Potential function model construction and training method, system and device and storage medium

Abstract

The invention relates to a potential function model construction method, system and device and a storage medium, and belongs to the technical field of digital data processing. The construction method of the potential function model comprises the following steps: determining a neighbor atom set for each atom in an atom system according to a truncation radius; constructing a neighbor environment descriptor of each atom based on the neighbor atom set of each atom; inputting the neighbor environment descriptor of each atom into an independently configured neural network corresponding to the element type of the neighbor environment descriptor, and performing forward propagation calculation from an input layer to an output layer of the neural network to obtain energy of each atom; performing back propagation calculation and descriptor back calculation on the energy of each atom from the output layer to the input layer through each independently configured neural network to obtain partial derivative of the energy of each atom to the position of the adjacent atom; and obtaining the stress of each atom based on the partial derivative of the energy of each atom to the position of the adjacent atom. The potential function model has both precision and calculation efficiency.

Description

Construction, training methods, systems, devices, and storage media of potential function models Technical Field

[0001] This invention relates to the field of digital data processing technology, and in particular to a method, system, device, and storage medium for constructing and training a potential function model. Background Technology

[0002] Molecular dynamics (MD) simulation is an important computational method for studying the structure and properties of materials at the atomic scale. It numerically solves for the motion of atoms or molecules under the influence of interaction forces, thereby obtaining the structural evolution and physical properties of material systems under different temperatures, pressures, and external fields. This method has been widely applied in fields such as metallic materials, semiconductor materials, ceramic materials, and nanomaterials, and is of great significance in studying the mechanical behavior, thermal properties, defect evolution, phase transition processes, and interface behavior of materials.

[0003] In molecular dynamics (MD) simulations, interatomic interactions are typically described using potential functions. These potential functions characterize the potential energy surface (PES) of the system, thereby determining the interaction forces experienced by each atom. Their accuracy and applicability directly determine the reliability of the MD simulation results. Therefore, the construction and selection of potential functions is one of the core issues in molecular dynamics simulations.

[0004] Traditional classical potential functions are typically constructed based on empirical or semi-empirical methods. For example, a fixed functional form and parameter expression are pre-defined, and then the parameters are manually fitted and adjusted based on different material systems or structural conditions. The advantages of classical potential functions are their fast computation and ability to perform large-scale simulations in molecular dynamics (MD) simulations; generally, classical potentials can simulate millions of atoms at the scale of hundreds of nanoseconds. However, the disadvantages of classical potentials are also significant: insufficient accuracy, simulation results often deviating greatly from reality, poor generalization ability, and a significantly limited scope of application.

[0005] Compared to empirical potential functions, first-principles calculation methods (such as density functional theory, DFT) can provide a more accurate description of atomic-scale interactions without the need for empirical parameters. However, first-principles methods are computationally expensive and difficult to apply directly to dynamic simulations of large-scale atomic systems or long-term timescales, thus being constrained by computational resources and efficiency in practical materials simulations.

[0006] To overcome the shortcomings of insufficient accuracy in traditional potential functions and the high computational cost of first-principles methods, machine learning-based potential function modeling techniques have gradually emerged in recent years. These techniques learn the mapping relationship between atomic structure and system energy, atomic forces, and stress from a large amount of first-principles calculation data, thereby constructing an interatomic interaction model without pre-setting a specific potential function form. Currently, the performance evaluation of machine learning potential functions mainly focuses on two core metrics: computational efficiency (call speed) and prediction accuracy (the error between the result and the first-principles calculation, usually characterized by mean absolute error (MAE)).

[0007] In existing technologies, typical machine learning potential models include those built based on local descriptors and neural networks, such as DeepMD, MTP, GAP, and ANI. While maintaining high accuracy, these models are typically 100 to 1000 times more computationally efficient than traditional classical potential functions, meaning their computational complexity is significantly higher. However, they can still support molecular dynamics simulations at the scale of tens of thousands of atoms and nanosecond timescales, thus possessing certain practical applications in engineering calculations.

[0008] In terms of accuracy, higher potential function prediction accuracy usually means a reduction in the amount of first-principles data required in the potential function construction stage, greater system stability during molecular dynamics simulations, and simulation results that are closer to experimental phenomena or high-precision theoretical calculations. However, in complex systems, such as organic polymer systems, high-entropy alloy systems, or multi-component disordered systems, the expressive power of existing typical machine learning potential functions is still insufficient due to the highly complex interatomic interactions and drastic changes in the local environment, making it difficult to further reduce prediction errors.

[0009] To enhance model expressiveness, high-order model architectures based on equivariant message passing mechanisms have emerged in recent years, such as MACE, Allegro, and NequIP. These models significantly enhance their ability to express complex local environments by explicitly constructing tensor equivariant features and multibody coupling terms. On most public test sets, their mean absolute error (MAE) can be reduced to about half or even one-third of that of traditional models, demonstrating excellent prediction accuracy. However, these high-precision models typically require high-order tensor feature propagation and multi-layer message passing calculations, significantly increasing computational complexity. The computation time is usually about 1000 to 10000 times that of classical potential functions, limiting their practical application to simulations of systems at the thousand-atom scale and making it difficult to meet the demands of large-scale molecular dynamics calculations.

[0010] Therefore, existing machine learning potential function techniques generally exhibit the following development trends and technical contradictions: traditional models based on fixed descriptors have high computational efficiency, but their accuracy improvement is limited in complex systems; high-order models based on equivariant tensor message passing have higher prediction accuracy, but their computational cost increases significantly, limiting large-scale simulation applications.

[0011] In other words, existing technologies face the challenge of balancing model expressiveness and computational efficiency. Improving expressiveness often comes at the cost of computational speed, while increasing computational efficiency can limit accuracy. Therefore, achieving a machine learning potential function model that balances high accuracy and high efficiency has become a pressing technical problem to be solved in this field. Summary of the Invention

[0012] To address the technical problems existing in the prior art, this invention proposes a method, system, device, and storage medium for constructing a potential function model, which combines accuracy and computational efficiency.

[0013] According to one aspect of the present invention, a method for constructing a potential function model is provided. The potential function model is used to predict the energy of an atomic system and the forces acting on atoms. The method includes: determining a set of nearest-neighbor atoms for each atom in the atomic system based on a cutoff radius; constructing a nearest-neighbor environment descriptor for each atom based on the position information and element type information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, wherein the nearest-neighbor environment descriptor satisfies symmetry; inputting the nearest-neighbor environment descriptor of each atom into an independently configured neural network corresponding to its element type, and calculating the energy of each atom through forward propagation from the input layer to the output layer of the neural network; summing the energies of all atoms in the atomic system to obtain the energy of the atomic system; performing backward propagation calculation of the energy of each atom from the output layer to the input layer through each independently configured neural network to obtain the partial derivative of the energy of each atom with respect to its nearest-neighbor environment descriptor; performing backward calculation of the nearest-neighbor environment descriptor on the partial derivative of the energy of each atom with respect to the position of its nearest-neighbor atoms to obtain the partial derivative of the energy of each atom with respect to the position of its nearest-neighbor atoms; and obtaining the forces acting on each atom based on the partial derivative of the energy of each atom with respect to the position of its nearest-neighbor atoms.

[0014] Optionally, when determining the nearest neighbor atom set for each atom in the atomic system based on the cutoff radius, multiple nearest neighbor atom sets with different cutoff radii are determined for each atom in the atomic system; correspondingly, when constructing the nearest neighbor environment descriptor for each atom, the corresponding nearest neighbor environment descriptor is constructed based on the nearest neighbor atom sets with different cutoff radii, and all the nearest neighbor environment descriptors with different cutoff radii are concatenated as the final nearest neighbor environment descriptor.

[0015] Optionally, when constructing a nearest-neighbor environment descriptor for each atom based on the position information and element type information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, a first type of descriptor and / or a second type of descriptor are constructed respectively. The first type of descriptor has more information than the second type of descriptor. When the first type of descriptor and the second type of descriptor are constructed, the first type of descriptor and the second type of descriptor are concatenated as the final nearest-neighbor environment descriptor.

[0016] Optionally, when constructing the first type of descriptor based on the position information and element type information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, the nearest-neighbor environment descriptor of each atom is constructed based on the following formula (1-1): (1-1) Wherein, Here, represents the nearest neighbor environment descriptor for target atom i, where i represents the target atom index (i = 0, 1, 2, 3, 4, ..., N-1), N is the total number of atoms in the atomic system, k represents the dimensional index for element type expansion (k = 0, 1), and n represents the radial order (n = 0, 1, 2, 3, 4, ...). ; l represents the angular order, l = 0, 1, 2, 3, 4, ... ; m represents the angular component number, m = -l, -l+1, ..., l; The atomic expansion coefficient is shown in formula (1-2); The atomic expansion coefficients are complex conjugates; (1-2) Wherein, This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ... ; This represents the total number of elemental species in the atomic system. The weights representing the extended information of element types, when k=0, When k=1, ; Represents spherical harmonic functions. This indicates the direction from target atom i to its nearest neighbor atom j; The radial basis functions are represented as shown in equation (1-3): (1-3) This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of target atom i. j Represents the coordinates of the nearest neighbor atom j; Represents a Chebyshev polynomial of the first kind; The smooth cutoff function is shown in formula (1-4): (1-4).

[0017] Alternatively, real spherical harmonics can be used according to the following formula (1-5). Calculate the spherical harmonic function : (1-5) Optionally, when constructing the second type of descriptor based on the position information and element type information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, the nearest-neighbor environment descriptor of each atom is constructed based on the following formula (2-1): (2-1) Wherein, Here, represents the nearest neighbor environment descriptor for target atom i, where i represents the target atom index (i = 0, 1, 2, 3, 4, ..., N), N is the total number of atoms in the atomic system, k represents the dimensional index for element type expansion (k = 0, 1), and n represents the radial order (n = 0, 1, 2, 3, 4, ...). ; This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ... ; This represents the total number of elemental species in the atomic system. The weights representing the extended information of element types, when k=0, When k=1, ; The radial basis functions are represented as shown in equation (1-3): (1-3) This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of target atom i. j Represents the coordinates of the nearest neighbor atom j; For a Chebyshev polynomial of the first kind; indicating The smooth cutoff function is shown in formula (1-4): (1-4).

[0018] Optionally, the weight of element type extended information Replace with the value calculated according to the following formula (2-2): (2-2) Wherein, The Kronecker symbol indicates that the element type number is One-hot encoding is performed on the category information, where k = 0, 1, 2, ... .

[0019] According to another aspect of the present invention, a potential function model construction system is provided, the potential function model being used to predict the energy and forces acting on atoms in an atomic system. The system includes: a nearest-neighbor atom set construction module, configured to determine a nearest-neighbor atom set for each atom in the atomic system based on a cutoff radius; a descriptor construction module, configured to construct a nearest-neighbor environment descriptor for each atom based on the positional information and elemental information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, the nearest-neighbor environment descriptor satisfying symmetry; and a neural network module, configured to input the nearest-neighbor environment descriptor of each atom into an independently configured neural network corresponding to its elemental type, and pass the descriptor from the input layer of the neural network to... The forward propagation of the output layer calculates the energy of each atom; the backward propagation of each atom's energy from the output layer to the input layer is performed through each independently configured neural network to obtain the partial derivative of each atom's energy with respect to its nearest neighbor environment descriptors; an energy calculation module is configured to sum the energies of all atoms in the atomic system to obtain the energy of the atomic system; a descriptor backward calculation module is configured to perform backward calculation of the nearest neighbor environment descriptors for the partial derivative of each atom's energy with respect to its nearest neighbor atom positions to obtain the partial derivative of each atom's energy with respect to its nearest neighbor atom positions; and an atom force calculation module is configured to obtain the force on each atom based on the partial derivative of each atom's energy with respect to its nearest neighbor atom positions.

[0020] According to another aspect of the present invention, the present invention also provides a training method for a potential function model constructed by the aforementioned method, comprising the following steps: obtaining samples from a sample set, wherein the samples are arbitrary atomic configuration samples containing atomic position information and element type information, one atomic configuration sample corresponds to one atomic system, and the sample labels include the energy of the atomic configuration, the atomic force, and the system stress; obtaining the energy of each atom, the atomic force, and the energy of each sample based on the potential function model constructed by the aforementioned method; calculating the system stress of the sample based on the atomic force; calculating at least the weighted sum of the energy loss value, the force loss value, and the system stress loss value as the total loss value for this round of training based on the sample labels and the loss function; evaluating whether a preset termination condition is met, and ending the training process in response to meeting the preset termination condition; in response to not meeting the preset termination condition, performing backpropagation calculation on the total loss value according to the respective calculation processes of energy and atomic force, and accumulating the calculation results to obtain the gradient of the total loss value with respect to the parameters of each layer of the neural network; and optimizing the neural network parameters by an optimizer based on the gradient of the total loss value with respect to the parameters of each layer of the neural network.

[0021] According to another aspect of the present invention, the present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a set of computer program instructions that, when the processor executes the set of computer program instructions in the memory, implement the aforementioned potential function model construction method or potential function model training method.

[0022] According to another aspect of the present invention, the present invention also provides a computer-readable storage medium, wherein a computer program instruction set is stored on the computer-readable storage medium, and the computer program instruction set, when executed by a processor, implements the aforementioned potential function model construction method or potential function model training method.

[0023] According to another aspect of the present invention, the present invention also provides a computer program product comprising a computer program instruction set, which, when executed by a processor, implements the aforementioned potential function model construction method or potential function model training method.

[0024] The nearest neighbor environment descriptor constructed in this invention has a strong ability to describe atomic information and high prediction accuracy of the potential function model. It makes full use of multi-layer neural networks to calculate the forces on atoms, resulting in fast calculation speed and high efficiency. Attached Figure Description

[0025] The preferred embodiments of the present invention will now be described in further detail with reference to the accompanying drawings, in which: Figure 1 is a flowchart of a potential function model construction method according to an embodiment of the present invention; Figure 2 is a flowchart of a method for determining a set of nearest-neighbor atoms according to an embodiment of the present invention; Figure 3 is a partial schematic diagram of an atomic system when determining the set of nearest-neighbor atoms of a target atom i according to an embodiment of the present invention; Figure 4 is a schematic diagram of the calculation path of atomic force according to an embodiment of the present invention; Figure 5 is a block diagram of the principle of a potential function model construction system according to an embodiment of the present invention; Figure 6 is a flowchart of a potential function model training method according to an embodiment of the present invention; Figure 7 is a schematic diagram comparing the time and accuracy of various potential functions in calculating the force of an atom according to an embodiment of the present invention; Figure 8 is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] In the following detailed description, reference can be made to the accompanying drawings, which form part of this application and illustrate specific embodiments of the present application. In the drawings, similar reference numerals describe substantially similar components in different figures. Specific embodiments of the present application are described in sufficient detail below to enable those skilled in the art to implement the technical solutions of the present application. It should be understood that other embodiments may also be utilized, or structural, logical, or electrical changes may be made to the embodiments of the present application.

[0028] Referring to Figure 1, which is a flowchart of a potential function model construction method according to an embodiment of the present invention, the potential function model is used to predict the energy and atomic forces of an atomic system. The atomic system is, for example, the crystal configuration, atomic configuration, etc. of a specific material system. The method includes the following steps: Step 110, determining the nearest neighbor atom set for each atom in the atomic system based on the cutoff radius.

[0029] Step 120: Construct a nearest neighbor environment descriptor for each atom based on the position information and element type information of all nearest neighbor atoms in the nearest neighbor atom set of each atom. The nearest neighbor environment descriptor satisfies rotational symmetry.

[0030] Step 130: Input the nearest neighbor environment descriptor of each atom into a neural network with an independent configuration corresponding to its element type, and calculate the energy of each atom by forward propagation from the input layer to the output layer of the neural network.

[0031] Step 140: Summing up the energies of all atoms in the atomic system to obtain the total energy of the atomic system.

[0032] Step 150: The energy of each atom is calculated by backpropagation from the output layer to the input layer through each independently configured neural network to obtain the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor.

[0033] Step 160: Perform reverse calculation of the nearest neighbor environment descriptor for the partial derivative of the energy of each atom with respect to the position of its nearest neighbor atom.

[0034] Step S170: The force on each atom is obtained based on the partial derivative of the energy of each atom with respect to the position of its nearest neighbor atoms.

[0035] In order to improve the speed of obtaining the nearest neighbor atom set of each atom, in one embodiment of the present invention, referring to Figure 2, Figure 2 is a flowchart of a method for determining the nearest neighbor atom set according to an embodiment of the present invention, specifically including the following steps: Step 111, dividing the atomic system space into multiple spatial grid units according to the cutoff radius, wherein the side length of the spatial grid unit is not less than the cutoff radius.

[0036] Step 112: Construct atomic index information within each spatial grid cell based on the atomic position information (such as three-dimensional coordinates) of the atomic system. The atomic index information includes the atomic number, atomic position information, and the spatial grid cell number where the atom is located.

[0037] Step 113: Determine the spatial grid cell in which the target atom is located and its adjacent spatial grid cells based on the target atom's position information.

[0038] Step 114: Traverse the spatial grid cells containing the target atom and the atoms in adjacent spatial grid cells. Atoms that meet the condition of having a radius smaller than the cutoff radius are designated as the nearest neighbors of the target atom, thus obtaining the set of nearest neighbors, denoted as […]. , This represents the distance between target atom i and its nearest neighbor atom j. , , Let i be the coordinates of the target atom. Let j be the coordinates of the nearest neighbor atom j. The cutoff radius is [value].

[0039] For example, referring to Figure 3, which is a partial schematic diagram of the atomic system for determining the set of nearest-neighbor atoms of a target atom i according to an embodiment of the present invention. It should be noted that the atomic system is a three-dimensional space. To facilitate and clearly illustrate the method for determining the set of nearest-neighbor atoms, Figure 3 shows the atomic system space in a planar manner. Each square divided by the dashed lines in the figure is a spatial grid cell, and each small circle in the spatial grid cell represents an atom. The black circle represents the target atom i. The large circle represents the boundary determined by the cutoff radius. The gray squares are the search areas used to determine the set of nearest-neighbor atoms of the target atom i. Using the method shown in Figure 2, only atoms within the gray area need to be searched, reducing the traversal complexity from O(N^2) to O(N^2). 2 The traversal efficiency has been reduced to O(N), where N is the total number of atoms in the atomic system space, thus effectively improving the traversal efficiency.

[0040] In step S120, when constructing the nearest neighbor environment descriptor for each atom based on the position information and element type information of all nearest neighbor atoms in the nearest neighbor atom set of each atom, this process can be described by the following formula (1-0): (1-0) where Pi is the usual representation of the nearest neighbor environment descriptor of atom i. The element type numbering for nearest neighbor atom j, t j =1, 2, ..., ; This represents the total number of elemental species in the atomic system. This represents a symmetric function that obtains the nearest neighbor environment descriptor of atom i.

[0041] In constructing the nearest neighbor environment descriptor, the nearest neighbor environment descriptor can be a first-class descriptor with a large amount of information or a second-class descriptor with a small amount of information.

[0042] In one embodiment, the first type of descriptor is constructed based on the following formula (1-1): (1-1) Wherein, The descriptor represents the nearest neighbor environment of target atom i, where i represents the target atom index, i = 0, 1, 2, 3, 4, ..., N-1; N is the total number of atoms in the atomic system; k represents the dimension index extended for element type, which is used to indicate whether the descriptor is related to the element type. k = 0 indicates that the construction of the descriptor is independent of the element type, and a uniform weight is used to capture the overall local atomic density; when k = 1, the weights related to element type are determined through empirical mapping; n represents the radial order, n = 0, 1, 2, 3, 4, ... ; l represents the angular order, l = 0, 1, 2, 3, 4, ... ; m represents the angular component number, m = -l, -l+1, ..., l; The atomic expansion coefficient is represented as shown in formula (1-2): The expansion coefficient of the i-th atom is the complex conjugation; (1-2) Wherein, This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ..., ; This represents the total number of elemental species in the atomic system. The weights represent information related to the element's type; when k=0, When k=1, The symbol is used to indicate that different types of elements are assigned different symbols and sizes, and is used to distinguish the types of chemical elements.

[0043] Represents spherical harmonic functions. This indicates the direction from target atom i to its nearest neighbor atom j; The radial basis functions are represented as shown in equation (1-3): (1-3) This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of target atom i. j Represents the coordinates of the nearest neighbor atom j; Represents a Chebyshev polynomial of the first kind; Indicates the cutoff radius; The smooth cutoff function is shown in formula (1-4): (1-4) Wherein, the feature information and the number of dimensions in the nearest neighbor environment descriptor are determined by the radial order. Angular order Cut-off radius The radial order is determined together with the dimension index k of the element type extension. and angular order and cutoff radius This is a hyperparameter.

[0044] In this embodiment, in application When calculating spherical harmonics, use the real spherical harmonics according to the following formula (1-5). To calculate the spherical harmonic function part: (1-5) Correspondingly, the aforementioned formula (1-1) is equivalent to the following formula (1-6): (1-6) In another implementation, the second type of descriptor is constructed based on the following formula (2-1): (2-1) Wherein, This represents the nearest neighbor environment descriptor for target atom i, where i represents the target atom index (i = 0, 1, 2, 3, 4, ..., N-1), N is the total number of atoms in the atomic system, k represents the dimensional index for element type expansion (k = 0, 1), and n represents the radial order (n = 0, 1, 2, 3, 4, ...). ; This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ..., ; The weight represents the extended information weight of the element type. When k=0, When k=1, ; The radial basis functions are represented as shown in equation (1-3): (1-3) This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of target atom i. j Represents the coordinates of the nearest neighbor atom j; It is a Chebyshev polynomial of the first kind; The smooth cutoff function is shown in formula (1-4): (1-4) Wherein, the feature information and the number of dimensions in the nearest neighbor environment descriptor are determined by the radial order. Cut-off radius Together with the dimension index k that expands for element types, it is determined.

[0045] In the construction process of the aforementioned nearest neighbor environment descriptors (including the first type of descriptors and the second type of descriptors), information related to the element type (i.e.) The algorithm provides two channels: the k=0 channel provides a global structural description of the local atomic environment independent of the chemical element type, and the k=1 channel projects all element types into a single chemical element channel through a compressed empirical mapping. Descriptors constructed in this way can effectively describe atomic systems with a limited number of element types.

[0046] In cases where there are many types of elements in an atomic system, to prevent the loss of distinguishable information and the resulting decrease in accuracy, in another embodiment of the present invention, the weight of the extended information on element types is calculated according to the following formula (2-2). : (2-2) Wherein, The Kronecker symbol indicates that the element type number is One-hot encoding is performed on the category information, where k = 0, 1, 2, ... .

[0047] In this embodiment, structural channels independent of element type, i.e., k=0 channels, are retained; and each element type corresponds to a chemical element channel to represent element discrimination information. Therefore, the extended information of element type is specifically represented by the explicit one-hot representation of atomic element type.

[0048] This embodiment, by preserving the structural channel at k=0, enables the potential function model to capture the overall geometric arrangement of neighboring atoms, thereby improving the completeness of the descriptor and helping to suppress overfitting.

[0049] Since the second type of descriptor does not contain angular information and has a simpler form, it reduces a significant amount of computation compared to the first type of descriptor, resulting in faster computation speed and allowing for a larger cutoff radius within an acceptable computation time. and / or increase the radial order The number of possible values.

[0050] Based on the aforementioned formulas (1-1) to (1-6) and (2-1), construct the nearest neighbor environment descriptor. When, the radial order Angular order for the first type of descriptor and cutoff radius Together, they constitute the hyperparameter θ. Following formula (1-7), neighbor descriptors with different hyperparameter values ​​(even first- and second-class neighbor descriptors) are concatenated to form a hybrid descriptor. .

[0051] (1-7) The dimension index k of element type expansion can be designed by merging descriptors with different hyperparameter settings, so that the final constructed hybrid descriptor can be Balancing computational efficiency and accuracy. Since a larger cutoff radius significantly increases computational complexity, a common implementation combines smaller cutoff radii. The first type of descriptor that possesses angular information, and has a large cutoff radius. and radial order The second type of descriptor, which lacks angular information but offers faster computation, can perform calculations including angular information quickly without sacrificing long-cut-radius interactions, thus balancing efficiency and accuracy. Furthermore, in practice, increasing the cut-off radius for a single descriptor (either a first-type or second-type descriptor) reduces its descriptive power, potentially leading to a decrease in accuracy in many cases. Therefore, in another embodiment, multiple descriptors with different cut-off radii can be mixed. The first type of descriptor allows for the introduction of interactions with longer truncation radii while retaining high descriptive power under short truncation radii, thus overcoming the trade-off between accuracy and speed caused by the choice of truncation radius.

[0052] This invention configures an independent multi-layer neural network architecture for each atom, with neural networks of the same element type having identical parameters. In step S130, the nearest neighbor environment descriptor of each atom is input to the independently configured multi-layer fully connected neural network corresponding to its element type. The energy of each atom is calculated through forward propagation from the input layer to the output layer of the neural network. Each neural network includes an input layer, at least one hidden layer, and an output layer. The input layer receives the nearest neighbor environment descriptor of the atom (which is a multi-dimensional vector), passes it sequentially through the hidden layers, and finally outputs it from the output layer. In this invention, the input of the neural network is the nearest neighbor environment descriptor. The output is energy. Therefore, the forward propagation calculation process can be represented by the following equation (3-1): (3-1) Indicates the type of element in target atom i. This represents the neural network corresponding to the element type of the target atom i.

[0053] In step S140, the total energy E of the atomic system is calculated using the following formula (3-2): (3-2) N is the total number of atoms in the atomic system.

[0054] Referring to Figure 4, Figure 4 is a schematic diagram of the calculation path of atomic forces according to an embodiment of the present invention. For ease of annotation and explanation, a nearest neighbor environment descriptor will be constructed. The process is called basis set computation. As shown by the black flow chart in Figure 4, the nearest neighbor environment descriptor is obtained from the atomic position information and element type information of the atomic system through basis set computation. Atomic energy is then obtained through forward propagation of a neural network. Then, the energy of each atom is processed by each independently configured neural network. Perform backpropagation calculations from the output layer to the input layer of the neural network to obtain the energy of each atom. Its neighboring environment descriptor partial derivatives Then, the partial derivative is then... Perform neighborhood environment descriptor Inverse basis set calculation. Each atom i has multiple nearest neighbor atoms j, and the partial derivatives are then used to calculate this. Perform neighborhood environment descriptor The energy of atom i is obtained by reverse basis set calculation. Partial derivative with respect to each nearest neighbor atom j For each nearest neighbor atom j, atom i is its nearest neighbor atom, and the energy of atom j... When performing backpropagation calculations, the energy of atom j is obtained. Partial derivative with respect to atom i Then, the energy of the original i is calculated using the following formula (3-3). Partial derivative with respect to the nearest neighbor atom j and the energy of atom j Partial derivative with respect to atom i The difference is used to calculate the force between atom i and atom j. Then, based on formula (3-4), the forces between atom i and all its nearest neighbor atom j are summed to obtain the force on atom i. .

[0055] (3-3) (3-4) In constructing the potential function model, the present invention adopts a neural network architecture and uses the back propagation of the neural network and descriptor to calculate the force on the atom, instead of the forward method commonly used in the prior art to directly calculate the partial derivative of the descriptor with respect to the coordinates. This simplifies the calculation process, reduces the memory usage during the calculation process, and lowers the requirements for device performance.

[0056] Referring to Figure 5, which is a block diagram of a potential function construction system according to an embodiment of the present invention, the potential function construction system in this embodiment includes a nearest-neighbor atom set construction module 10, a descriptor construction module 11, a neural network module 12, an energy calculation module 13, a descriptor reverse calculation module 14, and an atom force calculation module 15. Combining the aforementioned methods, the nearest-neighbor atom set construction module 10 determines the nearest-neighbor atom set for each atom in the atomic system based on a cutoff radius. When multiple cutoff radii are set, a corresponding nearest-neighbor atom set is determined for each atom in the atomic system based on each cutoff radius.

[0057] The descriptor construction module 11 constructs a nearest-neighbor environment descriptor for each atom based on the positional information and elemental type information of all nearest-neighbor atoms in each nearest-neighbor atom set of each atom. The nearest-neighbor environment descriptor includes multi-dimensional feature information and satisfies rotational symmetry. Specifically, when an atom has multiple nearest-neighbor atom sets corresponding to different cutoff radii, a nearest-neighbor environment descriptor is obtained for each nearest-neighbor atom set, and then all the nearest-neighbor environment descriptors are concatenated to obtain the final hybrid nearest-neighbor environment descriptor. Furthermore, the nearest-neighbor environment descriptor can be a first-type descriptor, a second-type descriptor, or both types of descriptors can be constructed simultaneously. For specific construction methods, please refer to the foregoing description, which will not be repeated here.

[0058] The neural network module 12 includes multiple independently configured neural networks, each corresponding to an atom. Neural networks of the same atom element type have identical parameters. When calculating sub-energy, the nearest neighbor environment descriptor of each atom obtained by the descriptor construction module 11 is input to the independently configured neural network corresponding to its element type. The energy of each atom is calculated through forward propagation from the input layer to the output layer of the neural network. When calculating the force on each atom, the energy of each atom is calculated through backward propagation from the output layer to the input layer via each independently configured neural network to obtain the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor. Therefore, when the nearest neighbor environment descriptor of an atom is input to the independently configured neural network corresponding to its element type, the energy of that atom is obtained from the output layer of each neural network. After backward propagation, the data obtained at the input layer is the partial derivative of the atom's energy with respect to its nearest neighbor environment descriptor. The neural network module 12 sends the data from the output layer to the energy calculation module 13 and the data obtained from the input layer to the descriptor backward calculation module 14.

[0059] The energy calculation module 13 receives the data sent by the neural network module 12, namely the energy of each atom, and sums the energies of all atoms in the atomic system to obtain the energy of the atomic system.

[0060] The descriptor inverse calculation module 14 receives the data from the input layer sent by the neural network module 12, namely the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor. It performs inverse calculation on this partial derivative using the nearest neighbor environment descriptor and sends the result to the atom force calculation module 15. The calculation result is the partial derivative of the atom's energy with respect to its position. The atom force calculation module 15 calculates the atom's force based on the partial derivative of the energy of each atom with respect to its position. See the aforementioned method and formulas (3-3) and (3-4) for details, which will not be repeated here.

[0061] Taking the nearest neighbor environment descriptor calculated by formula (2-1) as an example, the reverse calculation process of the descriptor reverse calculation module 14 is as follows: First, substitute the data obtained from the input layer into the following formula (4-1) to obtain... .

[0062] (4-1) Then then Substituting into the following formulas (4-2) and (4-3), we get and .

[0063] (4-2) (4-3) Finally, , Substituting into the following formula (4-4), we obtain the partial derivative of the energy with respect to each nearest neighbor atom j. .

[0064] (4-4) Then, the atomic force calculation module 15 calculates the force on each atom using formulas (3-3) and (3-4). .

[0065] Taking the calculation of the nearest neighbor environment descriptor using formula (2-1) as an example, the process of directly calculating the partial derivative of the descriptor with respect to coordinates using the existing forward calculation module is shown in formula (5-1): (5-1) Comparing formula (5-1) with steps (4-1) to (4-4) in the aforementioned process of this embodiment, it can be seen that this embodiment does not require the calculation of intermediate values. Therefore, the computational complexity is less than that of formula (5-1).

[0066] According to another aspect of the present invention, the present invention also provides a training method for the potential function model constructed by the aforementioned method. Referring to FIG6, FIG6 is a flowchart of a potential function model training method according to an embodiment of the present invention. In this embodiment, the potential function model training method includes the following steps: Step S210, obtaining samples from a sample set, wherein the samples are atomic configurations, one atomic configuration corresponds to one atomic system, and the sample labels include the energy of the atomic configuration, the atomic force, and the system stress.

[0067] Step S220: The potential function model constructed according to the aforementioned method is used to obtain the energy and force of each atom in each sample, as well as the energy of each sample.

[0068] Step S230: Calculate the system stress. Specifically, calculate the system stress based on the following formula (6-1).

[0069] S = W / V (6-1) where S is the system stress, V is the total volume of the atomic system, and W is the potential force. The calculation formula is shown in equation (6-2) below.

[0070] (6-2) Step S240: Calculate the weighted sum of the energy loss value per atom, the force loss value per atom, and the stress loss value of the system based on the sample labels and the loss function as the total loss value for this round of training.

[0071] In this context, the formula for calculating the total loss value L is shown in equation (6-3): (6-3) Among them, The energy per atom in the atomic system. The energy per atom in the sample label; F represents the force on the atom. S represents the atomic forces in the sample label; S represents the system stress. The system stress is shown in the sample label.

[0072] Let x be the loss function, where x represents the loss function in formula (6-3). 、F、S. The sample label values ​​are respectively those in formula (6-3). , , .

[0073] In one embodiment, the loss function is chosen as SmoothL1Loss, as shown in Equation (6-4): (6-4) These are the weights for energy loss, atomic force loss, and system stress loss, respectively, and their values ​​are, for example: , , .

[0074] It is worth mentioning that when calculating the total loss value L, regularization terms such as L1 regularization and L2 regularization can be added to suppress overfitting, control model complexity, stabilize the training process, balance multi-task optimization, and introduce parameter priors.

[0075] Step S250: Evaluate whether the preset termination condition has been met. If the preset termination condition has been met, end the training process. If the preset termination condition has not been met, in step S260: Perform reverse calculation of the total loss value according to the calculation process of energy and force respectively, and accumulate the calculation results to obtain the gradient of the total loss value with respect to the parameters of each layer of the neural network.

[0076] In step S270, the neural network parameters are optimized using an optimizer based on the gradient of the total loss value with respect to the parameters of each layer. Then, the process returns to step S210 to begin a new round of training.

[0077] The preset termination condition is, for example, reaching a preset number of training rounds. For instance, a total training rounds M are set, and during training, the number of training iterations is counted. When the set total number of rounds M is reached, training ends. Alternatively, the total loss value L is compared with a threshold; when the total loss value L is less than or equal to the threshold, the condition for ending training is considered met.

[0078] Alternatively, the preset conditions can be conditions set during testing. For example, after the training reaches the set total number of rounds M, the test is performed using test set samples. If the loss error obtained during testing meets the set requirements, the training ends; otherwise, training is restarted.

[0079] Alternatively, a total of M training rounds can be pre-set, and tests can be conducted after each training round to record the total loss value (i.e., error). After the total number of training rounds reaches M, the parameter with the smallest error can be selected as the final parameter.

[0080] Furthermore, when calculating the total loss value in reverse according to the respective calculation processes for energy and force, for the energy calculation process, the gradient of the total loss value with respect to energy is first obtained through backpropagation from the total loss value, and then backpropagation through a neural network based on the chain rule (reverse neural network) continues. For the force calculation process, the gradient of the total loss value with respect to force is first obtained through backpropagation from the total loss value, and then two reverse basis set calculations (reverse reverse basis set calculation) and two reverse propagation of the neural network are performed sequentially (reverse reverse neural network). In the calculation process of the aforementioned two paths, multiple gradients of the same neural network layer are accumulated, and then the calculation continues downward to finally obtain the gradient of the total loss value with respect to the parameters of each neural network layer.

[0081] Since the aforementioned backpropagation calculation does not require partial derivatives of the descriptor with respect to coordinates... By caching, compared to the existing methods that consume a lot of memory to utilize intermediate calculation results during potential function training, this invention requires less computing resources when training potential functions, thus reducing reliance on large computing resources.

[0082] Furthermore, research on existing machine learning potential functions reveals that the construction of atomic descriptors in current technologies is often based on complex spherical harmonic function expansions. However, complex number operations in high-dimensional systems incur significant computational overhead, increasing both memory usage and computation time. In force calculation, existing technologies typically obtain atomic forces by explicitly analytically differentiating the energy expression, requiring separate implementations for energy and force calculations, increasing algorithm complexity and implementation difficulty. Moreover, existing technologies often utilize readily available general-purpose algorithm modules for constructing machine learning potential function models, such as general-purpose neural network modules and equivariant tensor modules. These general-purpose modules are often insufficiently optimized for the numerous small matrix / tensor operations and unequal-length tensor operations inherent in machine learning potential functions, thus failing to effectively utilize CPU cache structures and single-instruction multiple-data (SIMDD) optimizations, thereby impacting computational efficiency.

[0083] This invention effectively improves computational efficiency through the following measures: First, it employs real spherical harmonics when constructing descriptors, avoiding the enormous computational overhead of complex number operations in high-dimensional systems. Second, it uses chain-like backpropagation when calculating atomic forces, especially during training, further reducing computational complexity and resource requirements. Third, in its implementation, developers can use C++ to write neural networks and backpropagation programs, instead of directly using existing libraries and algorithm models, allowing for more low-level optimizations. For example, it leverages C++ template programming, uses Single Instruction Multiple Data (SIMD) to accelerate computation, and optimizes logic. Therefore, compared to most existing machine learning potential function models, the potential function model provided by this invention is faster and requires fewer resources.

[0084] Regarding accuracy, see Table 1, which is a comparison table of errors for different machine learning potential functions on the small molecule benchmark dataset. The first column contains a small molecule benchmark dataset for each row; the second column contains error terms, where E represents energy error (meV) and F represents atomic force error (meV / Å); columns three through nine represent different potential function models, with column three being the potential function model constructed in this invention, abbreviated as NNAP (Neural Network Atomic Potential, atom potential based on neural networks); column four is ACE (Atomic Cluster Expansion, a systematic potential function based on many-body expansion of atomic clusters); column five is sGDML (symmetry Gradient Domain Machine Learning); column six is ​​FCHL (Faber-Christensen-Huang-Lilien feld, a quantum machine learning potential function); column seven is GAP (Gaussian Approximation Potential); column eight is ANI (ANAKIN-ME, Accurate NeurAlnetworKengINe for Molecular Energies); and column nine is FF (classical force field). The bolded data represents the lowest value, and the underlined data represents the second lowest. As can be seen from the data in Table 1, the potential function model NNAP constructed in this invention exhibits the smallest two types of errors on all test sets, meaning it has the highest accuracy.

[0085] Table 1

[0086] Referring to Figure 7, Figure 7 is a comparative schematic diagram of various potential function models according to an embodiment of the present invention when calculating the force on an atom. The horizontal axis represents the time required to calculate the force on an atom, and the vertical axis represents the force error. Different points of the same potential function model indicate the use of different model scales (e.g., increasing the number of layers and neurons in the neural network). When evaluating the performance of a potential function model, faster processing time and smaller error are better. Therefore, as can be seen from the curves in the comparison figure, the potential function model NNAP constructed in this invention is located in the lower left corner, indicating that the potential function model NNAP balances efficiency and accuracy.

[0087] The potential function model constructed in this invention balances computational efficiency and accuracy, enabling molecular dynamics simulations with millions of atoms and timescales of hundreds of nanoseconds. It can be applied to high-precision, large-scale simulations of many systems, such as high-entropy metallic glasses and the simulation of large-scale molecular reactions with small amounts of small element doping.

[0088] Furthermore, due to the low computational complexity of the potential function model constructed in this invention, developers no longer need to rely on existing libraries during implementation. Instead, they can fully leverage the advantages of independent programming to optimize the potential function calculation process to the greatest extent. This not only further improves the calculation accuracy and efficiency of the potential function but also enables cross-platform compatibility (e.g., efficient operation on Linux, Windows, and MacOS operating systems). Various functions and interfaces can be added as needed, such as providing an ASE calculator (Atomic Simulation Environment Calculators) interface and an SGCMC (Semi-Grand Canonical Monte Carlo) interface. Through the ASE calculator interface, structural optimization and NEB (Nudged elastic band) path searching can be performed using existing ASE workflows. Through the SGCMC interface, parallel SGCMC simulations can be performed in LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) to study component diffusion, short-range chemical ordering in solid solutions, etc.

[0089] Figure 8 is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. The electronic device can be implemented as a server, or as a personal PC, laptop computer, smart mobile terminal, etc. It includes a processor 601 and a memory 602. The memory 602 stores a program instruction set, and when the processor 601 executes the program instruction set in the memory 602, the aforementioned potential function model construction method and training method are implemented.

[0090] Specifically, the processor 601 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement embodiments of the present invention.

[0091] Memory 602 may include mass storage for data or instructions. For example, and not limitingly, memory 602 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 602 may include removable or non-removable (or fixed) media. Where appropriate, memory 602 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 602 is non-volatile solid-state memory.

[0092] The memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the potential function model construction and training methods provided by this invention.

[0093] In one example, the electronic device may also include a communication interface 603 and a bus 610. As shown in FIG8, the processor 601, memory 602, and communication interface 603 are connected via bus 610 and communicate with each other. The communication interface 603 is mainly used to realize communication between various modules, devices, units, and / or equipment in the embodiments of the present invention. Bus 610 includes hardware, software, or both. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 610 may include one or more buses. Although specific buses are described and shown in the embodiments of the present invention, the present invention contemplates any suitable bus or interconnect.

[0094] The present invention also provides a computer-readable storage medium storing computer program instructions thereon, which, when executed by a processor, implement the potential function model construction method and training method described in the foregoing embodiments. The computer-readable storage medium can be any medium that contains or stores computer-executable instructions for use by or in conjunction with an instruction execution system, apparatus, or device. The storage medium can be a transient computer-readable storage medium or a non-transitory computer-readable storage medium. Non-transitory computer-readable storage media may include, but are not limited to, magnetic storage devices, optical storage devices, and / or semiconductor storage devices. Examples of such storage devices include, for example, magnetic disks, optical discs based on CD, DVD, or Blu-ray technology, and persistent solid-state storage such as flash memory and solid-state drives.

[0095] This invention also provides a computer program product, which includes computer program instructions. When executed by a processor, the computer program instructions implement the potential function model construction method and training method described in the foregoing embodiments. The computer program product includes, but is not limited to, application installation packages and application plugins published on websites and in app stores.

[0096] The above embodiments are for illustrative purposes only and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the scope of the invention. Therefore, all equivalent technical solutions should also fall within the scope of the invention.

Claims

1. A method for constructing a potential function model, wherein the potential function model is used to predict the energy and forces acting on atoms in an atomic system, characterized in that, include: Determine the set of nearest neighbor atoms for each atom in the atomic system based on the cutoff radius; Based on the position information and element type information of all nearest neighbor atoms in the set of nearest neighbor atoms of each atom, a nearest neighbor environment descriptor is constructed for each atom, and the nearest neighbor environment descriptor satisfies symmetry; the nearest neighbor environment descriptor of each atom is input into an independently configured neural network corresponding to its element type, and the energy of each atom is calculated by forward propagation from the input layer to the output layer of the neural network; The energy of the atomic system is obtained by summing the energies of all atoms in the atomic system. The energy of each atom is calculated by backpropagation from the output layer to the input layer through each independently configured neural network to obtain the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor; the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor is calculated by backpropagation of the nearest neighbor environment descriptor to obtain the partial derivative of the energy of each atom with respect to the position of its nearest neighbor atom; and the force on each atom is obtained based on the partial derivative of the energy of each atom with respect to the position of its nearest neighbor atom.

2. The potential function model construction method according to claim 1, characterized in that, When determining the nearest neighbor atom set for each atom in the atomic system based on the cutoff radius, multiple nearest neighbor atom sets with different cutoff radii are determined for each atom in the atomic system; correspondingly, when constructing the nearest neighbor environment descriptor for each atom, the corresponding nearest neighbor environment descriptor is constructed based on the nearest neighbor atom sets with different cutoff radii, and all the nearest neighbor environment descriptors with different cutoff radii are concatenated as the final nearest neighbor environment descriptor.

3. The potential function model construction method according to claim 1, characterized in that, When constructing the nearest neighbor environment descriptor for each atom based on the position information and element type information of all nearest neighbor atoms in the nearest neighbor atom set of each atom, a first type of descriptor and / or a second type of descriptor are constructed respectively. The first type of descriptor has more information than the second type of descriptor. When the first type of descriptor and the second type of descriptor are constructed, the first type of descriptor and the second type of descriptor are concatenated to form the final nearest neighbor environment descriptor.

4. The potential function model construction method according to claim 3, characterized in that, When constructing the first type of descriptor based on the positional information and elemental information of all nearest-neighbor atoms in the set of nearest-neighbor atoms of each atom, the nearest-neighbor environment descriptor of each atom is constructed based on the following formula (1-1): (1-1) Wherein, This represents the nearest neighbor environment descriptor for target atom i, where i represents the target atom index (i = 0, 1, 2, 3, 4, ..., N-1), N is the total number of atoms in the atomic system, k represents the dimensional index for element type expansion (k = 0, 1), and n represents the radial order (n = 0, 1, 2, 3, 4, ...). ; l represents the angular order, l = 0, 1, 2, 3, 4, ... ; m represents the angular component number, m = -l, -l+1, ..., l; The atomic expansion coefficient is shown in formula (1-2); The atomic expansion coefficients are complex conjugates; (1-2) Wherein, This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ..., ； This represents the total number of elemental species in the atomic system. The weights representing the extended information of element types, when k=0, When k=1, ； Represents spherical harmonic functions. This indicates the direction from target atom i to its nearest neighbor atom j; The radial basis functions are represented as shown in equation (1-3): （1-3） This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of the target atom i. j Represents the coordinates of the nearest neighbor atom j; Represents a Chebyshev polynomial of the first kind; The smooth cutoff function is shown in formula (1-4): （1-4）。 5. The potential function model construction method according to claim 4, characterized in that, Use the real spherical harmonic function according to the following formula (1-5) Calculate the spherical harmonic function ： （1-5）。 6. The potential function model construction method according to claim 3, characterized in that, When constructing the second type of descriptor based on the positional information and elemental information of all nearest-neighbor atoms in the set of nearest-neighbor atoms of each atom, the nearest-neighbor environment descriptor of each atom is constructed based on the following formula (2-1): (2-1) Wherein, This represents the nearest neighbor environment descriptor for target atom i, where i represents the target atom index (i = 0, 1, 2, 3, 4, ..., N-1), N is the total number of atoms in the atomic system, k represents the dimensional index for element type expansion (k = 0, 1), and n represents the radial order (n = 0, 1, 2, 3, 4, ...). ； This indicates that the target atom i is at the cutoff radius. The set of nearest-neighbor atoms within; The element number representing the nearest neighbor atom j, t j =1, 2, ..., ， This represents the total number of elemental species in the atomic system. The weights representing the extended information of element types, when k=0, When k=1, ； The radial basis functions are represented as shown in equation (1-3): （1-3） This represents the distance between target atom i and its nearest neighbor atom j. , r i r represents the coordinates of the target atom i. j Represents the coordinates of the nearest neighbor atom j; It is a Chebyshev polynomial of the first kind; The smooth cutoff function is shown in formula (1-4): （1-4）。 7. The potential function model construction method according to claim 4 or 6, characterized in that, Weight of element type extended information Replace with the value calculated according to the following formula (2-2): (2-2) Wherein, The Kronecker symbol indicates that the element type number is One-hot encoding is performed on the category information, where k = 0, 1, 2, ... 。 8. A potential function model construction system, wherein the potential function model is used to predict the energy and forces acting on atoms in an atomic system, characterized in that, include: The nearest neighbor atom set building module is configured to determine the nearest neighbor atom set for each atom in the atomic system based on the cutoff radius. The descriptor construction module is configured to construct a nearest-neighbor environment descriptor for each atom based on the position information and element type information of all nearest-neighbor atoms in the nearest-neighbor atom set of each atom, wherein the nearest-neighbor environment descriptor satisfies symmetry. The neural network module is configured to input the nearest neighbor environment descriptor of each atom into an independently configured neural network corresponding to its element type, and calculate the energy of each atom by forward propagation from the input layer to the output layer of the neural network. The energy of each atom is calculated by backpropagating from the output layer to the input layer through each independently configured neural network to obtain the partial derivative of the energy of each atom with respect to its nearest neighbor environment descriptor; An energy calculation module is configured to sum the energies of all atoms in an atomic system to obtain the energy of the atomic system. The descriptor inverse calculation module is configured to perform inverse calculation of the nearest-neighbor environment descriptor for the partial derivative of the energy of each atom with respect to the position of its nearest neighbor atom. And an atomic force calculation module, configured to obtain the force on each atom based on the partial derivative of each atom's energy with respect to the positions of its nearest neighbors.

9. A method for training a potential function model constructed by the method of any one of claims 1-7, characterized in that, Includes the following steps: Samples are obtained from a sample set. The samples are arbitrary atomic configuration samples containing atomic position information and element type information. One atomic configuration sample corresponds to one atomic system. The sample labels include the energy of the atomic configuration, the atomic force, and the system stress. The potential function model constructed based on any one of claims 1-7 yields the energy of each atom in each sample, the force on the atom, and the energy of each sample. The system stress is calculated based on the atomic force analysis sample. Based on the sample labels and loss function, calculate at least the weighted sum of the energy loss value, force loss value and system stress loss value as the total loss value for this round of training; Evaluate whether the preset termination conditions are met, and terminate the training process in response to the satisfaction of the preset termination conditions; In response to the failure to meet the preset termination condition, the total loss value is backpropagated according to the calculation process of energy and atomic force respectively, and the calculation results are accumulated to obtain the gradient of the total loss value with respect to the parameters of each layer of the neural network. Based on the gradient of the total loss value with respect to the parameters of each layer of the neural network, the neural network parameters are optimized by the optimizer.

10. An electronic device comprising a processor and a memory, wherein the memory stores a set of computer program instructions, characterized in that, The potential function model construction method of any one of claims 1-7 or the potential function model training method of claim 9 is implemented when the processor executes the computer program instruction set on the memory.

11. A computer-readable storage medium, wherein, The computer-readable storage medium stores a set of computer program instructions, characterized in that, when the set of computer program instructions is executed by a processor, it implements the potential function model construction method according to any one of claims 1-7 or the potential function model training method according to claim 9.

12. A computer program product comprising a computer program instruction set, characterized in that, When the computer program instruction set is executed by the processor, it implements the potential function model construction method of any one of claims 1-7 or the potential function model training method of claim 9.

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