown in the figure does not constitute a limitation on the computer device 600, and can include more or fewer components than the figure, or combine certain components, or use different component arrangements. Figure 6

[0233] ​​The embodiment of the present disclosure further provides a non-transitory computer-readable storage medium, when instructions in the storage medium are executed by a processor of a computer device, the computer device is enabled to perform the van der Waals heterostructure potential field simulation method provided in the embodiment of the present disclosure.

[0234] The embodiment of the present disclosure further provides a computer program product, comprising computer programs / instructions, when the computer programs / instructions are executed by a processor, the van der Waals heterostructure potential field simulation method provided in the embodiment of the present disclosure is realized.

[0235] The above merely provides optional embodiments of the present disclosure, and is not intended to limit the present disclosure, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for simulating the potential field of van der Waals heterostructures, characterized in that, The method comprises: obtaining a first data set and a first parameter set corresponding to the first data set, the first data set comprising a plurality of different single-layer van der Waals heterostructures, and the first parameter set comprising an intra-layer potential energy of each single-layer van der Waals heterostructure, a resultant force on each atom in each single-layer van der Waals heterostructure, and a virial stress tensor of each atom in each single-layer van der Waals heterostructure; training a machine learning potential function MLP based on the first data set and the first parameter set, the MLP being used to simulate an intra-layer potential energy of a van der Waals heterostructure; obtaining a second data set and a second parameter set corresponding to the second data set, the second data set comprising a plurality of different double-layer van der Waals heterostructures, and the second parameter set comprising an inter-layer potential energy of each double-layer van der Waals heterostructure in the second data set; fitting an anisotropic inter-layer potential function ILP based on the second data set and the second parameter set, the ILP being used to simulate an inter-layer potential energy of a van der Waals heterostructure; fitting the ILP based on a many-body effect to obtain a transition state ILP; obtaining a first function based on the MLP and the transition state ILP, the first function being used to simulate a transition state mixed potential energy of an intra-layer to inter-layer interaction of a van der Waals heterostructure.

2. The method of claim 1, wherein, The training of the machine learning potential function MLP based on the first data set and the first parameter set comprises: obtaining a first predicted parameter set corresponding to the first parameter set, the first predicted parameter set comprising an intra-layer potential energy of each single-layer van der Waals heterostructure predicted by the MLP, a resultant force on each atom in each single-layer van der Waals heterostructure predicted by the MLP, and a virial stress tensor of each atom in each single-layer van der Waals heterostructure predicted by the MLP; constructing a loss function of the MLP based on the first parameter set and the first predicted parameter set; minimizing the loss function of the MLP by using a separable natural evolution strategy to train the MLP.

3. The method of claim 2, wherein, The MLP is a neural network potential function NEP, and the obtaining of the first predicted parameter set comprises: processing the first data set by using a single-hidden-layer feedforward neural network to obtain a feature descriptor of atomic coordinates of each atom of each single-layer van der Waals heterostructure in the first data set; obtaining the first predicted parameter set based on the feature descriptor.

4. The method of claim 3, wherein, A first single-layer van der Waals heterostructure is any single-layer van der Waals heterostructure in the first data set, and in the first predicted parameter set, the intra-layer potential energy of the first single-layer van der Waals heterostructure predicted by the MLP is represented by the following formula: wherein E MLP a first single-layer van der Waals heterostructure is predicted by the MLP, E i is the energy of the i-th atom in the first single-layer van der Waals heterostructure, the single-hidden-layer feedforward neural network comprises N neu neurons, is a connection weight matrix corresponding to the μ-th neuron, μ ranges from 1 to N neu , each of the single-layer van der Waals heterostructures comprises N des feature descriptors, is a connection weight vector corresponding to the μ-th neuron and the v-th feature descriptor, v ranges from 1 to N des , is a bias vector corresponding to the μ-th neuron, b (1) is a bias term, is a feature descriptor of the atomic coordinates of the i-th atom, tanh is a hyperbolic tangent activation function, i ranges from 1 to N, N is the total number of atoms in the first single-layer van der Waals heterostructure, and i, μ, and v are all integers. In the first predicted parameter set, the resultant force on the i-th atom of the first single-layer van der Waals heterostructure predicted by the MLP is represented by the following formula: wherein, F is the resultant force on the i-th atom of the first monolayer van der Waals heterostructure, ij E is the force on the i-th atom by the j-th atom in the first monolayer van der Waals heterostructure, j E is the energy of the j-th atom, r ij r is the position vector of the i-th atom relative to the j-th atom, r ji r is the position vector of the j-th atom relative to the i-th atom, j is an integer, j ranges from 1 to N and j is not equal to i; In the first predicted parameter set, the virial stress tensor of the i-th atom of the first single-layer van der Waals heterostructure predicted by the MLP is represented by the following formula: where W i MLP is the Weissenberg stress tensor for the i-th atom of the first monolayer van der Waals heterostructure.

5. The method of claim 4, wherein, The loss function of the MLP is represented by the following formula: wherein L(z) is a loss function of the MLP, E MLP (n) is an intra-layer potential energy of the n-th single-layer van der Waals heterostructure in the first data set, E DFT (n) is a parameter in the first parameter set, E DFT (n) and E MLP (n) corresponds to the intra-layer potential energy of the n-th single-layer van der Waals heterostructure in the first data set calculated by using the density functional theory (DFT), F i DFT is a parameter in the first parameter set, F i DFT and F i MLP corresponds to the resultant force on the i-th atom in the first single-layer van der Waals heterostructure calculated by using the DFT, W i DFT (n) is a parameter in the first parameter set, W i DFT (n) and W i MLP (n) corresponds to W i DFT (n) represents the normal force stress tensor of the i-th atom in the n-th single-layer van der Waals heterostructure in the first data set calculated by using the DFT, N str represents the total number of single-layer van der Waals heterostructures in the first data set, and the value range of n is 1 to N str , z u is a parameter vector, and the parameter vector includes a connection weight matrix corresponding to the μ-th neuron a connection weight vector corresponding to the μ-th neuron and the v-th feature descriptor a bias vector corresponding to the μ-th neuron the bias b (1) and a to-be-fitted parameter in each of the feature descriptors, N par is a dimension of the parameter vector z u u is an integer, and the value range of u is 1 to N par , λ e , λ f , λ v λ1 and λ2 are neural network hyperparameters.

6. The method of claim 1, wherein, The anisotropic interlayer potential function ILP is fitted based on the second data set and the second parameter set, including: obtaining a second prediction parameter set corresponding to the second parameter set, the second prediction parameter set including the interlayer potential of each double-layer van der Waals heterostructure predicted by the MLP; based on the second prediction parameter set and the second parameter set, constructing an ILP objective function; based on the ILP objective function, fitting the parameters of the ILP using a least squares method algorithm.

7. The method of claim 6, wherein, The first double-layer van der Waals heterostructure is any double-layer van der Waals heterostructure in the second data set, and the first double-layer van der Waals heterostructure includes a second single-layer van der Waals heterostructure and a third single-layer van der Waals heterostructure, The ILP is expressed by the following formula: wherein V ILP is the ILP for predicting the interlayer potential energy of the first bilayer van der Waals heterostructure, represents the interlayer potential energy between the ath atom in the second monolayer van der Waals heterostructure and the bth atom in the third monolayer van der Waals heterostructure predicted by the ILP, wherein a and b are integers, a ranges from 1 to n1, b ranges from 1 to n2, n1 is the total number of atoms in the second monolayer van der Waals heterostructure, and n2 is the total number of atoms in the third monolayer van der Waals heterostructure. The interlayer potential between the a-th atom and the b-th atom predicted by the ILP is calculated by the following formula: where r ab is the position vector between the a-th atom and the b-th atom, n a is the normal vector of the a-th atom, n b is the normal vector of the b-th atom, V att (r ab ) represents a long-range van der Waals attraction term between the a-th atom and the b-th atom, V rep (r ab , n a , n b ) represents a Pauli repulsion term between the a-th atom and the b-th atom, Tap(r ab ) is a smooth cutoff function that smoothly reduces the potential function and its derivatives (up to third order) to zero when the interatomic distance exceeds a cutoff distance.

8. The method of claim 7, wherein, The second data set includes a first sub-data set and a second sub-data set, the first sub-data set includes a plurality of double-layer van der Waals heterostructures under different interlayer spacings, and the second sub-data set includes a plurality of double-layer van der Waals heterostructures under different horizontal slips at the equilibrium interlayer spacing, The ILP objective function is expressed by the following formula: wherein Φ(ξ) is the ILP objective function, M c is the number of bilayer van der Waals heterostructures in the first sub-data set, is the weight corresponding to the m-th bilayer van der Waals heterostructure in the first sub-data set, m is an integer, is the interlayer potential energy of the m-th bilayer van der Waals heterostructure in the first sub-data set predicted by the ILP, is a parameter in the second parameter set, corresponds to, , denotes the interlayer potential energy of the m-th bilayer van der Waals heterostructure in the first sub-data set calculated by the density functional theory (DFT), M s is the number of bilayer van der Waals heterostructures in the second sub-data set, is the weight corresponding to the m-th bilayer van der Waals heterostructure in the second sub-data set, is the interlayer potential energy of the m-th bilayer van der Waals heterostructure in the second sub-data set predicted by the ILP, is a parameter in the second parameter set, corresponds to, denotes the interlayer potential energy of the m-th bilayer van der Waals heterostructure in the second sub-data set calculated by the DFT, ||·||2 denotes the calculation of L2 norm.

9. The method of claim 7, wherein, The transition state ILP is expressed by the following formula: wherein E ILP is the transition state ILP for the a-th atom, represents the transition state potential between the a-th atom and the b-th atom. The transition state potential between the a-th atom and the b-th atom is expressed by the following formula: where S(·) is a transition function, C is the many-body effect for the case of minimum distance between the a-th atom and the b-th atom ab is a bond order function.

10. A van der Waals heterostructure potential field simulation apparatus, characterized by, The device includes: The first acquisition module is configured to acquire a first data set and a first parameter set corresponding to the first data set, the first data set including a plurality of different single-layer van der Waals heterostructures, and the first parameter set including the intra-layer potential of each single-layer van der Waals heterostructure, the resultant force on each atom in each single-layer van der Waals heterostructure, and the virial stress tensor of each atom in each single-layer van der Waals heterostructure; The training module is configured to train a machine learning potential function MLP based on the first data set and the first parameter set, the MLP being used to simulate the intra-layer potential of a van der Waals heterostructure; The second acquisition module is configured to acquire a second data set and a second parameter set corresponding to the second data set, the second data set including a plurality of different double-layer van der Waals heterostructures, and the second parameter set including the interlayer potential of each double-layer van der Waals heterostructure in the second data set; The first fitting module is configured to fit an anisotropic interlayer potential function ILP based on the second data set and the second parameter set, the ILP being used to simulate the interlayer potential of a van der Waals heterostructure; The second fitting module is configured to fit the ILP based on the many-body effect to obtain a transition state ILP; The simulation module is configured to obtain a first function based on the MLP and the transition state ILP, the first function being used to simulate the transition state mixed potential energy of the intra-layer to inter-layer interaction of a van der Waals heterostructure.

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