Active learning program, active learning method, and information processing apparatus

Abstract

To reduce the number of training data and to determine training data capable of improving the accuracy of an energy prediction value by a neural network.SOLUTION: The information processing device 100 inputs each of a plurality of pieces of structure data 10 corresponding to each of a plurality of materials to an active learning neural network 40, extracts a first feature amount 14 related to a structure of each material, and calculates a second feature amount 15 related to energy in the structure of each material based on the first feature amount 14 using the active learning neural network 40. On the basis of the first feature quantity 14 and the second feature quantity 15 corresponding to each material, one or more structure data 11 are determined from among the plurality of structure data as training data for training a neural network for energy prediction for predicting the energy of the material.SELECTED DRAWING: Figure 10

Description

[Technical Field]

[0001] The present invention relates to an active learning program, an active learning method, and an information processing device. [Background technology]

[0002] Materials informatics (MI) is used to explore materials. The reactivity of a particular material is determined by its electronic structure. Today, electronic structures are calculated using density functional theory (DFT) simulations based on quantum mechanics, which require a large amount of calculations. In DFT simulations, the total electronic energy of a material (sometimes simply called "energy") is an important prediction target. In some cases, adsorption energy is also predicted.

[0003] Recently, methods have been proposed for rapidly predicting the energy of materials by using neural networks such as graph neural networks (GNNs). However, supervised learning of GNN models requires labeled training data. Calculating the labels requires large-scale DFT simulations. Therefore, from the perspective of computational load and cost, it is difficult to prepare a sufficient amount of labeled training data.

[0004] In machine learning, a technique called active learning is used to improve energy prediction accuracy using less labeled training data. In active learning, a neural network (learning model) samples effective training data to improve its own prediction performance. Therefore, active learning improves the prediction performance of energy prediction values ​​while reducing the amount of training data. Since the amount of training data for which labels are to be calculated can be reduced, the computational load of the DFT simulation for calculating labels can be reduced.

[0005] For example, active learning has been proposed to realize efficient generation of structural data for Au-Li binary materials (see Non-Patent Document 1).

[0006] In materials search, it is desirable to find promising materials from a huge amount of material data with diverse structures and energies. Therefore, GNNs for materials search are trained with diverse training data. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] K. Shimizu, et al., “Phase stability of Au-Li binary systems studied using neural network”, Phys. Rev. B,103, 094112(2021) Summary of the Invention [Problem to be solved by the invention]

[0008] In conventional active learning, a training data set is selected that takes into account the diversity of material structures by applying active learning using geometric distance. However, in conventional active learning, it is difficult to select training data that are similar in structure but have different energies. As a result, it is difficult to improve the accuracy of energy prediction values ​​using neural networks when the number of training data is small.

[0009] In one aspect, an object of the present invention is to determine training data that can reduce the number of training data sets and improve the accuracy of energy prediction values ​​obtained by a neural network. [Means for solving the problem]

[0010] In one aspect, an active learning program causes a computer to execute the following processes. The processes include inputting each of a plurality of structural data corresponding to a plurality of materials into an active learning neural network to extract a first feature quantity related to the structure of each material. The processes include calculating, using the active learning neural network, a second feature quantity related to the energy of the structure of each material based on the first feature quantity. The processes include determining, based on the first feature quantity and the second feature quantity corresponding to each material, one or more structural data from among the plurality of structural data as training data for training an energy prediction neural network that predicts the energy of the material. [Effects of the Invention]

[0011] In one aspect, the present invention can determine training data that can reduce the number of training data sets and improve the accuracy of energy prediction values ​​by a neural network. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a diagram illustrating an overview of supervised learning of an energy prediction NN. [Figure 2] FIG. 1 is a diagram illustrating an overview of a NN training method that applies active learning. [Figure 3] FIG. 10 is a diagram illustrating a method for determining training data in active learning in a comparative example. [Figure 4] FIG. 10 is a diagram showing an example in which structure data constitutes a uniform population. [Figure 5] FIG. 10 is a diagram showing an example in which structure data constitutes a population of multiple clusters. [Figure 6] FIG. 10 is a diagram illustrating an example of a relationship between structural features and energy. [Figure 7] FIG. 10 is a diagram illustrating an example of a feature space in the case of dataset OC22. [Figure 8] FIG. 10 is a diagram illustrating an example of mean absolute error of energy prediction values ​​in various data regions in a comparative example. [Figure 9] 1 is a block diagram showing an example of the hardware (HW) configuration of a computer according to a first embodiment of the present invention. [Figure 10] FIG. 2 is a diagram illustrating an example of active learning in the first embodiment. [Figure 11] FIG. 2 is a block diagram illustrating an example of the functional configuration of a computer according to the first embodiment. [Figure 12] 4 is a flowchart showing an example of an active learning process by a computer in the first embodiment. [Figure 13] FIG. 10 is a diagram showing experimental results of mean absolute error for energy prediction values ​​by active learning in the first embodiment. [Figure 14] FIG. 10 is a block diagram showing an example of the functional configuration of a computer according to a second embodiment of the present invention. [Figure 15] 10 is a flowchart showing an example of an active learning process by a computer in the second embodiment. [Figure 16] FIG. 10 is a diagram showing the results of the effect of reducing the mean absolute error for the energy prediction value by active learning in the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. However, the embodiment described below is merely an example, and is not intended to exclude various modifications or application of techniques not explicitly described below. For example, this embodiment can be implemented with various modifications within the scope of its spirit. In the drawings used in the following description, parts with the same reference numerals represent the same or similar parts unless otherwise specified.

[0014] [First Example] [A] Explanation of neural networks (NN) and active learning for energy prediction FIG. 1 is a diagram showing an overview of supervised learning of an energy prediction NN. The energy values ​​of materials for a plurality of structure data 2 corresponding to each of a plurality of materials are calculated by a DFT calculation unit 20 using density functional theory (DFT) simulation based on quantum mechanics. The calculated energy values ​​become labels 3 (answers) of the structure data 2. The structure data 2 is an example of training data. The structure data 2 and the labels 3 become labeled training data 1. The structure data 2 of a material is data about the atomic or molecular structure of the material.

[0015] Structural data 2 is input as training data to an energy prediction NN 30. The energy prediction NN 30 outputs a predicted energy value 4 of the material. The energy prediction NN 30 is trained by backpropagating the "error" between the label 3 obtained by the DFT calculation and the predicted energy value 4 to the NN. The energy prediction NN 30 may be a machine learning model trained by machine learning (ML).

[0016] The energy prediction NN30 may be, for example, a graph neural network (GNN). In one example, a polarizable atom interaction neural network (PaiNN) and EquiformerV2 are used as the energy prediction NN30. EquiformerV2 is a type of NN that considers symmetry hidden in data as a strong inductive bias and incorporates it into the network design.

[0017] PaiNN is described in detail in, for example, KT Schuett, O.T. Unke, and M. Gastegger, “Equivariant message passing for the prediction of tensorial properties and molecular spectra,” in Proceedings of the International Conference on Machine Learning, pp. 9377-9388, 2021. EquiformerV2 is described in detail in, for example, Y.-L. Liao, B. Wood, A. Das, and T. Smidt, “EquiformerV2: Improved equivariant transformer for scaling to higher-degree representations,” arXiv preprint arXiv:2306.12059, 2023. Therefore, a detailed explanation will be omitted.

[0018] When material structure data is input, the energy prediction NN30 extracts feature quantities for the material structure. The extracted structural feature quantities (hereinafter referred to as structural feature quantities) are N-dimensional (N is the number of atoms for each input material structure). The dimension of the feature quantities is reduced to, for example, two dimensions by densMAP, an embedding method that reflects the density of the distribution of high-dimensional data. The energy prediction NN30 outputs an energy prediction value for each material structure based on the structural feature quantities. Note that the energy prediction NN30 is not limited to PaiNN and EquiformerV2.

[0019] Figure 2 shows an overview of a neural network training method that applies active learning. In machine learning, active learning is used to improve the accuracy of energy prediction using labeled training data1 with a reduced amount of data.

[0020] A large amount of structure data 10 with unknown energy is prepared (A1). The structure data is a plurality of structure data corresponding to a plurality of materials. The plurality of structure data 10 is input to an active learning NN 40 (A2). The active learning NN 40 selects one or more structure data 11 from the plurality of structure data 10 (A2). In other words, the active learning NN 40 determines the selected structure data as training data for training the energy prediction NN 30.

[0021] The active learning NN 40 is an active learning NN and may be a machine learning model. The active learning NN has a configuration similar to that of the energy prediction NN 30. The active learning NN 40 may be the energy prediction NN 30 or another energy prediction NN.

[0022] The DFT calculation unit 20 executes a DFT simulation calculation based on the structure data 11 determined as training data, and calculates the energy values ​​of the materials in the structure data as labels 3 of the training data (A3). In other words, labeled training data 13 is created. Note that the structure data 12 left unselected in A2 may be used for the next training data selection (A4).

[0023] As a result, by reducing the number of training data, the amount of calculation required for DFT simulation can be reduced, while still improving the accuracy of the energy prediction value.

[0024] 3 is a diagram showing a method for determining training data in active learning in a comparative example. Each of a plurality of structured data 10 is input to an active learning NN 40, which is an ML model, and a feature amount for each structured data 10 is extracted (B1).

[0025] The feature quantity for each structure data 10 may have two dimensions, SC1 and SC2, for example, after the dimension is reduced by densMAP.

[0026] In the feature space, the Euclidean distance between each extracted feature is calculated (B2). As shown in FIG. 3, in the feature space, each distance p between point S1 representing the structural feature of interest and points S2 to Sn (n is the number of structure data 10) representing the structural features other than S1 is calculated. 1,2 , p 1,3 , ···p 1,n-1 , p 1,n is calculated.

[0027] distance p 1,2 , p 1,3 , ···p 1,n-1 , p 1,n Among them, the minimum distance (in the case of Figure 3, p 1,2 ) is calculated. Similarly, the minimum distance is calculated for S2 to Sn. One or more structural features are selected in descending order of the minimum distance (B3). The number of structural features to be selected may be determined in advance. For example, 1000 structural features are selected. One or more structural data corresponding to the selected structural features are determined as training data.

[0028] According to the method for determining training data shown in Fig. 3, it is possible to capture the structural diversity of structured data 10 not only when the structured data constitutes a Gaussian distribution population as shown in Fig. 3, but also without relying on the distribution of the population as shown in Figs. 4 and 5. Fig. 4 is a diagram showing an example in which the structured data constitutes a uniform population. Fig. 5 is a diagram showing an example in which the structured data constitutes a population of multiple clusters. Fig. 5 includes a total of five clusters, including four clusters each having multiple points and a central cluster having only one data point. According to the method shown in Fig. 3, training data is selected from each of the five clusters, and unbiased training data is determined.

[0029] According to the method for determining training data shown in Fig. 3, it is possible to determine training data taking into account the diversity of structures. However, since the method shown in Fig. 3 mainly samples data using the characteristics of material structures, it is difficult to take into account the diversity of energy possessed by materials.

[0030] FIG. 6 is a diagram showing an example of the relationship between structural features (SC1, SC2) and energy. As in the first data group, there are cases where the structural features are similar but have different energies. On the other hand, as in the second data group, there are cases where the structures are different but the energies are similar. In FIG. 6, the hatched structural features are selected as training data when the comparative example shown in FIG. 3 is applied, and the structural features shown with white circles are not selected as training data when the comparative example shown in FIG. 3 is applied. For example, when point Si is selected as training data, point Sj, which is close to point Si in terms of the structural feature, is unlikely to be selected as training data. The structural data of point Sj has a significantly different energy from the data corresponding to Si collected by the determination method of FIG. 3. As a result, the prediction accuracy for the structural data of Sj decreases.

[0031] Figure 7 shows an example of the feature space for dataset OC22. OC22 (Open Catalyst 2022) is one of the largest publicly available catalyst datasets for predicting the total energy of catalysts.

[0032] As shown in Fig. 7, there are cases where the structural features (SC1 and SC2) are similar but the energies corresponding to the vertical axis are different. When the energy prediction NN30 is trained using the training data determined by the determination method of Fig. 3 in a region where the structural features are similar but the energies are different, the energy prediction accuracy of the energy prediction NN30 may decrease.

[0033] 8 is a diagram showing an example of mean absolute errors of energy prediction values ​​in various data regions in a comparative example. The horizontal axis indicates the number of training data, and the vertical axis indicates the mean absolute error (MAE) of the energy prediction value by the trained energy prediction NN30. The mean absolute error of the energy prediction value is also called the prediction error. The larger the number of training data, the smaller the MAE of the energy prediction value tends to be.

[0034] 8, the first data group, which has a similar structure but different energy, has a larger MAE and lower prediction accuracy of the energy prediction value than the second data group and the randomly sampled data group, which have similar energy. In the first embodiment of the present invention, it is possible to select data that has a similar structure but significantly different energy as training data, thereby improving the accuracy of the energy prediction value obtained by the neural network while reducing the amount of training data.

[0035] [B] Hardware configuration example The functions of the computer 100 according to one embodiment may be implemented by one computer or two or more computers. Furthermore, at least some of the functions of the computer 100 may be implemented using HW (Hardware) resources and NW (Network) resources provided by a cloud environment.

[0036] 9 is a block diagram showing an example of the hardware (HW) configuration of the computer 100 that realizes the functions of the computer 100 according to one embodiment. When multiple computers are used as HW resources that realize the functions of the computer 100, each computer may have the HW configuration exemplified in FIG.

[0037] As shown in FIG. 9, the computer 100 may include, as its HW configuration, a processor 100a, a memory 100b, a storage device 100c, an IF (Interface) device 100d, an IO (Input / Output) device 100e, and a reading device 100f, for example.

[0038] The processor 100a is an example of a processing unit that performs various controls and calculations. The processor 100a may be connected to each block in the computer 100 via a system bus 100i so that they can communicate with each other. The processor 100a may be a multiprocessor including multiple processors, a multi-core processor having multiple processor cores, or a configuration having multiple multi-core processors.

[0039] Examples of the processor 100a include integrated circuits (ICs) such as a CPU, MPU, GPU, APU, DSP, ASIC, and FPGA. Note that the processor 100a may be a combination of two or more of these integrated circuits. CPU is an abbreviation for Central Processing Unit, and MPU is an abbreviation for Micro Processing Unit. GPU is an abbreviation for Graphics Processing Unit, and APU is an abbreviation for Accelerated Processing Unit. DSP is an abbreviation for Digital Signal Processor, ASIC is an abbreviation for Application Specific IC, and FPGA is an abbreviation for Field-Programmable Gate Array. The GPU may be a GPGPU (General Purpose computing on Graphics Processing Unit).

[0040] The memory 100b is an example of HW that stores various types of data, programs, and other information. The memory 100b may be, for example, a volatile memory such as a dynamic random access memory (DRAM) or a non-volatile memory such as a persistent memory (PM), or both.

[0041] The storage device 100c is an example of HW that stores various types of data, programs, and other information. Examples of the storage device 100c include various storage devices such as a magnetic disk device such as a hard disk drive (HDD), a semiconductor drive device such as an SSD, and a nonvolatile memory. Examples of nonvolatile memory include a flash memory, a storage class memory (SCM), and a read-only memory (ROM).

[0042] The storage device 100c may store a program 100g (active learning program) that realizes all or part of the various functions of the computer 100. The program 100g may include an OS (Operating System) and the like in addition to the active learning program.

[0043] For example, the processor 100a can implement the function of a control unit (control unit 110 in FIG. 11, which will be described later) of the computer 100 by loading a program 100g stored in the storage device 100c into the memory 100b and executing it.

[0044] The computer 100 may execute an active learning program to perform each process of active learning.

[0045] The IF device 100d is an example of a communication IF that controls connections and communications between various networks including networks between the computer 100 and other devices.

[0046] For example, the IF device 100d may include an adapter that complies with a LAN (Local Area Network) such as Ethernet (registered trademark) or optical communication such as FC (Fibre Channel). The adapter may be compatible with either or both of wireless and wired communication methods.

[0047] The program 100g may be downloaded to the computer 100 from a network via the communication IF device 100d and stored in the storage device 100c.

[0048] The IO device 100e may include one or both of an input device and an output device. Examples of input devices include a keyboard, a mouse, and a touch panel. Examples of output devices include a monitor, a projector, and a printer. The IO device 100e may also include a touch panel that combines an input device and an output device.

[0049] The reading device 100f is an example of a reader that reads data or program information recorded on the recording medium 100h. The reading device 100f may include a connection terminal or device to which the recording medium 100h can be connected or inserted. Examples of the reading device 100f include an adapter that complies with USB (Universal Serial Bus) or the like, a drive device that accesses a recording disk, and a card reader that accesses a flash memory such as an SD card. Note that the recording medium 100h may store a program 100g, or the reading device 100f may read the program 100g from the recording medium 100h and store it in the storage device 100c.

[0050] Examples of the recording medium 100h include non-transitory computer-readable recording media such as magnetic / optical disks and flash memories. Examples of magnetic / optical disks include flexible disks, CDs (Compact Discs), DVDs (Digital Versatile Discs), Blu-ray Discs, and HVDs (Holographic Versatile Discs). Examples of flash memories include semiconductor memories such as USB memories and SD cards.

[0051] The above-described hardware configuration of computer 100 is an example. Therefore, the hardware within computer 100 may be increased or decreased (for example, adding or deleting any block), divided, or integrated in any combination, or buses may be added or deleted, as appropriate.

[0052] [C] Overview of the active learning process in the first embodiment 10 is a diagram showing an example of active learning in the first embodiment of the present invention. In the first embodiment, as in the comparative example, a plurality of structural data 10 corresponding to a plurality of materials is input to the active learning NN 40. The structural data 10 is data about the atomic or molecular structure of the material.

[0053] In one example, the active learning NN 40 is a GNN. The active learning NN 40 has a configuration similar to that of the energy prediction NN 30 using, for example, PaiNN and EquiformerV2. The active learning NN 40 generates structural features 14 for each of the structural data. The structural features 14 are an example of first features related to the structure of each material.

[0054] In the active learning NN 40, structural features 14 are extracted from the structural data 10. The active learning NN 40 calculates an energy prediction value 15 based on the structural features 14. The energy prediction value 15 is an example of a second feature related to the energy in the structure of each material, which is calculated based on the first feature using the active learning NN.

[0055] The control unit 110 (see FIG. 11) determines one or more pieces of structure data from the plurality of pieces of structure data as training data for training an energy prediction NN that predicts the energy of the material, based on the first feature amount and the second feature amount corresponding to each material.

[0056] In order to obtain data that captures the diversity of structures and energies, not only the structural features 14 of the structural data but also the energy prediction values ​​15 are used as features for calculating distances. For example, if the structural features 14 are two-dimensional, the structural features 14 and the energy prediction values ​​15 are combined to generate three-dimensional extended features 16. The extended features 16 are an example of combined features that combine the first and second features corresponding to each material.

[0057] In the feature space expanded to include the energy prediction value as a dimension, the Euclidean distance between each of the expanded features 16 is calculated. As shown in FIG. 10, in the expanded feature space, each distance p between a point S1 indicating the expanded feature of interest and points S2 to Sn (n is the number of structure data 10) indicating the other structural features other than S1 is calculated. 1,2 , p 1,3 , ···p 1,n-1 , p 1,n is calculated.

[0058] distance p 1,2 , p 1,3 , ···p 1,n-1 , p 1,n Among them, the minimum distance (in the case of Figure 10, p 1,2 ) is calculated. Similarly, the minimum distance is calculated for S2 to Sn. One or more extended features are selected in descending order of the minimum distance. The number of selected extended features may be determined in advance. One or more structured data corresponding to the selected extended features are determined as training data. [D] Example of functional configuration in the first embodiment 11 is a block diagram showing an example of the functional configuration of a computer 100 according to an embodiment. The computer 100 is an example of an information processing device.

[0059] 11 , the computer 100 includes a control unit 110 and a memory unit 120. The control unit 110 includes a structural data input unit 111, a structural feature extraction unit 112, an energy prediction value calculation unit 113, a feature combination unit 114, a distance calculation unit 115, and a selection unit 116. The DFT calculation unit 20 may be provided as one function of the computer 100.

[0060] The memory unit 120 is an example of a storage area, and stores various data used by the control unit 110. The memory unit 120 may be realized, for example, by a storage area included in one or both of the memory 100b and the storage device 100c shown in FIG.

[0061] 11, the memory unit 120 may be provided with, for example, an active learning NN 40. The memory unit 120 may store the structure data 12 and the like that remain unselected by the active learning.

[0062] The structural data input unit 111 inputs a plurality of structural data 10 corresponding to each of a plurality of materials to the active learning NN 40.

[0063] The active learning NN 40 may be a GNN. In this case, each node (corresponding to an atom) receives information from surrounding nodes (corresponding to atoms) and updates its own information through repeated message passing, allowing the node to share information with other nodes. As a result, the features of the entire graph can be handled. The GNN may include a convolutional layer and a pooling layer as intermediate layers. The convolutional layer updates node features based on message passing. Meanwhile, the pooling layer aggregates node features and extracts structural features 14 of the entire material, which are the features of the entire graph. Specific active learning NNs 40 are similar to energy prediction GNNs such as PaiNN and EquiformerV2, and therefore a detailed description will be omitted.

[0064] The intermediate layer of the active learning NN 40 functions as a structural feature extractor 41 that extracts structural features 14 from structural data 10. The active learning NN 40 has a header 42. The header 42 calculates and outputs an energy prediction value 15 according to the structure of the material based on the structural features 14 generated in the intermediate layer.

[0065] The structural feature extraction unit 112 extracts structural features 14 from the structural feature extractor 41 of the active learning NN 40, that is, from an intermediate layer such as a pooling layer.

[0066] The energy predicted value calculation unit 113 calculates the energy predicted value that is the output from the header 42 of the active learning NN 40.

[0067] The feature combining unit 114 normalizes the structural features 14 and the energy predicted values ​​15, and then combines them to generate the extended features 16. Combining may mean generating a new feature vector including the basis (m in this case) of the feature vector of the structural features 14 and the basis (one in this case) of the feature vector of the energy predicted values ​​15 (energy features).

[0068] The distance calculation unit 115 calculates the Euclidean distance between each extended feature 16 in the feature space extended to include the energy predicted value 15 as a dimension. As shown in Fig. 10 , the distance calculation unit 115 calculates, for each of the combined features, the minimum distance among the distances between a point indicating the extended feature 16 of interest and points indicating multiple combined features other than the point in the extended feature space.

[0069] The selection unit 116 selects one or more extended features in descending order of the minimum distance among the extended features 16. The selection unit 116 determines one or more structured data corresponding to the selected extended features as training data.

[0070] The DFT calculation unit 20 calculates the energy value of the material in the structural data 11 as the label 3 of the training data by density functional theory calculation based on the structural data 11 selected as training data by the selection unit 116.

[0071] [E] Operation in the first embodiment FIG. 12 is a flowchart showing an example of active learning processing by a computer in the first embodiment.

[0072] The structural data input unit 111 acquires structural data 10 with unknown energy (step S10).

[0073] The structure data input unit 111 inputs the acquired structure data 10 to the active learning NN 40, and the structural feature extraction unit 112 extracts structural features 14 of the structure data (step S11). In other words, the structural feature extraction unit 112 generates a feature map for the structure of the structure data.

[0074] The energy predicted value calculation unit 113 calculates (predicts) the energy predicted value 15 using the header 42 of the active learning NN 40 (step S12).

[0075] The feature combining unit 114 normalizes the structural feature 14 and the energy predicted value 15 of the structural data (step S13). This allows appropriate weighting to be obtained when combining the structural feature 14 and the energy predicted value 15. In other words, the importance of the structural feature and the energy predicted value can be made uniform.

[0076] The feature combining unit 114 combines the normalized structural features 14 and the energy prediction values ​​15 to generate the extended features 16 (step S14).

[0077] The distance calculation unit 115 calculates the Euclidean distance between each extended feature in the dimension-extended feature space. The distance calculation unit 115 calculates the minimum distance among the distances between a point indicating the extended feature 16 of interest and points indicating multiple combined features other than the point in the extended feature space for each of the combined features (step S15).

[0078] The selection unit 116 selects a predetermined number of extended features 16 in descending order of the minimum distance among the extended features 16 (step S16). The selection unit 116 determines the structure data 11 corresponding to the selected extended features as training data.

[0079] The DFT calculation unit 20 assigns the calculated label 3 to the selected structure data 11 (step S17). As a result, the control unit 110 creates labeled training data 1. As shown in FIG. 1, the control unit 110 trains the energy prediction NN 30 using the labeled training data 1 (step S18).

[0080] The control unit 110 acquires accuracy information of the energy predicted value by the energy prediction NN 30. The accuracy information may be, for example, MAE. If the accuracy of the energy predicted value by the energy prediction NN 30 does not satisfy the target value (see the NO route of step S19), the control unit 110 acquires the remaining structure data 12 (step S20) and repeats the processes of steps S11 to S19. On the other hand, if the accuracy of the energy predicted value by the energy prediction NN 30 satisfies the target value (see the YES route of step S19), the control unit 110 completes the process. Note that if the accuracy does not satisfy the target value, it may be that the MAE is equal to or greater than a predetermined value, and if the accuracy satisfies the target value, it may be that the MAE is less than the predetermined value.

[0081] [F] Effects of the first embodiment Fig. 13 is a diagram showing experimental results of the mean absolute error for the energy prediction value by active learning in Example 1. Fig. 13 shows an example in which 100 pieces of training data are determined by active learning and the determined training data are used to predict the energy of a catalyst for ammonia production.

[0082] In Fig. 13, line 201 shows the results when training was performed using training data determined by active learning according to the first embodiment, and line 202 shows the results when training was performed using training data determined by active learning in the comparative example shown in Fig. 3. Line 203 shows the results when data was selected randomly.

[0083] By training using the training data determined by active learning in the first embodiment, it was possible to reduce the mean absolute error in the energy prediction NN30 compared to training using the training data determined by active learning in the comparative example.

[0084] In addition, the comparative example shown in Figure 3 and uncertainty sampling based on the variance of predicted values ​​by Gaussian process regression (GPR), a method other than random sampling, were also compared with the active learning method of Example 1 using the OC22 dataset. The active learning method of Example 1 achieved a lower MAE than uncertainty sampling, even when the amount of training data was limited.

[0085] In addition, structural data sets other than OC22, such as NRR (catalyst for nitrogen reduction reaction) and ORR (catalyst for oxygen reduction reaction), are used to predict the adsorption energy in catalyst-adsorbent systems. Even in these cases, the method of the first embodiment achieved the lowest MAE among all methods, despite the limited amount of training data.

[0086] According to the active learning technology of this embodiment, the processor 100a inputs each of a plurality of structure data 10 corresponding to a plurality of materials into an active learning NN to extract structural features 14 (i.e., first features) related to the structure of each material. The processor 100a uses an active learning NN 40 to calculate an energy prediction value 15 (i.e., second features) related to the energy in the structure of each material based on the structural features 14. The processor 100a determines one or more structure data 11 from the plurality of structure data 10 as training data for training an energy prediction NN 30 that predicts the energy of a material based on the structural features 14 and the energy prediction value 15 corresponding to each material.

[0087] This allows us to consider not only the features related to the structure of the material, but also the features related to the energy. Because we can take into account the diversity of energy, it is possible to determine structural data that are similar in structure but have significantly different energies as training data. Therefore, by training using the determined training data, we can improve the prediction error of the energy prediction NN even with a small amount of training data.

[0088] In the process of determining the training data, the processor 100a generates an extended feature 16 (combined feature) by combining a structural feature 14 (first feature) corresponding to each material with an energy prediction value 15 (second feature). The processor 100a calculates, in a feature space, the minimum distance between a point indicating the extended feature 16 and points indicating multiple combined features other than the point in question, for each extended feature 16. The processor 100a selects one or more extended features in descending order of the minimum distance for each extended feature, and determines one or more structural data corresponding to the selected extended feature as the training data.

[0089] This allows not only feature quantities related to the structure of a material but also feature quantities related to energy to be considered by distance in the same feature space, making it easier to implement on a computer and reducing the processing load.

[0090] The second feature amount is an energy prediction value 15 in the structure calculated by the active learning NN 40.

[0091] This allows the use of the energy prediction value 15 calculated by the active learning NN 40 and the structural feature 14 extracted in the active learning NN 40, making it easier to implement on a computer and reducing the processing load.

[0092] Furthermore, the processor 100a calculates the energy value of the material in the structure data 11 as the label 3 of the training data by density functional theory calculation based on the structure data 11 determined as the training data.

[0093] This allows the training of the energy prediction NN30 to be more accurate based on the labels 3 obtained by density functional theory calculations, and also allows the number of training data to be appropriately narrowed down, thereby reducing the computer processing burden and cost in density functional theory calculations.

[0094] [Second Example] [G] Example of functional configuration in the second embodiment The process in which the control unit 110 determines one or more structural data from among a plurality of structural data as training data for training the energy prediction NN that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each material is not limited to the case of the first embodiment. In the second embodiment, an energy gradient is used as the second feature amount.

[0095] The hardware configuration of the computer 100 in the second embodiment is the same as that in the first embodiment shown in FIG. 9, and therefore a repeated description will be omitted.

[0096] Fig. 14 is a block diagram showing an example of the functional configuration of a computer 100 according to a second embodiment of the present invention. In the second embodiment, an energy gradient calculation unit 117, a structural feature distance calculation unit 118, a first selection unit 119, and a second selection unit 132 are provided instead of the feature combination unit 114, the distance calculation unit 115, and the selection unit 116 shown in Fig. 11. The configuration other than these components is the same as the configuration in the first embodiment.

[0097] The energy gradient calculation unit 117 calculates the energy gradient 17. The energy gradient 17 is calculated by dividing the distance Δp i,j The change in energy prediction 15 in the structure Δei,j is the percentage.

[0098] The energy gradient calculation unit 117 calculates the point S i and point S j The energy gradient between is calculated using the following formula:

number

[0099] The structural feature distance calculation unit 118 calculates the Euclidean distance between each of the extracted structural features 14 in the feature space. As in the case shown in FIG. 3, the structural feature distance calculation unit 118 calculates each distance p between the point S1 indicating the structural feature of interest in the feature space and the points S2 to Sn indicating the structural features other than S1. 1,2 , p 1,3 , ···p 1,n-1 , p 1,n Calculate.

[0100] The structural feature distance calculation unit 118 calculates the distance p 1,2 , p 1,3 , ···p 1,n-1 , p 1,nThe first selection unit 119 calculates the minimum distance among these. Similarly, the first selection unit 119 calculates the minimum distance for S2 to Sn. The first selection unit 119 selects one or more structural features in descending order of the minimum distance. The number of structural features to be selected may be determined in advance.

[0101] The second selecting unit 132 may select one or more structural features 14 in descending order of the maximum energy gradient 17 for the structural data selected by the first selecting unit 119. The first selecting unit 119 may select candidates based on the Euclidean distance, and the second selecting unit 132 may sample structural data from the candidates in descending order of the energy gradient.

[0102] According to the active learning of the second embodiment, the data is narrowed down without relying on the population distribution by using the "Euclidean distance", and then the second selection unit 132 selects the training data to be finally used by the energy gradient calculation unit 117. [H] Operation in the second embodiment FIG. 15 is a flowchart illustrating an example of active learning processing by a computer in the second embodiment.

[0103] Steps S30 to S32 in FIG. 15 are the same as steps S10 to S12 in FIG.

[0104] The structural feature distance calculation unit 118 calculates the Euclidean distance between the extracted structural features 14 in the feature space (step S33).

[0105] The energy gradient calculation unit 117 calculates the energy gradient 17 between the structural features 14 (step S34).

[0106] The first selection unit 119 selects one or more structural features in descending order of the minimum distance (step S35). The number of structural features to be selected may be determined in advance.

[0107] The second selection unit 132 selects one or more structural features 14 from the structural data selected by the first selection unit 119 in descending order of the maximum energy gradient 17 (step S36).

[0108] The processing in steps S37 to S40 is the same as the processing in steps S17 to S20 in FIG. 12, and therefore a repeated explanation will be omitted.

[0109] [I] Effects of the second embodiment Fig. 16 is a diagram showing experimental results of the mean absolute error for the energy prediction value by active learning in Example 2. Fig. 16 shows an example in which 1000 pieces of training data were determined by active learning and the determined training data were used to predict the energy of a catalyst for ammonia production.

[0110] In Figure 16, line 211 shows the results when training was performed using training data determined by active learning according to the second embodiment, and line 212 shows the results when training was performed using training data determined by active learning in the comparative example shown in Figure 3. Line 213 shows the results when data was selected randomly, and line 214 shows the results when training data was selected based only on gradients.

[0111] By training using the training data determined by active learning in the second embodiment, it was possible to reduce the mean absolute error in the energy prediction NN30 compared to training using the training data determined by active learning in the comparative example.

[0112] To evaluate the active learning of this embodiment, we applied it to energy prediction GNNs using three catalyst datasets: OC22, nitrogen reduction catalysts, and oxygen reduction catalysts. The energy prediction GNNs used were PaiNN and PaiNN and EquiformerV2. The active learning method described in this embodiment improved prediction accuracy under all conditions, despite the limited training data.

[0113] According to the active learning technique of this embodiment, the second feature is a gradient, which is a change in the predicted value of energy in the structure with respect to each distance between a point indicating the first feature and multiple points indicating other first features other than the point in feature space.

[0114] This allows us to consider not only the features related to the structure of the material, but also the features related to the energy. Because we can take into account the diversity of energy, it is possible to determine structural data that are similar in structure but have significantly different energies as training data. Therefore, by training using the determined training data, we can improve the prediction error of the energy prediction NN even with a small amount of training data.

[0115] In the process of determining the training data, the processor 100a calculates the maximum gradient among the gradients in the feature space for each of the structural features 14. The processor 100a selects one or more structural features 14 in descending order of the maximum gradient for each of the structural features 14, and determines one or more structural data corresponding to the selected first feature as the training data.

[0116] This allows us to take into account data groups with high gradients that have a higher impact on prediction errors than other data groups, and can improve the prediction error of the energy prediction NN even with a small amount of training data. As explained in the first and second examples, the active learning of this embodiment considers not only the characteristics of the material structure but also the predicted energy value. Therefore, it is possible to sample a training data set that takes into account both the structural diversity and the energy diversity of the material data. This helps improve the accuracy of the material energy prediction using a small amount of training data.

[0117] [J] Note The following additional notes are further disclosed regarding the above embodiment.

[0118] (Appendix 1) inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training a neural network for energy prediction that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An active learning program that causes a computer to perform processing.

[0119] (Appendix 2) The process of determining the training data includes: generating a combined feature by combining the first feature and the second feature corresponding to each of the materials; calculating, in a feature space, the minimum distance among distances between a point indicating the bond feature and a plurality of other points indicating bond features other than the point, for each of the bond features; selecting one or more bond features in descending order of the minimum distance among the bond features, One or more structural data corresponding to the selected binding features are determined as the training data. 2. The active learning program of claim 1, comprising:

[0120] (Appendix 3) the second feature is a predicted value of energy in the structure calculated by the active learning neural network; The active learning program described in Appendix 1.

[0121] (Appendix 4) the second feature amount is a gradient that is a change in a predicted value of energy in the structure with respect to each distance between a point that indicates the first feature amount and a plurality of points that indicate other first feature amounts other than the point in a feature amount space; The active learning program described in Appendix 1.

[0122] (Appendix 5) The process of determining the training data includes: calculating a maximum gradient among the gradients for each of the first features in the feature space; selecting one or more first feature amounts in descending order of the maximum gradient of each of the first feature amounts; One or more structure data corresponding to the selected first feature amount are determined as the training data. 5. The active learning program of claim 4, comprising:

[0123] (Appendix 6) Furthermore, based on the structural data determined as the training data, a value of the energy of the material in the structural data is calculated as a label of the training data by density functional theory calculation. 6. An active learning program according to any one of claims 1 to 5, which causes the computer to execute a process.

[0124] (Appendix 7) inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training a neural network for energy prediction that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An active learning method in which processing is performed by a computer.

[0125] (Appendix 8) The process of determining the training data includes: generating a combined feature by combining the first feature and the second feature corresponding to each of the materials; calculating, in a feature space, the minimum distance among distances between a point indicating the bond feature and a plurality of other points indicating bond features other than the point, for each of the bond features; selecting one or more bond features in descending order of the minimum distance among the bond features, One or more structural data corresponding to the selected binding features are determined as the training data. 8. The active learning method of claim 7, comprising:

[0126] (Appendix 9) the second feature is a predicted value of energy in the structure calculated by the active learning neural network; 8. The active learning method of claim 7.

[0127] (Appendix 10) the second feature amount is a gradient that is a change in a predicted value of energy in the structure with respect to each distance between a point that indicates the first feature amount and a plurality of points that indicate other first feature amounts other than the point in a feature amount space; 8. The active learning method of claim 7.

[0128] (Appendix 11) The process of determining the training data includes: calculating a maximum gradient among the gradients for each of the first features in the feature space; selecting one or more first feature amounts in descending order of the maximum gradient of each of the first feature amounts; One or more structure data corresponding to the selected first feature amount are determined as the training data. 11. The active learning method of claim 10, comprising:

[0129] (Appendix 12) Furthermore, based on the structural data determined as the training data, a value of the energy of the material in the structural data is calculated as a label of the training data by density functional theory calculation. 12. The active learning method according to any one of claims 7 to 11, wherein the processing is performed by the computer.

[0130] (Appendix 13) inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training a neural network for energy prediction that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An information processing device having a processor.

[0131] (Appendix 14) The process of determining the training data includes: generating a combined feature by combining the first feature and the second feature corresponding to each of the materials; calculating, in a feature space, the minimum distance among distances between a point indicating the bond feature and a plurality of other points indicating bond features other than the point, for each of the bond features; selecting one or more bond features in descending order of the minimum distance among the bond features, One or more structural data corresponding to the selected binding features are determined as the training data. 14. The information processing device of claim 13, further comprising:

[0132] (Appendix 15) the second feature is a predicted value of energy in the structure calculated by the active learning neural network; 14. The information processing device according to claim 13.

[0133] (Appendix 16) the second feature amount is a gradient that is a change in a predicted value of energy in the structure with respect to each distance between a point that indicates the first feature amount and a plurality of points that indicate other first feature amounts other than the point in a feature amount space; 14. The information processing device according to claim 13.

[0134] (Appendix 17) The process of determining the training data includes: calculating a maximum gradient among the gradients for each of the first features in the feature space; selecting one or more first feature amounts in descending order of the maximum gradient of each of the first feature amounts; One or more structure data corresponding to the selected first feature amount are determined as the training data. 17. The information processing device of claim 16, further comprising:

[0135] (Appendix 18) The processor calculates, as a label of the training data, an energy value of a material in the structural data determined as the training data by density functional theory calculation based on the structural data determined as the training data. 18. The information processing device according to any one of appendices 13 to 17, which executes processing. [Explanation of symbols]

[0136] 1. Labeled training data 2. Structural Data 3. Labels 4 Energy Prediction 10 Multiple Structure Data 11 Selected structural data 12 Remaining structural data 13 Labeled training data 14 Structural features 15 Energy Prediction 16 Extended Features 17 Energy Gradients 20 DFT calculation section 30 Energy Prediction NN 40 Active Learning Neural Networks 41 Structural Feature Extractor 42 Header 100a processor 100b memory 100c storage device 100d IF device 100e IO device 100f reader 100h recording medium 100i Bus 100g Program 110 control section 111 Structural data input section 112 Structural feature extraction unit 113 Energy prediction value calculation unit 114 Feature Joint 115 Distance calculation unit 116 Selection Section 117 Energy gradient calculation unit 118 Structural feature distance calculation unit 119 First Selection Section 120 Memory section 132 Second Selection Section 121 Set Information

Claims

1. inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training an energy prediction neural network that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An active learning program that causes a computer to perform processing.

2. The process of determining the training data includes: generating a combined feature by combining the first feature and the second feature corresponding to each of the materials; calculating, in a feature space, the minimum distance among distances between a point indicating the bond feature and a plurality of other points indicating bond features other than the point, for each of the bond features; selecting one or more bond features in descending order of the minimum distance among the bond features, One or more structural data corresponding to the selected binding features are determined as the training data. The active learning program of claim 1 , further comprising:

3. the second feature is a predicted value of energy in the structure calculated by the active learning neural network; The active learning program according to claim 1 .

4. the second feature amount is a gradient that is a change in a predicted value of energy in the structure with respect to each distance between a point that indicates the first feature amount and a plurality of points that indicate other first feature amounts other than the point in a feature amount space; The active learning program according to claim 1 .

5. The process of determining the training data includes: calculating a maximum gradient among the gradients for each of the first features in the feature space; selecting one or more first feature amounts in descending order of the maximum gradient of each of the first feature amounts; One or more structure data corresponding to the selected first feature amount are determined as the training data. The active learning program according to claim 4 , further comprising:

6. Furthermore, based on the structural data determined as the training data, a value of the energy of the material in the structural data is calculated as a label of the training data by density functional theory calculation.

6. The active learning program according to claim 1, which causes the computer to execute processing.

7. inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training an energy prediction neural network that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An active learning method in which processing is performed by a computer.

8. inputting each of a plurality of structural data corresponding to each of a plurality of materials into an active learning neural network to extract a first feature amount relating to the structure of each material; calculating a second feature amount related to energy in the structure of each of the materials based on the first feature amount using the active learning neural network; determining one or more pieces of structure data from the plurality of pieces of structure data as training data for training an energy prediction neural network that predicts the energy of the material based on the first feature amount and the second feature amount corresponding to each of the materials; An information processing device having a processor.

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