Method and device for determining hyper-parameter of potential energy model based on graph neural network

Abstract

The invention provides a method and a device for determining hyper-parameters of a potential energy model based on a graph neural network. The method comprises the following steps: acquiring a key sample from a plurality of samples of a data set for molecular dynamics simulation; determining a truncation radius configuration of the potential energy model based on the key sample, the truncation radius configuration including a truncation radius of each element combination; training of the potential energy model is performed based on the key sample and the truncation radius configuration, and the truncation radius configuration is adjusted based on an inference result of the trained potential energy model, where an input of the potential energy model is an atomic graph determined based on the key sample and the truncation radius configuration, and an output of the potential energy model is an atomic graph determined based on the key sample and the truncation radius configuration. The output of the potential energy model comprises energy parameters and force parameters of atoms.

Description

Technical Field

[0001] The present disclosure relates to the field of molecular dynamics simulation, and is particularly applicable to molecular dynamics simulation of semiconductor material manufacturing processes, and specifically to a method and device for determining hyperparameters of a potential energy model based on a graph neural network. Background Art

[0002] Molecular dynamics (MD) simulation is a technique that uses computers to simulate the motion of molecular particles to study the properties and behavior of matter. With the development of the field of artificial intelligence, more and more artificial intelligence models (such as graph neural networks (GNNs)) are used to implement MD simulation technology.

[0003] However, the methods of performing MD simulations using existing GNN-based potential energy models often have many defects. For example, the unreasonable hyperparameter configuration of the GNN-based potential energy model causes the training process of the GNN-based potential energy model to be time-consuming or the inference performance of the GNN-based potential energy model to be poor. The GNN-based potential energy model has high requirements on operating conditions and cannot be used.

[0004] Therefore, there is a need for a technology that can be suitable for reasonably determining the hyperparameters of the GNN-based potential energy model so as to improve the efficiency of the training process of the GNN-based potential energy model in terms of time cost and computational cost. Summary of the invention

[0005] In order to at least solve the above-mentioned problems and / or disadvantages, embodiments of the present disclosure provide a method and apparatus for determining hyperparameters of a potential energy model based on a graph neural network.

[0006] According to a first aspect of an embodiment of the present disclosure, a method for determining hyperparameters of a potential energy model based on a graph neural network is provided, the method comprising: obtaining key samples from multiple samples of a data set for molecular dynamics simulation; determining a cutoff radius configuration of the potential energy model based on the key samples, wherein the cutoff radius configuration includes a cutoff radius for each element combination; performing training of the potential energy model based on the key samples and the cutoff radius configuration, and adjusting the cutoff radius configuration based on an inference result of the trained potential energy model, wherein an input of the potential energy model is an atomic graph determined based on the key samples and the cutoff radius configuration, and an output of the potential energy model includes energy parameters and force parameters of atoms.

[0007] Optionally, the step of obtaining key samples from a plurality of samples of a data set for molecular dynamics simulation includes: selecting the key samples from the plurality of samples by using a weighted support vector regressor.

[0008] Optionally, each of the multiple samples includes at least one atom, and the step of selecting a key sample from the multiple samples by using a weighted support vector regressor includes: determining weights of the multiple samples based on statistical characteristics of the multiple samples in the data set; obtaining multiple weighted samples by multiplying the multiple samples with the determined weights respectively; and obtaining a support vector as the key sample based on the multiple weighted samples by using a weighted support vector regressor.

[0009] Optionally, the step of determining the cutoff radius configuration based on the key sample includes: based on the key sample, determining the influence factor of each element combination of atoms in the key sample, wherein the influence factor indicates the degree of influence of the element combination on the number of edges in the atomic graph; based on the influence factor of each element combination, determining the cutoff radius configuration.

[0010] Optionally, based on the key sample, the step of determining the influence factor of each element combination of atoms in the key sample includes: calculating the mutual coordinates of the atoms in the key sample and the element ratios of the neighboring atoms of the atoms, wherein the mutual coordinates indicate the property characteristics and geometric characteristics of the atoms, and the neighboring atoms are other atoms within the cutoff radius of the atom centered on the atom; determining the influence factor of each element combination based on the mutual coordinates of the atoms and the element ratios of the neighboring atoms.

[0011] Optionally, the step of calculating the mutual coordinates of atoms in the critical sample comprises: determining the mutual coordinates based on position parameters and force parameters of the atom and the neighboring atoms.

[0012] Optionally, the step of determining the cutoff radius configuration based on the influence factor of each element combination includes: determining a cutoff radius within a predetermined cutoff radius range for each element combination based on the influence factor of each element combination.

[0013] Optionally, the step of adjusting the truncation radius configuration based on the inference result of the trained potential energy model includes: calculating the loss based on the inference result, the truncation radius and the key sample; and adjusting the truncation radius configuration based on the loss.

[0014] According to a second aspect of an embodiment of the present disclosure, a device for determining hyperparameters of a potential energy model based on a graph neural network is provided, the device comprising: a key sample acquisition module, configured to acquire key samples from multiple samples of a data set for molecular dynamics simulation; a hyperparameter initial value determination module, configured to determine a cutoff radius configuration of the potential energy model based on the key samples, wherein the cutoff radius configuration includes a cutoff radius for each element combination; a hyperparameter adjustment module, configured to perform training of the potential energy model based on the key samples and the cutoff radius configuration, and adjust the cutoff radius configuration based on an inference result of the trained potential energy model, wherein the input of the potential energy model is an atomic graph determined based on the key samples and the cutoff radius configuration, and the output of the potential energy model includes energy parameters and force parameters of atoms.

[0015] Optionally, the key sample acquisition module is configured to acquire key samples from a plurality of samples of the data set for molecular dynamics simulation by the following operation: selecting the key samples from the plurality of samples by using a weighted support vector regressor.

[0016] Optionally, each of the multiple samples includes at least one atom, and the key sample acquisition module is configured to select the key sample from the multiple samples by using a weighted support vector regressor through the following operations: determining the weights of the multiple samples based on the statistical characteristics of the multiple samples in the data set; obtaining multiple weighted samples by multiplying the multiple samples with the determined weights respectively; and obtaining a support vector as the key sample based on the multiple weighted samples by using a weighted support vector regressor.

[0017] Optionally, the hyperparameter initial value determination module is configured to determine the cutoff radius configuration based on the key sample through the following operations: based on the key sample, determine the influence factor of each element combination of atoms in the key sample, wherein the influence factor indicates the degree of influence of the element combination on the number of edges in the atomic graph; based on the influence factor of each element combination, determine the cutoff radius configuration.

[0018] Optionally, the hyperparameter initial value determination module is configured to determine the influence factor of each element combination of atoms in the key sample based on the key sample through the following operations: calculating the mutual coordinates of the atoms in the key sample and the element ratios of the neighboring atoms of the atoms, wherein the mutual coordinates indicate the property characteristics and geometric characteristics of the atoms, and the neighboring atoms are other atoms within the cutoff radius of the atom centered on the atom; determining the influence factor of each element combination based on the mutual coordinates of the atoms and the element ratios of the neighboring atoms.

[0019] Optionally, the hyperparameter initial value determination module is configured to calculate the mutual coordinates of atoms in the key sample by the following operation: determining the mutual coordinates based on position parameters and force parameters of the atom and the neighboring atoms.

[0020] Optionally, the hyperparameter initial value determination module is configured to determine the truncation radius configuration based on the influence factor of each element combination by the following operations: based on the influence factor of each element combination, determine the truncation radius within a predetermined truncation radius range for each element combination.

[0021] Optionally, the hyperparameter adjustment module is configured to adjust the truncation radius configuration based on the inference result of the trained potential energy model by the following operations: calculating the loss based on the inference result, the truncation radius and the key sample; and adjusting the truncation radius configuration based on the loss.

[0022] According to a third aspect of an embodiment of the present disclosure, there is provided an electronic device, comprising: at least one processor; and at least one memory storing computer executable instructions, wherein the computer executable instructions, when executed by the at least one processor, prompt the at least one processor to execute the method described above.

[0023] According to a fourth aspect of an embodiment of the present disclosure, a computer-readable storage medium is provided, wherein, when instructions in the computer-readable storage medium are executed by at least one processor, the at least one processor is prompted to execute the method as described above.

[0024] According to the methods and devices of various embodiments of the present disclosure, the data set of the potential energy model based on GNN can be sampled to obtain samples that do not lose accuracy and reduce the amount of computation, thereby reducing unnecessary waste of computing resources; relatively reasonable hyperparameters can be set. Specifically, the optimal truncation radius configuration can be adaptively set for the data set of the potential energy model based on GNN, thereby reducing the time cost of tuning the hyperparameters of the potential energy model; a new balanced loss function can also be defined, which can take into account both the accuracy index and the computational index of the model, thereby flexibly controlling the training of the model and the adjustment of the hyperparameters.

[0025] According to an embodiment of the present disclosure, the training of a GNN-based potential energy model can be implemented using a set optimal cutoff radius configuration, so that the model training can be completed quickly while achieving high accuracy, and the computational complexity of the model training can also be kept low.

[0026] In addition, the present disclosure also proposes a new measurement method to accurately measure the influence of different elements on the number of edges in the atomic graph generated by the potential energy model, thereby providing reference guidance when the user adjusts the truncation radius configuration.

[0027] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The above and other aspects, features and advantages of certain embodiments of the present disclosure will become more apparent through the following description in conjunction with the accompanying drawings, in which:

[0029] Figure 1 is a diagram illustrating a process of determining hyperparameters of a potential energy model based on a graph neural network;

[0030] Figure 2 is a flowchart showing a method for determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure;

[0031] Figure 3 is a diagram showing a brief process of determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure;

[0032] Figure 4 is a diagram showing an example of an atom graph according to an embodiment of the present disclosure;

[0033] Figure 5 is a diagram showing a detailed process of determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure;

[0034] Figure 6 is a diagram illustrating a process of acquiring key samples according to an embodiment of the present disclosure;

[0035] Figure 7 is a diagram illustrating a process of determining sample weights according to an embodiment of the present disclosure;

[0036] Figure 8 is a diagram illustrating a fitting process using weighted SVR according to an embodiment of the present disclosure;

[0037] Fig. 9 is a diagram showing neighborhood changes of SiN molecules before and after applying a cutoff radius configuration according to an embodiment of the present disclosure; and

[0038] Fig.10 is a block diagram showing an apparatus for determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0039] In order to enable ordinary persons in the art to better understand the technical solutions of the present disclosure, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the accompanying drawings.

[0040] The terms "include" or "comprising" used in this specification indicate the existence of the stated features, wholes, steps, operations, elements, components and / or combinations thereof, but do not exclude the existence or addition of one or more other features, wholes, steps, operations, elements, components and / or combinations thereof. It should be understood that although the terms "first", "second", "third", etc. are used to describe various information, the information should not be limited by these terms. These terms are only used to distinguish one type of information from another type of information. For example, without departing from the scope of the present disclosure, the first information may be referred to as the second information; and similarly, the second information may also be referred to as the first information. As used herein, the term "in response to..." may be understood to mean "when...", "at..." or "if," depending on the context.

[0041] In addition, the phrase "at least one of..." that appears in the present disclosure includes three types of parallel situations: "any one of...", "any combination of...", and "the whole of..." For example, "including at least one of A and B" includes the following three parallel situations: (1) including A; (2) including B; (3) including A and B. For another example, "performing at least one of step 1 and step 2" includes the following three parallel situations: (1) performing step 1; (2) performing step 2; (3) performing step 1 and step 2.

[0042] Unless otherwise defined, all terms used herein (including technical terms and scientific terms) have the same meaning as those generally understood by ordinary technicians in the field to which the present disclosure belongs based on the understanding of the disclosure of this application, and should not be interpreted in an idealized or overly formal way. Here, the use of the term "may" with respect to examples or embodiments (for example, "... may include") indicates that there is at least one example or embodiment that includes or implements such features, and all examples are not limited to this. Unless otherwise clearly defined, terms in the singular also include plural forms.

[0043] In the related art, there are various techniques for MD simulation, but these techniques all have drawbacks.

[0044] For example, the Neural Equivariant Interatomic Potentials (NequIP) method can be used to implement MD simulations. The NequIP method is an E(3)-equivariant graph neural network method that learns interatomic potentials from non-in-situ calculations of molecular dynamics simulations. The method is based on a message passing mechanism. Although the NequIP method can have relatively high accuracy, the process of training the potential energy model in this method cannot be adaptively adjusted (for example, only a fixed cutoff radius value is used for training the potential energy model), which has many disadvantages, such as the presence of redundant information, slow training speed, poor inference performance, and inability to parallelize calculations.

[0045] In addition, the Allegro model can be used to implement MD simulation. The Allegro model is a strict local equivariant deep learning interatomic potential method that can simultaneously demonstrate excellent accuracy and scalability for parallel computing. However, this method has the disadvantages of large computational complexity, slow simulation process, and poor inference performance.

[0046] In order to explain the related art in more detail, the following will first refer to Figure 1 The method for determining the hyperparameters of the related GNN-based potential energy model is described.

[0047] Figure 1 is a diagram illustrating a process of determining hyperparameters of a potential energy model based on a graph neural network.

[0048] Reference Figure 1 ,First, an initial value of the truncation radius as one of the hyper ,parameters and a data set (also referred to as a training set in the present ,disclosure) are input into the training framework of the GNN-based potential ,energy model to determine the atomic graph as the input of the potential ,energy model.

[0049] Hereinafter, a data set (or training set) includes many unit cells of a large number of atoms, for example, the data set may include a molecular data set or an atomic data set.

[0050] Then, by using the training framework of the GNN-based potential energy model, the training of the potential energy model is performed based on the determined atomic graph. Here, the input of the potential energy model can be the atomic graph, and the output of the potential energy model can be the energy parameters and force parameters of the atoms.

[0051] exist Figure 1 In the case shown in , the initial value of the truncation radius is a random value or a preset fixed value. In the related art, the hyperparameters (especially the truncation radius) of the potential energy model based on GNN are one of the most important parameters for determining the model scale and model accuracy. Figure 1The initial value of the truncation radius in can only be determined by a random process or can be a pre-set fixed value. Therefore, the truncation radius that cannot be adaptively adjusted has a greater negative impact on the training of the potential energy model. In addition, since the forward calculation process of the potential energy model based on GNN is slow, the time cost of training the potential energy model using the truncation radius is very large.

[0052] When the potential energy model training in the training framework is completed, the energy accuracy E is inferred using the trained potential energy model. e , force accuracy E f and the number of edges N in the atomic graph e Based on the inferred inference parameters (i.e., energy accuracy E e , force accuracy E f and the number of edges in the atomic graph N e ) determines whether the currently trained potential energy model meets the requirements for performing MD simulations.

[0053] When the currently trained potential energy model meets the requirements, the currently trained potential energy model is determined as the final GNN-based potential energy model. When the number of currently trained potential energy models does not meet the requirements, the loss of the currently trained potential energy model is calculated based on the inference parameters, the value of the truncation radius is adjusted based on the loss, and the training of the GNN-based potential energy model in the training framework is re-executed to determine a GNN-based potential energy model that meets the requirements.

[0054] Specifically, the loss is calculated by the loss function defined in Equation 1 below:

[0055] Loss = αE e + βE f +γN e Equation 1

[0056] Among them, Loss represents the loss of the calculated training potential model, α, β and γ represent the proportion of the corresponding calculation items in the requirements, and E e is the energy accuracy, E f is the force accuracy, and N e is the number of edges in the atomic graph (also referred to as “edge number” for short in this disclosure).

[0057] Based on the calculation results of the above loss function, use the parameter tuner to adjust the hyperparameters. Figure 1 In the case shown, the value of the adjusted cutoff radius is still a randomly generated initial value. Finally, the training of the GNN-based potential energy model in the training framework is re-executed using the adjusted cutoff radius value and the training set of the large-scale atomic number. In this case, an undesirable model may still be obtained after completing the training.

[0058] Therefore, in the related art, a large amount of training data is used to perform the training of the potential energy model based on GNN. A large amount of data will result in a considerable amount of training calculations, wasting computing resources. In addition, due to the use of random or fixed values ​​of the cutoff radius, it is necessary to try multiple times to adjust the hyperparameters of the potential energy model (especially the cutoff radius) to obtain relatively ideal results. The time cost and computational cost introduced in the parameter adjustment process are also quite large. In addition, the relevant loss function only considers the accuracy index without considering the amount of calculation. The calculation process of the loss function converges slowly, resulting in a large amount of computational workload. In summary, the conventional training of the potential energy model based on GNN has at least the problems described above.

[0059] In order to at least solve the above-mentioned problems, the present disclosure proposes a method and device that can determine the hyperparameters including the truncation radius configuration of the potential energy model based on the graph neural network (GNN). According to the methods and devices of various embodiments of the present disclosure, the data set of the potential energy model based on the GNN can be sampled to obtain samples that do not lose accuracy and reduce the amount of calculation, thereby reducing unnecessary waste of computing resources; relatively reasonable hyperparameters can be set, for example, the optimal truncation radius configuration can be adaptively set for the data set of the potential energy model based on the GNN, thereby reducing the time cost of tuning the hyperparameters of the potential energy model; a new balanced loss function can also be defined, which can consider both the accuracy index and the model's computational index, thereby flexibly controlling the model training and hyperparameter adjustment. According to an embodiment of the present disclosure, the set optimal truncation radius configuration can be used to implement the training of the potential energy model based on the GNN, so that the model can quickly complete the model training while achieving high accuracy, and the model training can also maintain a low computational amount. In addition, the present disclosure also proposes a new measurement method to accurately measure the influence of different elements on the number of edges in the atomic graph generated by the potential energy model, thereby providing reference guidance when the user adjusts the truncation radius configuration.

[0060] The technical solutions according to the embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0061] Figure 2 is a flowchart illustrating a method for determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure. Figure 3 is a diagram illustrating a brief process of determining hyperparameters of a GNN-based potential energy model according to an embodiment of the present disclosure.

[0062] Reference Figure 2 , in operation S210 , a key sample is obtained from a plurality of samples of a data set for molecular dynamics simulation.

[0063] For example, refer to Figure 3, through key sample selection, key samples (such as, Figure 3 That is, the original data set is sampled to obtain key samples with corresponding data features but smaller sample size.

[0064] Here, the data set used for molecular dynamics simulation may include, for example, Figure 1 The described large-scale atomic number training set, for example, a molecular data set or an atomic data set. In the present disclosure, the original data set may consist of several unit cells, each unit cell further includes one or more atoms, and the number and distribution of atoms in each unit cell may be the same or different.

[0065] According to an embodiment of the present disclosure, a data set may include multiple unit cells, wherein each unit cell may be a sample, that is, an original data set including multiple unit cells includes multiple samples. In addition, a sample may also include multiple unit cells, which is not limited by the present disclosure. In this article, a sample may also be referred to as a unit cell sample.

[0066] In the related art, a training set with a large number of atoms is usually used to directly perform the training of the potential energy model. The initial data with a huge sample size makes the training of the model take a lot of time. Therefore, the present disclosure proposes a method for obtaining key samples from multiple samples of a data set for molecular dynamics simulation by key sample selection. Figure 5 to Figure 6 Operation S210 is described in detail.

[0067] After the key samples are acquired, in operation S220 , a truncation radius configuration of the potential energy model is determined based on the key samples, wherein the truncation radius configuration includes a truncation radius for each element combination.

[0068] According to an embodiment of the present disclosure, the truncation radius configuration refers to the configured value of the truncation radius for one or more different element combinations. Figure 3 , by using the acquired critical samples, the hyperparameters including the initial values ​​of the optimized cutoff radius configuration can be determined.

[0069] In the related art, the training of potential energy models usually only sets a single random or fixed truncation radius value each time. Inappropriate truncation radius values ​​will lead to high time and computational costs in the model training process. In the embodiments of the present disclosure, considering the characteristics of the data set about atoms or molecules, different truncation radii can be configured for different element combinations, so that the setting of the model's hyperparameters is more reasonable and the model has better adaptability. Figure 5 and Fig. 9 Operation S220 is described in detail.

[0070] In operation S230 , training of a potential energy model is performed based on the key samples and the cutoff radius configuration, and the cutoff radius configuration is adjusted based on an inference result of the trained potential energy model.

[0071] For example, refer to Figure 3 , based on the determined key samples and the determined initial value of the truncation radius configuration, an atomic graph as an input for training the potential energy model in the training framework of the GNN-based potential energy model is determined.

[0072] Refer to the following Figure 4 Specific details of an atom graph according to an embodiment of the present disclosure are described. Figure 4 is a diagram illustrating an example of an atom graph according to an embodiment of the present disclosure.

[0073] Figure 4 (a) shows an example of an original data set according to an embodiment of the present disclosure, wherein a small dot represents an atom, and it can be seen that the original data set has a large amount of data.

[0074] Figure 4 (b) shows an atomic diagram of a cutoff radius of a basic unit according to an embodiment of the present disclosure.

[0075] In the present disclosure, an atom graph may be used as an input to a potential energy model to predict the motion of atoms, and the atom graph may include nodes and edges. Figure 4 In (b), a node of the atomic graph (i.e., Figure 4 The circle in (b) represents an atom in the data set. When the distance between two atoms is less than the cutoff radius ( Figure 4 (b), the cutoff radius is one unit), there is an edge between the two atoms (i.e., Figure 4 The connecting line between the two circles in (b).

[0076] Therefore, the number of edges in the atomic graph increases rapidly as the value of the cutoff radius increases. Figure 4 (c) shows an atomic graph of two basic units of cutoff radius according to an embodiment of the present disclosure. It can be seen that the value of the cutoff radius has a great influence on the number of edges in the atomic graph. As the cutoff radius increases, the number of edges in the atomic graph increases significantly, which increases the amount of data input to the potential energy model. In the present disclosure, the number of edges in the atomic graph can be used to evaluate the amount of calculation. The more edges there are in the atomic graph, the more calculations there are.

[0077] Therefore, according to an embodiment of the present disclosure, a suitable input of a potential energy model is obtained by adaptively determining a cutoff radius configuration.

[0078] Return to reference Figure 3 According to an embodiment of the present disclosure, based on the atomic graph determined according to the key samples and the cutoff radius configuration, the training of the GNN-based potential energy model is performed in the training framework of the GNN-based potential energy model.

[0079] According to an embodiment of the present disclosure, the training framework of the GNN-based potential energy model may include multiple neural layers for performing training, etc. Here, in order to avoid unnecessary details obscuring the present disclosure, the description of the specific training process of the training framework of the potential energy model will be omitted, and any relevant potential energy model training method can be used to train the GNN-based potential energy model according to an embodiment of the present disclosure.

[0080] According to an embodiment of the present disclosure, when the training of the potential energy model based on GNN is completed, the energy accuracy E is inferred using the currently trained potential energy model. e , force accuracy E f and the number of edges N in the atomic graph e , and determine whether the currently trained potential energy model meets the requirements for performing MD simulations based on the determined inference parameters.

[0081] For example, in the present disclosure, the requirements for performing MD simulations may include accuracy requirements and / or performance requirements while satisfying computing capability conditions, and the computing capability conditions may include limitations on the computing capability used to perform MD simulations, for example, memory limitations (such as, for example, graphics processing units (GPUs)), computing power limitations, resource limitations, etc., but the present disclosure is not limited thereto.

[0082] According to an embodiment of the present disclosure, when the currently trained potential energy model meets the requirements, this means that the currently trained potential energy model can be used to perform MD simulation. In this case, the currently trained potential energy model is determined as the final graph neural network-based potential energy model.

[0083] According to an embodiment of the present disclosure, when the currently trained potential energy model does not meet the requirements, this means that the currently trained potential energy model cannot be used to perform MD simulation. For example, the model may not be used due to current computing power limitations. Therefore, it is necessary to adjust the hyperparameters of the potential energy model (for example, the cutoff radius configuration) and re-execute the training of the GNN-based potential energy model in the training framework to determine a GNN-based potential energy model that meets the requirements.

[0084] Regarding the operation of adjusting the hyperparameters in operation S230, the embodiment of the present disclosure provides a loss function that considers the balance of the accuracy index and the performance index at the same time to perform the tuning of the hyperparameters. Figure 5 This operation is described in detail.

[0085] In addition, according to an embodiment of the present disclosure, operation S230 can be repeatedly performed, that is, in each repeated operation, the training of the potential energy model is repeatedly performed in the training framework based on the key samples and the truncation radius configuration adjusted by the parameter tuner, and the truncation radius configuration is adjusted based on the inference result of the trained potential energy model until the current potential energy model is determined to meet the requirements based on the inference result of the trained potential energy model.

[0086] In addition, the requirements here may include, for example, the requirements for performing MD simulations as described above and any other user requirements for the potential energy model, but the present disclosure is not limited thereto, as long as the requirements can be used to determine whether the final GNN-based potential energy model is obtained.

[0087] Refer to the following Figure 5 right Figure 2 and Figure 3 A more detailed description of each operation is given in the following. Figure 5 is a diagram illustrating a detailed process of determining hyperparameters of a GNN-based potential energy model according to an embodiment of the present disclosure.

[0088] According to an embodiment of the present disclosure, the step of acquiring key samples from a plurality of samples of a data set for molecular dynamics simulation in operation S220 includes: selecting key samples from a plurality of samples by using a weighted support vector regressor (SVR).

[0089] For example, refer to Figure 5 , by selecting multiple samples of a dataset (e.g., a training set of a large number of atoms) using a weighted support vector regressor, key samples are determined from multiple samples of a dataset.

[0090] Refer to the following Figures 6 to 8 The operation of obtaining key samples by using weighted SVR is described in detail. Figure 6 is a diagram illustrating a process of acquiring key samples according to an embodiment of the present disclosure. Figure 7 is a diagram illustrating a process of determining a sample weight according to an embodiment of the present disclosure. Figure 8 is a diagram illustrating a fitting process using weighted SVR according to an embodiment of the present disclosure.

[0091] Reference Figure 6 , showing multiple unit cell samples of a cubic structure and multiple weights corresponding to the multiple unit cell samples, wherein each cubic structure represents a unit cell sample including at least one atom. In the present disclosure, the weight of a unit cell sample may also be referred to as a sample weight or a sample weight.

[0092] According to an embodiment of the present disclosure, in operation S610, weights of a plurality of samples in a data set are determined based on statistical features of the plurality of samples.

[0093] According to an embodiment, the statistical characteristics of the sample may include, for example, the number of samples with the same or similar characteristics in the data set. For example, the statistical characteristics of the sample may be a statistical characteristic of the sample related to the number of atoms, such as the number of unit cell samples with the same number of atoms, but the present disclosure is not limited thereto, and the statistical characteristics of the sample may be determined in any appropriate manner.

[0094] For example, refer to Figure 6 , the number of atoms N can be determined based on the number of atoms included in the unit cell sample 1 A collection of unit cell samples with N atoms 2 A collection of unit cell samples with N atoms 3 The collection of unit cell samples and the number of atoms is N 4 A collection of unit cell samples, and so on.

[0095] Specifically, refer to Figure 7 , taking the number of atoms as an example to describe the determination of sample weights. According to an embodiment, the step of determining the weights of multiple samples includes: obtaining multiple samples from an original data set (for example, determining each unit cell (or multiple unit cells) in the data set as a unit cell sample); collecting statistical features of multiple samples in the data set (for example, statistical features related to the number of atoms in the unit cell sample); and determining the weights of multiple samples based on the collected statistical features of the multiple samples.

[0096] According to an embodiment, one or more atoms having a number N may be obtained from the original data set. 1 A unit cell sample of one or more atoms N 2 A unit cell sample of one or more atoms N 3 A unit cell sample of one or more atoms N 4 A unit cell sample of ...

[0097] According to an embodiment, the step of collecting statistical features of a plurality of samples in a data set may include: determining the number of atoms as N 1 The count (or number) of the unit cell sample L 1 , the number of atoms is N 2 The number of unit cell samples L 2 , the number of atoms is N 3 The number of unit cell samples L 3 , the number of atoms is N 4 The number of unit cell samples L 4...; calculating the total number L of counts of all unit cell samples; and determining the ratio of the counts of unit cell samples having the same number of atoms to the total number L of counts of all unit cell samples.

[0098] According to an embodiment, based on the collected statistical features of the plurality of samples, the step of determining the weights of the plurality of samples may include determining the weights of the corresponding unit cell samples as the ratio of the counts of unit cell samples having the same or similar features to the total counts of all unit cell samples.

[0099] That is to say, since the number of atoms and atomic distribution in each unit cell sample may be different, the present disclosure proposes to use the number of atoms in each unit cell sample as a reference and calculate the ratio of unit cell samples with a certain number of atoms to all unit cell samples in the entire data set as a weight to measure the importance of the unit cell sample.

[0100] After the sample weights are determined, return Figure 6 In operation S620, a plurality of weighted samples are obtained by respectively multiplying the plurality of samples by the determined weights, and a support vector is obtained as a key sample based on the plurality of weighted samples by using weighted SVR.

[0101] According to an embodiment of the present disclosure, a weighted sample may be obtained by multiplying the unit cell sample with the sample weight. Here, although the sample is weighted by multiplication, other weighting methods may be used to obtain a weighted sample according to an embodiment of the present disclosure, and the present disclosure is not limited thereto.

[0102] According to an embodiment of the present disclosure, weighted samples are used to fit a weighted support vector regressor based on a support vector machine (SVM).

[0103] Specifically, refer to Figure 8 , SVM can use appropriate kernel functions to make the samples linearly separable in the feature space. For MD simulation tasks, the true energy and force values ​​in the unit cell samples are predicted as regression tasks. Figure 8 In , f(x) is the analytical expression of the classification interval plane, which can be understood as an SVM model, where w and b are the parameters of the SVM model, w is the weight parameter matrix of the SVM model, and b is the offset parameter matrix of the SVM model. Figure 8In , the thick solid line may represent the hyperplane, the dotted line may represent the soft interval (or soft boundary), the shaded area may represent the σ boundary band, the samples marked with dotted circles will be regarded as correct samples in the regression task, and the samples marked with solid circles may represent the samples closest to the soft interval (or soft boundary) (that is, the samples marked with solid circles are support vectors). Therefore, the samples located near the soft interval (or soft boundary) can be used as support vectors, and the support vectors can be used as key samples (for example, Figure 6 ).

[0104] The embodiments of the present disclosure use SVR as an effective method for selecting key samples. The key samples (i.e., support vectors) obtained by fitting are often half or even less than the original samples, which can greatly reduce the amount of calculation. In addition, since the characteristic of SVR is that most of the training samples after training will not be retained, the final SVM model is only related to the support vectors. Therefore, accordingly, the result of sampling the original data set can maintain a structural distribution that is substantially the same as the original data set, without losing the distribution characteristics of the original data, thereby maintaining a high accuracy while greatly saving the time of model training.

[0105] In addition, although the present disclosure shows that the weighted SVR is used to sample the original data set to obtain key samples, the manner of obtaining key samples in the present disclosure is not limited thereto, and other sampling methods may be used to obtain key samples.

[0106] Return to reference Figure 5 , key samples are obtained by sampling the original data set, and then the hyperparameter determination process is performed based on the key samples.

[0107] According to an embodiment of the present disclosure, the step of determining the truncation radius configuration based on the key sample in operation S220 includes: based on the key sample, determining the influence factor of each element combination of atoms in the key sample, wherein the influence factor indicates the degree of influence of the element combination on the number of edges in the atomic graph; based on the influence factor of each element combination, determining the truncation radius configuration.

[0108] Fig. 9 is a diagram illustrating neighborhood changes of SiN molecules before and after applying a cutoff radius configuration according to an embodiment of the present disclosure.

[0109] In semiconductor materials, in addition to silicon Si, there are often other chemical elements, for example, Fig. 9 , in the silicon and nitrogen (SiN) data set, there are two types of atoms, silicon (Si) atoms and nitrogen (N) atoms.

[0110] Fig. 9(a) shows an atomic diagram in a training framework of a potential energy model using a fixed cutoff radius value in the related art. Fig. 9 (a) of FIG. 1 , the same fixed cutoff radius value (Rmax) is used for the nitrogen-nitrogen (NN) element combination, the nitrogen-silicon (N-Si) element combination, and the silicon-silicon (Si-Si) element combination, i.e., 6.0 angstroms. Fig. 9 In case (a), the nitrogen atom as the central atom has a larger neighborhood range.

[0111] According to an embodiment of the present disclosure, neighbor atoms are other atoms within the cutoff radius range of a certain atom as the central atom (i.e., the neighborhood of the atom), for example, Fig. 9 (a) shows all neighboring atoms of the nitrogen atom as the central atom.

[0112] Since the cutoff radius can often determine the number of neighboring atoms of a central atom, it has a great impact on the model calculation amount and accuracy. In order to accelerate the process of adjusting the cutoff radius configuration and to obtain a better initial value of the cutoff radius, the present disclosure proposes a method for determining the cutoff radius configuration using different cutoff radii for different element combinations.

[0113] Specifically, in order to configure more suitable values ​​of each truncation radius, each truncation radius is determined by considering the influence of different element combinations on the number of edges of the atomic graph. The following first takes the truncation radii of the three element combinations of nitrogen-nitrogen, nitrogen-silicon and silicon-silicon (respectively expressed as R_N_N, R_N_Si and R_Si_Si) as examples to describe in detail the operation of determining the influence factor of each element combination of atoms.

[0114] Since the existing indicators of similarity of general data are usually not applicable to the measurement of atomic data sets, and usually only focus on the position or force of the atom itself when judging similarity, but in fact, in a unit cell, in addition to the local characteristics of atoms, multiple atoms also have overall characteristics. Therefore, before determining the influencing factors, the present disclosure also proposes a comprehensive indicator for simultaneously measuring the attribute characteristics (i.e., local characteristics (for example, the physical properties of the atoms themselves)) and geometric characteristics (i.e., overall characteristics) of atoms - the mutual coordinate M.

[0115] According to an embodiment of the present disclosure, based on the key sample, the step of determining the influence factor of each element combination of atoms in the key sample includes: calculating the mutual coordinates of atoms (e.g., the i-th atom) in the key sample and the element ratios of neighboring atoms (e.g., the j-th atom) of the atoms; based on the mutual coordinates of the atoms and the element ratios of neighboring atoms, determining the influence factor of each element combination.

[0116] According to an embodiment of the present disclosure, the step of calculating the mutual coordinates of atoms in the key sample may include: determining the mutual coordinates based on the position parameters and force parameters of the atom (e.g., the i-th atom) and the neighboring atom (e.g., the j-th atom). Specifically, the mutual coordinates M indicating the property characteristics and geometric characteristics of the atoms may be calculated by equation 2:

[0117]

[0118] Among them, M i It can represent the mutual coordinates of the i-th atom, N R is the number of atoms in the region divided based on the preset cutoff radius reference value R, wherein the cutoff radius reference value R as one of the hyperparameters can be preset according to the computing capacity size, X i Can represent the position coordinates of the i-th atom, X j It can represent the position coordinates of the jth atom, where the jth atom is the neighboring atom within the range divided based on R with the i-th atom as the center, and F i represents the force coordinate of the i-th atom, F j represents the force coordinate of the jth atom, ω p represents the weight of the atomic position coordinate in the system, ω F represents the weight of the atomic force coordinate in the system, ω p and ω F , the two parameters can be set according to the user's actual simulation scenario. For example, in a system that satisfies periodic boundary conditions, the two weights are both 1:1.

[0119] In addition, Z in Equation 2 i is an optional energy shift parameter that represents the offset of the coordinates of the displacement under periodic boundary conditions and can be used to determine whether to use Z based on specific conditions. i For example, when certain conditions (periodic boundary conditions) are not met, the energy transfer parameter Z may not be used. i For example, when certain conditions (periodic boundary conditions) are met, the energy transfer parameter Z can be used i Periodic boundary conditions represent conditions that keep the number of particles in a simulation system constant as the particles move.

[0120] The parameters in the above equations can all be set in the model training configuration file. According to an embodiment of the present disclosure, the property characteristics of atoms are reflected by using parameters representing force coordinates, and the spatial characteristics or geometric characteristics of atoms in a unit cell are reflected by using parameters representing position coordinates, so as to capture the distribution of atomic data in a data set, and the calculated mutual coordinates can be used to further calculate the influence factor that measures the sensitivity of the influence of element combinations on the number of edges in an atomic graph.

[0121] According to an embodiment of the present disclosure, the element ratio of a neighbor atom may represent the proportion of the element of the neighbor atom in all elements in the neighborhood of the central atom.

[0122] According to an embodiment of the present disclosure, the step of calculating the element ratio of neighbor atoms of an atom in a key sample may include: determining the count of neighbor atoms of the atom corresponding to each element; calculating the total count of neighbor atoms of the atom; and determining the ratio of the count of neighbor atoms corresponding to each element to the total count of neighbor atoms of the atom as the element ratio.

[0123] For example, refer to Fig. 9 (a), assuming that the elemental species of the nitrogen atom as the central atom is the number of neighboring atoms of nitrogen C N is 25, and the element type of the nitrogen atom is the number of neighboring atoms of silicon C Si is 36, then the total number of counts of the neighboring atoms of the nitrogen atom is C total = 25 + 36 = 61, by C N Divide by C total The element ratio of the nitrogen neighboring atoms of the nitrogen atom (i.e., the nitrogen-nitrogen element combination) is Ratio N It is determined to be 25 / 61≈40.98%. Similarly, by Si Divide by C total The element ratio of the silicon neighbor atoms of the nitrogen atom (i.e., the element combination of nitrogen and silicon) is Si Determined to be 36 / 61≈59.02%.

[0124] According to an embodiment of the present disclosure, after the mutual coordinates of atoms and the element ratios of neighboring atoms are determined as described above, the influence factor of each element combination can be determined. The process of determining the influence factor is specifically described below through Table 1.

[0125] Table 1 Algorithm process for calculating impact factors

[0126]

[0127]

[0128] According to an embodiment of the present disclosure, based on the mutual coordinates of atoms and the element ratios of neighboring atoms, the step of determining the influence factor of each element combination may include: based on the mutual coordinates of all atoms included in the unit cell sample, selecting a predetermined number (such as, K) of atoms from all atoms in the unit cell sample; for each element combination, based on the element ratio of a specific neighboring atom of a specific atom among the predetermined number of atoms (for example, for the element combination of nitrogen-nitrogen, the specific atom is a nitrogen atom, and the specific neighboring atom is a nitrogen atom), the average value of the element ratio of the specific neighboring atom of the specific atom is determined as the influence factor of the element combination. Below, an example process of calculating mutual coordinates and element ratios is described with reference to the example of Table 3.

[0129] Table 3 Examples of calculating mutual coordinates and element ratios

[0130]

[0131] Table 3 shows the mutual coordinates of the i-th atom and the element ratios of the neighboring atoms of the i-th atom calculated based on the above operation, taking the SiN data set as an example. Specifically, the mutual coordinates of the first atom are M 1 , and the element ratio of the nitrogen neighboring atoms of the first atom is Ratio N The element ratio of silicon neighbor atoms is 40.98%. Si is 59.02%; the mutual coordinates of the second atom are M 2 , and the element ratio of the nitrogen neighboring atoms of the second atom is Ratio N The element ratio of silicon neighbor atoms is 34.15%. Si is 65.85%; the mutual coordinates of the third atom are M 3 , and the element ratio of the nitrogen neighboring atoms of the third atom is Ratio N The element ratio of silicon neighbor atoms is 45.60%. Si is 54.40%, …. If the value of K is 3000, then based on M 1 、M 2 、M 3 , ..., 3000 atoms are selected from all the atoms in the unit cell sample, and the influence factor of each element combination is calculated by the following equation 4:

[0132]

[0133] Among them, Importance (N,N) It can represent the impact factor of NN element combination, Importance (N,Si) It can represent the impact factor of N-Si element combination, Importance (Si,Si)The influence factor that can represent the Si-Si element combination, and k can represent the number of specific atoms among K atoms, which is less than or equal to K.

[0134] For example, for the N-N element combination, the silicon atoms among the current K atoms cannot form the N-N element combination. At this time, k can be equal to the value obtained by subtracting the number of silicon atoms among the K atoms from K, and i can represent the i-th atom among the k atoms. That is, when the element type of a certain atom among the current K atoms does not belong to any element in the element combination for which the influence factor is to be calculated, the calculation regarding this atom is omitted when calculating the average value. Therefore, for each element combination, based on the element ratios of the specific neighboring atoms of the k specific atoms among the K atoms, the average value of the element ratios of the specific neighboring atoms of the k specific atoms is determined as the influence factor of this element combination.

[0135] The influence factor determined through the above operations can be used to evaluate the sensitivity of the element combination to the number of edges of the atomic graph, so as to configure hyperparameters for potential energy model training for different sensitivities.

[0136] Return reference Figure 5 According to an embodiment of the present disclosure, in the case where the influence factor of each element combination is determined, the step of determining the cutoff radius configuration based on the influence factor of each element combination may include: for each element combination, determining the cutoff radius within a predetermined cutoff radius range based on the influence factor of each element combination.

[0137] According to an embodiment of the present disclosure, the order of element combinations sorted by importance can be determined based on the influence factor of each element combination (for example, the sorting of the magnitudes of the influence factors). The larger the influence factor, the greater the importance of this element combination, the greater the influence of this element combination on the number of edges in the atomic graph, that is, the atoms in this element combination are more sensitive to neighboring atoms. Correspondingly, this element combination is also the most sensitive to the amount of calculation. For example, in the SiN dataset, the importance of the N-N element combination (such as 0.2114) < the importance of the Si-Si element combination (such as 0.2561) < the importance of the N-Si element combination (such as 0.6232). Correspondingly, different cutoff radii can be assigned to different element combinations considering the importance.

[0138] According to an embodiment of the present disclosure, a predetermined cutoff radius range can be preset or determined. For example, the range of values of the allowable cutoff radius can be determined according to requirements, such as 4 angstroms to 7 angstroms. As the cutoff radius increases, the number of neighboring atoms also increases, the corresponding number of edges increases, and the amount of calculation will also increase accordingly.

[0139] Therefore, according to an embodiment of the present disclosure, based on the impact factor of the element combination (for example, based on the order of the size of the impact factor), the truncation radius configuration is set within a predetermined truncation radius range. For example, the truncation radius of the element combination with the smallest importance can be set to the largest, the truncation radius of the element combination with greater importance can be set to a smaller value, and the truncation radius of the element combination with the greatest importance can be set to the smallest value in ascending order based on the predetermined truncation radius range. This is shown only as an example, and the present disclosure is not limited thereto. The truncation radius can also be configured by other influencing parameters regarding the truncation radius based on the consideration of the importance determined based on the impact factor. That is, the truncation radius can also be configured in other ways based on the impact factor.

[0140] Return to reference Fig. 9 (b) shows, as an example, a diagram of a configuration having different values ​​of the cutoff radius, for example, the cutoff radius R_N_N of the NN element combination is 5.5 angstroms, the cutoff radius R_N_Si of the N-Si element combination is 6.0 angstroms, and the cutoff radius R_Si_Si of the Si-Si element combination is 5.5 angstroms (R_Si_Si is not shown). Fig. 9 Compared with (a), according to the embodiment of the present disclosure, the truncation radius configuration is determined. Fig. 9 The number of N atoms in the region divided based on the cutoff radius in (b) is reduced, and the number of corresponding neighbor atoms is also reduced. By flexibly setting the configuration of the cutoff radius of different element combinations according to the embodiment, the influence of different element combinations on the number of edges in the atomic graph is more balanced, and the set cutoff radius configuration will be closer to the initial value of the cutoff radius of the optimal solution of the potential energy model.

[0141] Return to reference Figure 5 , the potential energy model is trained based on the determined key samples and the determined truncation radius configuration. After the training is completed, according to an embodiment of the present disclosure, the step of adjusting the truncation radius configuration based on the inference result of the trained potential energy model includes: calculating the loss based on the inference result, the truncation radius and the key samples; and adjusting the truncation radius configuration based on the loss.

[0142] According to an embodiment of the present disclosure, a related parameter adjustment toolkit Neural Network Intelligence (NNI) can be used to perform the operation of adjusting hyperparameters.

[0143] The present disclosure proposes a balanced loss function. Specifically, based on the inference result, the truncation radius and the key sample, the loss is calculated by the loss function defined in the following equation 3:

[0144]

[0145] Among them, LossBalance The equalization loss calculated by the loss function according to the embodiment of the present disclosure may be represented. The following Table 2 shows a brief description of each variable in Equation 3 according to the embodiment of the present disclosure:

[0146] Table 2 Description of variables in the equalization loss function

[0147]

[0148] In Table 2, the energy prediction value and the force prediction value may be the prediction values ​​output by using a potential energy model based on a graph neural network. In addition, in Table 2, the energy truth value and the force truth value may be the truth data about atoms obtained from a data set by using a toolkit, for example, using VASP based on first-principles material atomic modeling simulation to generate the energy truth value and force truth value of atoms in the data set, which is not limited by the present disclosure.

[0149] According to an embodiment of the present disclosure, a loss function as shown in Equation 3 can be defined by a user using a toolkit. Since related loss functions tend to fluctuate greatly and converge slowly, in the equalization loss function in Equation 3, by limiting a regularization term for normalization related to the number of edges in the atomic graph and a term related to the weight and atomic mass of the sample for stabilizing the loss function, rapid convergence and stabilization of the loss function are achieved, thereby reducing the amount of calculation.

[0150] By using the new equalization loss function defined above, a loss function with less fluctuation and faster convergence can be provided while comprehensively considering accuracy indicators (for example, energy accuracy, force accuracy, etc.) and performance indicators (for example, computational amount indicators (such as the number of edges in the atomic graph, the atomic mass in key samples, etc.)), thereby greatly improving the computational efficiency during parameter adjustment.

[0151] Reference Figure 3 , the truncation radius configuration is adjusted using a parameter tuner based on the loss determined according to the loss function, and the training of the potential energy model is performed again based on the adjusted truncation radius configuration and the key samples.

[0152] According to an embodiment of the present disclosure, the parameter tuner uses a Sequential Model-Based Optimization for General Algorithm Configuration (SMAC) algorithm for general algorithm configuration, which can solve the situation where the parameter type in the Gaussian regression process cannot be discrete. The SMAC algorithm can adjust the most important model categories in the relevant technology (such as Gaussian random process models) and introduce a random forest model category in sequential model-based optimization (SMBO) to process classification parameters.

[0153] In the embodiments of the present disclosure, the accuracy and computational workload of the model can be flexibly controlled based on the parameters in the proposed loss function, which has a positive impact on the improvement of the training of the potential energy model.

[0154] In addition, according to an embodiment of the present disclosure, when training a potential model based on GNN, the relevant training framework often does not support parallel training models. In order to save time and effectively utilize computing resources, according to an embodiment of the present disclosure, the Allegro model can also be combined with the toolkit NNI through code modification and optimization, and the training framework of the model can be modified to enable experiments to run in parallel.

[0155] The researchers of the present invention also tested the method of determining the hyperparameters of the potential energy model based on the graph neural network according to the embodiment of the present invention from multiple aspects.

[0156] Specifically, when using the method for determining hyperparameters according to an embodiment of the present disclosure, the inference results of the trained potential energy model are basically close to the model accuracy in the related art in terms of the Mean Absolute Error (MAE) used to measure the accuracy of model inference, but the computing performance when performing molecular dynamics simulations (for example, the computing performance of different numbers of GPUs) is greatly improved.

[0157] In addition, in order to simulate the scenario of real production of semiconductor materials, the R&D personnel also conducted ablation experiments on each operation to verify their independent effects. According to the experiment, the key samples selected in the method for determining the hyperparameters according to the embodiment of the present disclosure have the same or similar distribution as the original data set. Therefore, compared with the effect of training with the original data set, the training using the key samples can achieve similar accuracy. In addition, the model accuracy using the key samples has the same trend as the accuracy using the original data set. In the case of using wide interval SVR (NuSVR), which is an optimized version of SVR, the training time based on key samples is significantly shortened, and the model accuracy is almost the same as the model accuracy based on all samples.

[0158] In addition, the researchers also conducted tests to verify whether the impact factor can measure the importance of various element combinations. Specifically, the researchers calculated the impact factor of each element combination in the data set based on the mutual coordinates of the data set, and determined that the most important element combination (i.e., the element combination that has the greatest impact on the number of edges in the atomic graph) is the nitrogen-silicon element combination, which is most sensitive to the number of neighboring atoms of the atom. Therefore, this element combination is most sensitive to the amount of calculation. In order to verify the results of the above-mentioned determination of the impact factor, the researchers tested all configurations using the control variable method. The conclusions of the test are consistent with the most important element combination calculated by the mutual coordinates. The method for calculating the impact factor of the embodiment of the present disclosure is feasible and effective.

[0159] Then, the researchers also verified the influence of the influence factor calculated based on the mutual coordinates on the value of setting the cutoff radius. The hyperparameters set based on the influence factor of the mutual coordinates can effectively reduce the number of hyperparameter adjustments of the model and save unnecessary resource waste. In addition, the use of the mutual coordinates that combine the position coordinates and the force coordinates disclosed in the present invention makes it possible to set the hyperparameters to the optimal value close to the optimal solution as quickly as possible.

[0160] Finally, the researchers also verified the correctness of the optimal solution obtained based on the loss function proposed in this disclosure. The model using the loss function according to the embodiment of the present disclosure can determine the optimal truncation radius configuration after measuring the model accuracy and computational complexity, thereby better balancing the model accuracy (for example, force accuracy) and computational complexity results.

[0161] In summary, based on the results of each individual ablation experiment, it can be seen that the significant improvement effect of each operation is achieved. The GNN-based model trained by the method of the embodiment of the present disclosure can ensure the accuracy of the model and accelerate the computational performance of molecular (e.g., silicon mixture) dynamics simulation.

[0162] The device according to the embodiment of the present disclosure is described in detail below. Fig.10 is a block diagram showing an apparatus for determining hyperparameters of a potential energy model based on a GNN according to an embodiment of the present disclosure.

[0163] Reference Fig.10 A device 1000 for determining hyperparameters of a potential energy model based on a GNN may include a key sample acquisition module 1010 , a hyperparameter initial value determination module 1020 , and a hyperparameter adjustment module 1030 .

[0164] According to an embodiment, the key sample acquisition module 1010 is configured to acquire key samples from multiple samples of a data set for molecular dynamics simulation, the hyperparameter initial value determination module 1020 is configured to determine a cutoff radius configuration of a potential energy model based on the key samples, wherein the cutoff radius configuration includes a cutoff radius for each element combination, and the hyperparameter adjustment module 1030 is configured to perform training of the potential energy model based on the key samples and the cutoff radius configuration, and adjust the cutoff radius configuration based on the inference result of the trained potential energy model, wherein the input of the potential energy model is an atomic graph determined based on the key samples and the cutoff radius configuration, and the output of the potential energy model includes energy parameters and force parameters of atoms.

[0165] That is, the key sample acquisition module 1010 can execute the same Figure 2 The operation corresponding to operation S210 of the method described above, the hyperparameter initial value determination module 1020 can perform the same operation as described above with reference to Figure 2 The operation corresponding to operation S220 of the method described above, the hyperparameter adjustment module 1030 may perform the same operation as described above with reference to Figure 2 The operation S230 of the method described above corresponds to an operation. Accordingly, the various details described above regarding the method for determining hyperparameters of a potential energy model based on GNN can be applied to the apparatus 1000 for determining hyperparameters of a potential energy model based on GNN.

[0166] According to an embodiment of the present disclosure, the key sample acquisition module 1010 is configured to acquire key samples from a plurality of samples of a data set for molecular dynamics simulation by the following operation: selecting key samples from the plurality of samples by using a weighted support vector regressor.

[0167] According to an embodiment of the present disclosure, each of the plurality of samples includes at least one atom.

[0168] According to an embodiment of the present disclosure, the key sample acquisition module 1010 is configured to select key samples from multiple samples by using a weighted support vector regressor through the following operations: determining weights of the multiple samples based on statistical features of the multiple samples in the data set; obtaining multiple weighted samples by multiplying the multiple samples by the determined weights respectively; and obtaining support vectors as key samples based on the multiple weighted samples by using a weighted support vector regressor.

[0169] According to an embodiment of the present disclosure, the hyperparameter initial value determination module 1020 is configured to determine the truncation radius configuration based on the key samples through the following operations: based on the key samples, determine the influence factor of each element combination, wherein the influence factor indicates the degree of influence of the element combination on the number of edges in the atomic graph; based on the influence factor of each element combination, determine the truncation radius configuration.

[0170] According to an embodiment of the present disclosure, the hyperparameter initial value determination module 1020 is configured to determine the influence factor of each element combination based on the key sample through the following operations: calculating the mutual coordinates of atoms in the key sample and the element ratios of neighboring atoms of the atoms, wherein the mutual coordinates indicate the property characteristics and geometric characteristics of the atoms, and the neighboring atoms are other atoms within the cutoff radius of the atom centered on the atom; determining the influence factor of each element combination based on the mutual coordinates of the atoms and the element ratios of the neighboring atoms.

[0171] According to an embodiment of the present disclosure, the hyperparameter initial value determination module 1020 is configured to calculate the mutual coordinates of atoms in the key sample by the following operation: determining the mutual coordinates based on position parameters and force parameters of the atom and neighboring atoms.

[0172] According to an embodiment of the present disclosure, the hyperparameter initial value determination module 1020 is configured to determine the truncation radius configuration based on the influence factor of each element combination through the following operations: based on the influence factor of each element combination, determine the truncation radius for each element combination within a predetermined truncation radius range.

[0173] According to an embodiment of the present disclosure, the hyperparameter adjustment module 1030 is configured to adjust the truncation radius configuration based on the inference result of the trained potential energy model through the following operations: calculating the loss based on the inference result, the truncation radius and the key samples; and adjusting the truncation radius configuration based on the loss.

[0174] In addition, it should be understood that the various modules in the device 1000 according to the exemplary embodiment of the present disclosure may be implemented as hardware components and / or software components. Those skilled in the art may implement the various modules, for example, using a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC), according to the processing performed by the defined various modules.

[0175] According to an embodiment of the present disclosure, an electronic device is also provided, comprising: at least one processor; and at least one memory storing computer executable instructions. When the computer executable instructions are executed by the at least one processor, the at least one processor is prompted to execute the method for determining hyperparameters of the potential energy model based on the GNN as described above.

[0176] According to an embodiment of the present disclosure, the electronic device may be a PC, a tablet device, a personal digital assistant, a smart phone, or other device capable of executing the above-mentioned instruction set. Here, the electronic device is not necessarily a single electronic device, but may also be any device or circuit capable of executing the above-mentioned instruction (or instruction set) individually or jointly. The electronic device may also be part of an integrated control system or a system manager, or may be configured as a portable electronic device interconnected with a local or remote (e.g., via wireless transmission) interface.

[0177] In electronic devices, the processor may include a central processing unit (CPU), a graphics processing unit (GPU), a programmable logic device, a dedicated processor system, a microcontroller or a microprocessor. As an example and not limitation, the processor may also include an analog processor, a digital processor, a microprocessor, a multi-core processor, a processor array, a network processor, etc.

[0178] The processor can execute instructions or codes stored in the memory, wherein the memory can also store data. Instructions and data can also be sent and received through the network via the network interface device, wherein the network interface device can adopt any known transmission protocol.

[0179] The memory may be integrated with the processor, for example, RAM or flash memory is arranged within an integrated circuit microprocessor or the like. In addition, the memory may include a separate device, such as an external disk drive, a storage array, or any other storage device that can be used by a database system. The memory and the processor may be operatively coupled, or may communicate with each other, such as through an I / O port, a network connection, etc., so that the processor can read files stored in the memory.

[0180] In addition, the electronic device may also include a video display (such as a liquid crystal display) and a user interaction interface (such as a keyboard, a mouse, a touch input device, etc.) All components of the electronic device may be connected to each other via a bus and / or a network.

[0181] According to an embodiment of the present disclosure, a computer-readable storage medium may also be provided, wherein, when the instructions in the computer-readable storage medium are executed by at least one processor, the at least one processor is prompted to execute the method for determining hyperparameters of the GNN-based potential energy model as described above.

[0182] According to an exemplary embodiment of the present disclosure, examples of computer-readable storage media include read-only memory (ROM), random access programmable read-only memory (PROM), electrically erasable programmable read-only memory (EEPROM), random access memory (RAM), dynamic random access memory (DRAM), static random access memory (SRAM), flash memory, nonvolatile memory, CD-ROM, CD-R, CD+R, CD-RW, CD+RW, DVD-ROM, DVD-R, DVD+R, DVD-RW, DVD+RW, DVD-RAM, BD-ROM, BD-R, BD-R LTH, BD-RE, Blu-ray or optical disk storage, hard disk drive (HDD), solid state drive (SSD), card storage (such as, multimedia card, secure digital (SD) card or extreme digital (XD) card), magnetic tape, floppy disk, magneto-optical data storage device, optical data storage device, hard disk, solid state disk and any other device, any other device is configured to store computer programs and any associated data, data files and data structures in a non-transitory manner and provide the computer programs and any associated data, data files and data structures to a processor or computer so that the processor or computer can execute the computer program. The computer program in the above-mentioned computer-readable storage medium can be run in an environment deployed in electronic devices such as clients, hosts, proxy devices, servers, etc. In addition, in one example, the computer program and any associated data, data files and data structures are distributed on a networked computer system, so that the computer program and any associated data, data files and data structures are stored, accessed and executed in a distributed manner by one or more processors or computers.

[0183] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses or adaptations of the present disclosure, which follow the general principles of the present disclosure and include common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the claims.

[0184] It should be understood that the present disclosure is not limited to the exact structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the claims.

Claims

1. A method for determining hyperparameters of a potential energy model based on a graph neural network, the method comprising: Obtain key samples from multiple samples of the dataset used for molecular dynamics simulations; Determining a cutoff radius configuration of the potential energy model based on the key samples, wherein the cutoff radius configuration includes a cutoff radius for each element combination; performing training of the potential energy model based on the key samples and the cutoff radius configuration, and adjusting the cutoff radius configuration based on an inference result of the trained potential energy model, The input of the potential energy model is an atomic graph determined based on the key sample and the cutoff radius configuration, and the output of the potential energy model includes energy parameters and force parameters of atoms.

2. The method according to claim 1, wherein: The steps to obtain critical samples from multiple samples of the dataset for molecular dynamics simulations include: The key samples are selected from the plurality of samples by using a weighted support vector regressor.

3. The method according to claim 2, wherein: Each sample of the plurality of samples includes at least one atom, The step of selecting key samples from the plurality of samples by using a weighted support vector regressor comprises: Determining weights of the multiple samples based on statistical characteristics of the multiple samples in the data set; Obtaining a plurality of weighted samples by multiplying the plurality of samples by the determined weights respectively; By using a weighted support vector regressor, a support vector is obtained as the key sample based on the plurality of weighted samples.

4. The method according to claim 1, wherein: The step of determining the cutoff radius configuration based on the key sample comprises: Based on the key sample, determining an influence factor of each element combination of atoms in the key sample, wherein the influence factor indicates the degree of influence of the element combination on the number of edges in the atom graph; The cutoff radius configuration is determined based on the impact factor for each element combination.

5. The method according to claim 4, wherein: Based on the key sample, the step of determining the influence factor of each element combination of atoms in the key sample comprises: Calculating mutual coordinates of atoms in the key sample and element ratios of neighboring atoms of the atoms, wherein the mutual coordinates indicate property characteristics and geometric characteristics of the atoms, and the neighboring atoms are other atoms within a cutoff radius of the atom as the central atom; The influence factor of each element combination is determined based on the mutual coordinates of the atoms and the element ratios of the neighbor atoms.

6. The method according to claim 5, wherein: The step of calculating the mutual coordinates of atoms in the key sample comprises: The mutual coordinates are determined based on position parameters and force parameters of the atom and the neighboring atoms.

7. The method according to claim 4, wherein: Based on the influencing factor of each element combination, the step of determining the cutoff radius configuration comprises: Based on the influencing factor of each element combination, a cutoff radius is determined for each element combination within a predetermined cutoff radius range.

8. The method according to claim 1, wherein: The step of adjusting the cutoff radius configuration based on the inference result of the trained potential energy model includes: Calculating a loss based on the inference result, the cutoff radius, and the key sample; Based on the loss, the cutoff radius configuration is adjusted.

9. A device for determining hyperparameters of a potential energy model based on a graph neural network, the device comprising: a key sample acquisition module configured to acquire key samples from a plurality of samples of a data set for molecular dynamics simulation; A hyperparameter initial value determination module is configured to determine a truncation radius configuration of the potential energy model based on the key samples, wherein the truncation radius configuration includes a truncation radius of each element combination; a hyperparameter adjustment module, configured to perform training of the potential energy model based on the key samples and the cutoff radius configuration, and adjust the cutoff radius configuration based on the inference result of the trained potential energy model, The input of the potential energy model is an atomic graph determined based on the key sample and the cutoff radius configuration, and the output of the potential energy model includes energy parameters and force parameters of atoms.

10. An electronic device, comprising: at least one processor; at least one memory storing computer executable instructions, When the computer executable instructions are executed by the at least one processor, the at least one processor is prompted to perform the method according to any one of claims 1 to 8.

11. A computer-readable storage medium, wherein: When the instructions in the computer-readable storage medium are executed by at least one processor, the at least one processor is prompted to perform the method according to any one of claims 1 to 8.

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