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Definitions

• the present disclosure relates to an information processing device, a trained model generation device, an information processing method, a trained model generation method, an information processing program, and a trained model generation program.
• the purpose of this disclosure is to represent a field that represents the structure of a substance composed of atomic point groups.
• the information processing device disclosed herein is an information processing device that includes a processing unit that uses a neural network model to represent a field that represents the structure of a substance composed of atomic point groups.
• the information processing method disclosed herein is an information processing method in which a computer executes processing to represent a field that represents the structure of a substance composed of atomic point groups using a neural network model.
• the information processing program disclosed herein is an information processing program for causing a computer to execute processing that utilizes a neural network model to represent a field that represents the structure of a substance composed of atomic point groups.
• the information processing device, information processing method, and information processing program disclosed herein can represent a field that represents the structure of a substance composed of atomic point groups.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• 1 is a block diagram showing a hardware configuration of an information processing device according to an embodiment of the present invention.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• FIG. 1 is a diagram for explaining the present embodiment.
• NeSF neural structure field
• MI informatics
• MI Magnetic ink Characterization
• the crystal structure of an inorganic material is a regular and periodic arrangement of atoms in three-dimensional (3D) space. This arrangement is usually described by lattice constants, which define the 3D positions and types of atoms in a unit cell and the movement of the unit cell in 3D space.
• the atoms in a unit cell have no clear order, and their number can vary from one to hundreds.
• NeSF Neural Structure Field
• NeSF the target material information is given as a fixed-dimensional vector z, and consider the problem of recovering the crystal structure from z.
• the input z can specify, for example, information about the crystal structure of the material, or some desired criteria for the material to be generated.
• the neural network f instead of the neural network f directly outputting the crystal structure as f(z), the neural network f is used as an implicit function to indirectly represent the crystal structure embedded in z. Specifically, f is treated as a vector field on a 3D Cartesian coordinate p, and is conditioned on the target material information z.
• the network f is trained to output a 3D vector pointing from a query point p to the nearest atomic position a.
• the output s is expected to be a-p. If the position field is ideally trained, then at any query point p, the nearest atomic position a can be obtained as p+f(p,z).
• the position field is a scalar potential
• the scalar potential can be interpreted as the gradient vector field - ⁇ (p) of the nearest atom's position, where p is the query point and p is the nearest atom's position, a i .
• the kind field is trained to output a categorical probability distribution indicating the kind of the nearest atom.
• the output dimension of the kind field is the number of candidate atom kinds.
• the proposed NeSF is inspired by the concept of vector fields in classical physics and implicit neural representations in computer vision [30-34]. Implicit neural representations have been recently proposed to handle several representation problems in 3D computer vision applications, such as 3D shape estimation of objects [31-33] and free-viewpoint image synthesis [30, 34].
• 3D shape estimation having a neural network directly output a 3D mesh or point cloud leads to representation problems similar to those encountered in crystal structures.
• a signed distance function (SDF) is utilized in DeepSDF [31], where a neural network f(p) models the 3D shape by indicating with a positive or negative sign whether a query point p is outside or inside the object volume and outputs a respective scalar.
• NeSF follows the basic idea of implicit neural representations and further extends it to the estimation of crystal structures described by the positions and species of atoms. The accurate description of atomic positions in crystal structures is of great importance in materials science. Thus, NeSF outputs vectors pointing to the nearest atoms, representing the positions of atoms more directly than existing implicit neural representations of 3D geometry.
• the ICSG3D method uses 32 ⁇ 32 ⁇ 32 voxels to represent crystal structures and estimates them using a 3D convolutional neural network (CNN).
• CNN 3D convolutional neural network
• voxel-based 3DCNNs are computationally and memory intensive, a resolution of 32 ⁇ 32 ⁇ 32 voxels is roughly the limit for training voxel-based models on standard computing systems.
• existing crystal structures contain more than a few dozen atoms in the unit cell, or the unit cell is stretched or distorted. Therefore, a sufficiently high resolution is required to accurately represent diverse crystal structures in voxels.
• NeSF can only indirectly provide atomic positions in a representation such as the peak of a scalar field of electron density discretized in voxel space.
• the proposed NeSF overcomes the limitations of voxelization. With NeSF, there is essentially no trade-off between spatial resolution and required memory. In theory, NeSF can achieve infinitely high spatial resolution by using a compact (memory- and parameter-efficient) neural network instead of a costly 3DCNN. Moreover, NeSF can effectively represent any crystal structure, including elongated or distorted unit cells. Moreover, NeSF can directly provide Cartesian coordinates of atomic positions, rather than the peaks of scalar fields. We believe that the proposed NeSF will break through the technical bottleneck of the MI approach for crystal structure estimation and contribute to the progress of MI research in this direction.
• NeSF successfully recovers a wide range of crystal structures, from the relatively basic structures of perovskite materials to the complex structures of cuprate superconductors. Extensive quantitative evaluation results show that NeSF outperforms the voxelized approach of ICSG3D [24].
• estimating the crystal structure from z amounts to estimating the positions and species of atoms in the unit cell along with the lattice constants.
• the lattice constants are modeled as lengths a, b, and c and angles ⁇ , ⁇ , and ⁇ , and are estimated by a simple multilayer perceptron (MLP) using the input z.
• MLP simple multilayer perceptron
• the atomic positions and species are estimated by the position field fp and type field fs of the NeSF, respectively, as described in the previous section.
• Score the particles Score each particle p i and filter outliers. Since the norm of the output of the position field
• NeSF NeSF Training Training Training
• 3D query points ⁇ p s i ⁇ in the unit cell we randomly sample 3D query points ⁇ p s i ⁇ in the unit cell and calculate the loss values of the field output at these points.
• f p (p s i , z) and f s (p s i , z) we monitor the query points densely.
• a query point sampling strategy is required for training.
• Existing implicit neural representations for 3D shape estimation such as DeepSDF [31], sample training query points near the surface.
• Curriculum DeepSDF [35] further introduces curriculum learning, in which the sampling density is enhanced near the surface as training progresses.
• Global grid sampling This method considers 3D grid points that uniformly cover the entire unit cell and samples the points with perturbations that follow a Gaussian distribution.
• Local grid sampling This method considers local 3D grid points centered on each atomic position and samples the points with perturbations that follow a Gaussian distribution.
• the proposed NeSF-based autoencoder consists of an encoder and a decoder.
• the encoder is a neural network that converts the input crystal structure (i.e., the positions and species of atoms in the unit cell, and the lattice constants) into an abstract latent vector z.
• the decoder using NeSF, reconstructs the input crystal structure from the latent vector z.
• Autoencoders are typically used to learn latent vector representations of data via self-supervised learning, where the input data can be supervised through the reconstruction loss.
• the ICSG3D dataset [24] is a materials collection of three datasets that includes 7897 materials with limited crystal systems (cubic) and prototypes (i.e., AB, ABX2, and ABX3).
• the LCS6 ⁇ dataset consists of 6005 materials with unit cell sizes of 6 ⁇ or less along the x, y, and z axes, with no restrictions on crystal systems and prototypes.
• the YBCO-like dataset consists of 100 materials with narrow unit cells along the c-axis. These structures typically include those of yttrium barium copper oxide (YBCO) superconductors. Due to its complex structure and relatively few samples, the YBCO-like dataset is the most challenging of the three datasets evaluated. For more details on these data sets, see Figure 27, section 4.1.
• YBCO yttrium barium copper oxide
• each dataset was randomly split into a training (90.25%), validation (4.75%), and test (5%) set.
• the training set was used only for training the ML model.
• the validation set was used to pre-validate the trained ML model, and the test set was used to calculate the final evaluation score after training, validation, and tuning of hyperparameters.
• the hyperparameters were tuned based on the validation scores of the LCS6 ⁇ dataset.
• the YBCO-like dataset had only 100 samples, so it was treated a little differently from the other two evaluated datasets.
• Atom number error is the fraction of material in which the number of atoms in the unit cell is incorrectly estimated.
• Position error is the average error in the reconstructed atom positions. Depending on the denominator of the metric, position error was evaluated in two ways. The actual metric was used to evaluate the average position error at the actual atomic sites of the crystal structure by calculating the shortest distance to the estimated atomic sites. In contrast, the detected metric was used to evaluate the error at the estimated sites by calculating the shortest distance to the actual atomic sites. The actual metric is more sensitive to errors associated with underestimation of atom number, whereas the detected metric is more sensitive to errors associated with overestimation.
• Type error is the average fraction of atoms whose type is incorrectly estimated. Similar to the position error, type error was evaluated using the actual and detected metrics. Lower values of these metrics indicate better performance.
• Table 1 shows the reconstruction error of the proposed NeSF-based autoencoder and the ICSG3D baseline on the test set of the three datasets. Overall, the proposed method consistently outperforms ICSG3D on all evaluation metrics, with significant improvements in performance on the type error of all datasets and all metrics on the YBCO-like dataset.
• Figure 3 shows the crystal structures from the three evaluated datasets, comparing the test samples with the reconstruction results by the proposed autoencoder and ICSG3D.
• ICSG3D For the ICSG3D dataset, the simplest of the three datasets, ICSG3D achieved good performance for atom number error and position error, but with a larger species error (about 65% for both real and detected metrics). In contrast, the proposed method achieved a slight improvement in position error and atom number error, and a significant reduction in species error (about 4%). This is likely because ICSG3D estimates atomic species via electron density maps, whereas the proposed method more directly represents atomic species as categorical distributions. Extending ICSG3D to estimate categorical distributions for each voxel is impractical, as it would require about 100x323 times more memory usage at the output (i.e., 100 species categories per 323 voxels are needed in addition to one electron density map).
• the performance advantage of the proposed method is even clearer, especially with regard to positional errors.
• the LCS6 ⁇ dataset contains a variety of crystal structures (non-cubic, distorted crystal structures, etc.), while the YBCO-like dataset contains a very narrow crystal structure.
• the YBCO-like dataset contains very few samples, which may lead to overfitting of the model (i.e., the performance of the test set may be significantly degraded).
• the proposed method is able to accurately estimate the positions and species of atoms.
• Fig. 4 shows the distribution of reconstruction errors in 10 test trials for materials from the ICSG3D and LCS6 ⁇ datasets according to the number of atoms given as the median (point) and the 68% range around them (colored area).
• the YBCO-like dataset is excluded from this analysis since it contains only materials with 13 atoms in the unit cell.
• Fig. 4a and 4b show the signed error between the detected and real atom counts.
• Fig. 4c and 4d show the distribution of position errors
• Fig. 4e and 4f show the distribution of type errors.
• the atom count is either correctly or underestimated by both methods, so we report the error in the real metric.
• the proposed method provides the correct type of both atoms for more than 68% of diatomic materials, while ICSG3D often erroneously estimates one of the two atom types.
• the errors of the three types by both methods tend to increase with the number of atoms, but they consistently perform better than ICSG3D for materials with varying numbers of atoms.
• the performance of ICSG3D tends to degrade more significantly for materials with a large number of atoms.
• ICSG3D tends to underestimate the number of atoms (Fig. 4b), and this tendency is likely due to the spatial resolution of ICSG3D being limited to 32 ⁇ 32 ⁇ 32 voxels. This suggests that ICSG3D is unable to capture polyatomic structures.
• the remarkable high performance of the proposed method can be attributed to two reasons.
• our method does not use discretization, which makes it more advantageous than grid-based ICSG3D for estimating complex crystal structures.
• spatial resolution is limited by cubically increasing computation and memory usage.
• the proposed NeSF is free from such a trade-off between resolution and computational complexity, and therefore can effectively represent complex structures.
• the model size of the proposed NeSF using MLP is much smaller than that of the 3DCNN architecture of ICSG3D.
• the number of training samples required for an ML model is correlated with the number of trainable parameters.
• Grid-based methods use layers of 3D convolution filters that contain many trainable parameters.
• NeSF uses an implicit neural representation to indirectly describe the 3D space as fields rather than voxels. It is therefore efficiently implemented by MLP with fewer parameters than 3DCNN. Specifically, the NeSF-based autoencoder has 760,000 parameters, which is only 2.24% of the number of parameters of the 3DCNN-based ICSG3D (34 million parameters). This difference gives NeSF an advantage over grid-based methods, especially on small datasets such as the YBCO-like dataset.
• the interpolation result from ZnS (mp-10695) to CdS (mp-2469) is shown in Figure 5.
• the resulting compositional transition is ZnS ⁇ MgZn 3 S 4 (Mg 0.25 Zn 0.75 S) ⁇ MgZnS 2 (Mg 0.5 Zn 0.5 S) ⁇ Mg 3 ZnS 4 (Mg 0.75 Zn 0.25 S) ⁇ MgS ⁇ MgCd 3 S 4 (Mg 0.25 Cd 0.75 S) ⁇ CdS.
• composition AX and cubic structure are mostly preserved. Moreover, the composition changes continuously along the interpolation path without collapse.
• NeSF employs a relatively simple network architecture, and architectural design choices were not fully explored.
• NeSF treats elements as mutually independent categorical (one-hot) vectors.
• it does not explicitly train the model using the physical properties or similarities of the elements.
• other developments have attempted to explicitly inject the physical properties and features of elements into the model.
• existing crystal structure encoders [16] use fingerprints such as group and period, electron density, atomic radius, and electronegativity to represent input elements instead of using one-hot vectors.
• ICSG3D24 the output of atomic species is trained using the mean squared error of atomic numbers, rather than the categorical loss considered in our method.
• NeSF does not explicitly consider the space group symmetry. Therefore, the local spatial arrangement of atoms in a conventional unit cell estimated by NeSF does not necessarily follow the space group symmetry.
• ICSG3D [24] has the same limitation, symmetry is an important concept in crystallography. Therefore, incorporating space group symmetry constraints into NeSF is an important direction for future work.
• NeSF should be applied to generative models in future work with appropriate performance analysis.
• NeSF uses neural networks to estimate crystal structures. It is difficult to directly determine crystal structures using neural networks, because these structures are essentially represented as unordered sets containing various numbers of atoms.
• NeSF overcomes this problem by treating crystal structures as continuous vector fields rather than as discrete sets of atoms.
• the idea of NeSF is borrowed from vector fields in physics and recent implicit neural representations in computer vision.
• Implicit neural representations are ML methods that use neural networks to represent 3D geometry. NeSF extends this method by introducing position and type fields to estimate atomic positions and species in crystal structures, respectively. Unlike existing grid-based approaches for representing crystal structures, NeSF has no tradeoff between spatial resolution and computational complexity and can represent arbitrary crystal structures.
• NeSF was applied as an autoencoder for crystal structures and demonstrated its performance and expressiveness on a dataset with diverse crystal structures. Quantitative performance analysis showed clear advantages of the NeSF-based autoencoder over existing grid-based methods, especially in estimating complex crystal structures. Furthermore, qualitative analysis of the learned latent space revealed that the autoencoder captures similarities between crystal structures rather than randomly mapping them.
• NeSF can be easily incorporated into powerful deep generative models such as variational autoencoders and generative adversarial networks to discover new crystal structures. Such generative models of crystal structures will be important for the inverse design of materials, a major challenge in MI. NeSF can overcome the technical bottleneck of ML in crystal structure estimation and pave the way for the development of next-generation materials.
• FIG. 7 is a block diagram showing the hardware configuration of an information processing device 10 according to this embodiment.
• the information processing device 10 has a CPU (Central Processing Unit) 12, a memory 14, a storage device 16, an input/output I/F (Interface) 18, a storage medium reading device 20, and a communication I/F 22.
• Each component is connected to each other so as to be able to communicate with each other via a bus 24.
• the storage device 16 stores information processing programs for executing the various processes described below.
• the CPU 12 is a central processing unit that executes various programs and controls each component. That is, the CPU 12 reads the programs from the storage device 16 and executes the programs using the memory 14 as a working area. The CPU 12 performs the various arithmetic processes described above in accordance with the programs stored in the storage device 16.
• Memory 14 is made up of RAM (Random Access Memory) and temporarily stores programs and data as a working area.
• Storage device 16 is made up of ROM (Read Only Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), etc., and stores various programs including the operating system, and various data.
• the input/output I/F 18 is an interface for inputting data from an external device and outputting data to an external device.
• an input device for performing various inputs such as a keyboard or a mouse
• an output device for outputting various information such as a display or a printer
• a touch panel display may be used as the output device to function as an input device.
• the storage medium reader 20 reads data stored in various storage media such as CD (Compact Disc)-ROM, DVD (Digital Versatile Disc)-ROM, Blu-ray Disc, and USB (Universal Serial Bus) memory, and writes data to the storage media.
• CD Compact Disc
• DVD Digital Versatile Disc
• USB Universal Serial Bus
• the communication I/F 22 is an interface for communicating with other devices, and uses standards such as Ethernet (registered trademark), FDDI, and Wi-Fi (registered trademark).
• the information processing device 10 of this embodiment uses the method described above to train an autoencoder that includes an encoder and a decoder. This makes it possible to use a neural network model to represent a field that represents the structure of a substance that is composed of a group of atomic points.
• the information processing device 10 functionally includes a learning acquisition unit 102, a learning unit 104, an acquisition unit 108, and a processing unit 110.
• a data storage unit 100 and a trained model storage unit 106 are provided in a predetermined storage area of the information processing device 10.
• Each functional configuration is realized by the CPU 12 reading out each program stored in the storage device 16, expanding it in the memory 14, and executing it.
• the information processing device 10 trains a neural network model that represents a field that represents the structure of a substance composed of atomic point groups.
• the data storage unit 100 stores training crystal data that represents the crystal structure of a substance.
• the training crystal data includes position data that represents the positions of the atoms that make up the crystal of the substance, type data that represents the types of atoms that make up the crystal of the substance, and lattice constant data for the crystal of the substance.
• FIG. 9 is a diagram showing an example of multiple training crystal data stored in the data storage unit 100.
• one training crystal data is data representing the crystal structure of a certain substance.
• one training crystal data is stored in such a manner that position data representing the positions of multiple atoms constituting a crystal of a certain substance, type data representing the types of multiple atoms constituting the crystal of the substance, and lattice constant data of the crystal of the substance are associated with each other.
• the position data is three-dimensional position coordinate data for each of the multiple atoms.
• the type data is label data representing the type of each of the multiple atoms.
• the lattice constant data includes the length of the crystal axis and the angle between the axes.
• FIG. 10 is a diagram for explaining the structure of the autoencoder of this embodiment and an overview of the processing executed by the information processing device 10 of this embodiment.
• FIG. 10 is a more simplified diagram of FIG. 1(b).
• the autoencoder AE of this embodiment includes an encoder E, a first decoder D1, a second decoder D2, and a third decoder D3.
• the encoder E when a combination of position data P representing the positions of atoms constituting the crystal of a substance, type data S representing the type of atoms constituting the crystal of a substance, and lattice constant data L of the crystal of a substance is input, the encoder E outputs a latent vector z. Note that one crystal data representing the combination of position data P, type data S, and lattice constant data L is set for one crystal structure of a substance.
• the first decoder D1 when a combination of a query point p, which is a point of interest in a substance, and a latent vector z is input, the first decoder D1 outputs a position field fp representing the position field of atoms constituting the crystal of the substance. Based on this position field fp , estimated position data Pe of the atoms constituting the crystal of the substance is calculated. The calculation method will be described later.
• the second decoder D2 when a combination of a query point p, which is a point of interest in a substance, and a latent vector z is input, the second decoder D2 outputs a type field fs representing the field of the type of atoms that constitute the crystal of the substance. Based on this type field fs , estimated type data Se of the atoms that constitute the crystal of the substance is calculated. The calculation method will be described later.
• the third decoder D3 outputs estimated lattice constant data L e of the crystal of the material when a query point p, which is a point of interest in the material, and a latent vector z are input.
• a case where there is one third decoder D3 will be described as an example, but there may be two third decoders D3.
• the third decoder D3 is composed of a decoder that outputs the length of the crystal axis and a decoder that outputs the inter-axis angle.
• the information processing device 10 of this embodiment learns each parameter of the autoencoder AE by unsupervised machine learning (or self-supervised learning) so that a combination of position data P, type data S, and lattice constant data L input to the autoencoder AE matches a combination of estimated position data P e , estimated type data S e, and estimated lattice constant data L e output from the autoencoder AE.
• a trained first decoder D1, a trained second decoder D2, and a trained third decoder D3, which are components of the trained autoencoder AE are obtained.
• the learning acquisition unit 102 When the learning acquisition unit 102 receives an instruction signal to train the autoencoder AE, it reads out the learning crystal data stored in the data storage unit 100. The learning acquisition unit 102 also sets a learning query point, which is a point of interest within the learning material. The learning acquisition unit 102 may set the learning query point by randomly sampling positions in space within the learning material.
• the learning unit 104 trains the autoencoder AE using unsupervised machine learning, it inputs training crystal data to the encoder E of the autoencoder AE to obtain a latent vector z that represents the crystal structure of the training material.
• the encoder E can be realized, for example, by using the ideas of PointNet [28] or DeepSets [29] described above.
• the learning unit 104 obtains a position field fp representing the position field of atoms constituting the crystal of the training material by inputting a combination of the latent vector z and the training query point p to the first decoder D1 of the autoencoder AE. Then, the learning unit 104 estimates the positions of the atoms constituting the crystal of the training material based on the position field fp output from the first decoder D1.
• FIG. 11 is a diagram for explaining the setting of training query points and position fields. Note that FIG. 11 is a diagram similar to FIG. 2, but is shown again for the sake of explanation. As shown in FIG. 11, multiple training query points are set in space M within the substance. The white circles shown in FIG. 11 represent the training query points. Also, A1, A2, and A3 shown in FIG. 11(a) represent the actual positions of atoms in space M within the substance.
• the learning unit 104 obtains a position field fp as shown in Fig. 11(b) by inputting a combination of a learning query point p and a latent vector z to the first decoder D1.
• Each of the arrows shown in Fig. 11 corresponds to a position field fp .
• the learning unit 104 repeatedly updates the position of each of the multiple training query points according to the position field fp output from the first decoder D1. Specifically, the learning unit 104 generates the position of a new training query point by adding a vector represented by the position field fp to the position of each of the multiple training query points. As a result, as shown in Fig. 11(d), the position of each of the multiple training query points converges to the position of the actual atom. Then, the learning unit 104 obtains estimated positions P e 1 , P e 2, and P e 3 of atoms as shown in Fig. 11(e) based on the positions of each of the multiple training query points, for example, by using Non-max Suppression.
• the learning unit 104 obtains a type field fs representing the field of the types of atoms that make up the crystal of the training material by inputting a combination of the latent vector z and the training query point p to the second decoder D2 of the autoencoder AE.
• the learning unit 104 estimates the types of atoms that make up the crystal of the training material based on the type field fs output from the second decoder D2.
• FIG. 12 is a diagram for explaining the setting of training query points and the type field. Note that FIG. 12 is a diagram similar to FIG. 2, but is shown again for the sake of explanation. As shown in FIG. 12, multiple training query points are set in a space M within the substance. As in FIG. 12, the white circles shown in FIG. 12 represent training query points.
• the learning unit 104 sets a plurality of learning query points for the estimated positions P e 1, P e 2, and P e 3 of atoms and for positions surrounding the estimated positions P e 1, P e 2, and P e 3.
• the learning unit 104 obtains a type field f s by inputting a combination of the training query point p and the latent vector z to the second decoder D2.
• the type field f s corresponds to a probability representing the type of atom obtained for each training query point.
• the examples shown in Fig. 12(g) and (h) indicate that the type of atom located at a certain training query point is most likely to be iron (Fe), and the type of atom located at another training query point is most likely to be copper (Cu).
• the learning unit 104 estimates the type of atom corresponding to each position of the multiple learning query points according to the type field fs output from the second decoder D2. For example, for each of the estimated positions P e 1, P e 2, and P e 3, the learning unit 104 identifies the element with the highest probability at the learning query point corresponding to the estimated position and the element with the highest probability at the learning query points around the estimated position. Then, the learning unit 104 estimates the most frequently occurring element at the multiple learning query points set for each of the estimated positions P e 1, P e 2, and P e 3 as the type of atom at the estimated positions P e 1, P e 2, and P e 3.
• an estimated type S e 1 of the atom present at the estimated position P e 1 an estimated type S e 2 of the atom present at the estimated position P e 2, and an estimated type S e 3 of the atom present at the estimated position P e 3 are obtained.
• the type of atom located at estimated position P e 1 is estimated to be silicon Si
• the type of atom located at estimated position P e 2 is estimated to be iron Fi
• the type of atom located at estimated position P e 3 is estimated to be copper Cu.
• the learning unit 104 obtains lattice constant data L e of the crystal of the learning material by inputting the latent vector z to the third decoder D3 of the autoencoder AE.
• the lattice constant data L e output from the third decoder D3 includes the lengths of the crystal axes and the inter-axis angles.
• the learning unit 104 uses unsupervised machine learning to train the autoencoder AE so that the combination of the estimated atomic positions, estimated atomic types, and lattice constant data output from the third decoder D3 corresponds to the combination of the atomic positions, atomic types, and lattice constant data in the training crystal data, thereby generating a trained first decoder D1 and a trained second decoder D2.
• the learning unit 104 generates the learned first decoder D1 and the learned second decoder D2 by training the autoencoder AE using unsupervised machine learning so that the estimated positions P e 1, P e 2 , P e 3 of the estimated atoms match the atomic position data P1, P2, P3 in the training crystal data, the estimated types S e 1, S e 2, S e 3 of the estimated atoms match the atomic type data S1, S2 , S3 in the training crystal data, and the lattice constant data L e output from the third decoder D3 matches the lattice constant data L in the training crystal data.
• the learning unit 104 stores the trained autoencoder AE in the trained model storage unit 106. Since the trained autoencoder AE also includes a trained first decoder D1, a trained second decoder D2, and a trained third decoder D3, these trained models are also stored in the trained model storage unit 106.
• the trained encoder E when the trained encoder E is input with crystal data representing the crystal structure of a substance, the crystal data including position data representing the positions of the atoms constituting the crystal of the substance, type data representing the types of atoms constituting the crystal of the substance, and lattice constant data of the crystal of the substance, it outputs a latent vector z representing the crystal of the substance.
• the field data representing the field of the structure of a substance in this embodiment is represented by a position field representing the field of the position of the atoms constituting the crystal of the substance, and a type field representing the field of the type of the atoms constituting the crystal of the substance. Therefore, the trained first decoder D1, which is an example of a trained first neural network model, outputs a position field f p corresponding to the query point when an arbitrary vector and a query point are input.
• the trained first decoder D1 and the trained second decoder D2 are examples of trained neural network models that output field data representing the field of the structure of a substance at the query point when an arbitrary vector and a query point are input.
• the trained third decoder outputs lattice constant data L e of the crystal of the material when a combination of an arbitrary vector replacing the latent vector z and a query point is input.
• the acquisition unit 108 When the acquisition unit 108 receives an instruction signal to acquire field data of the crystal structure of the target substance, it reads out the trained first decoder D1 and trained second decoder D2 stored in the trained model storage unit 106. The acquisition unit 108 also acquires, for example, a target vector input by a user and a query point, which is a point of interest within the substance.
• the target vector is an arbitrary vector that replaces the latent vector z, and may be any vector that describes the properties of a material in the same way as the latent vector.
• the target vector may be a vector that represents the physical properties desired by the user.
• the trained first decoder D1 and the trained second decoder D2 are treated as pre-trained models, and are re-trained using the vector that represents the physical properties of the material, so that useful field data is output from the trained first decoder D1 and the trained second decoder D2.
• the processing unit 110 inputs the target vector and the query point acquired by the acquisition unit 108 to the trained first decoder D1 and the trained second decoder D2, thereby acquiring field data corresponding to the query point.
• the processing unit 110 inputs the target vector and the query point acquired by the acquisition unit 108 to the trained first decoder D1, thereby acquiring a position field fp corresponding to the query point. Also, the processing unit 110 inputs the target vector and the query point acquired by the acquisition unit 108 to the trained second decoder D2, thereby acquiring a type field fs corresponding to the query point.
• the field data output from the trained first decoder D1 and the trained second decoder D2 is data that represents the field of the structure of a substance according to the target vector and the query point.
• the target vector is a vector that represents the desired physical properties as described above
• field data corresponding to that vector is output.
• field data at those multiple query points is obtained, and it is also possible to generate a crystal structure of a material having the desired physical properties based on that field data.
• XRD X-ray diffraction
• step S ⁇ b>100 the learning acquisition unit 102 acquires a plurality of learning crystal data stored in the data storage unit 100 .
• step S102 the training acquisition unit 102 sets one training crystal data from the multiple training crystal data acquired in step S100. Then, the training unit 104 sets multiple training query points p i in the space within the substance represented by the set training crystal data, where i is an index for identifying the training query points.
• step S104 the learning unit 104 inputs the position data P, type data S, and lattice constant data L of the learning crystal data set in step S102 to the encoder E of the autoencoder AE, thereby obtaining the latent vector z.
• step S106 the learning unit 104 inputs a combination of the training query point p i set in step S102 and the latent vector z set in step S104 to the first decoder D1 to obtain a position field f p . Note that the learning unit 104 obtains a position field f p for each of the multiple training query points.
• step S108 the learning unit 104 inputs a combination of the training query point p i set in step S102 and the latent vector z set in step S104 to the second decoder D2 to obtain a type field f s . Note that the learning unit 104 obtains a type field f s for each of the multiple training query points.
• step S110 the learning unit 104 acquires lattice constant data L e by inputting a combination of the learning query point p i set in step S102 and the latent vector z set in step S104 to the third decoder D3. Note that the learning unit 104 acquires lattice constant data L e for each of the multiple learning query points.
• step S112 the learning unit 104 estimates the position of the atom based on the position field fp obtained in step S106.
• the learning unit 104 updates the positions of the multiple training query points by the above-mentioned method to obtain a final estimated position Pe .
• step S114 the learning unit 104 estimates the type of the atom based on the estimated position P e of the atom obtained in step S112 and the type field f s obtained in step S108. In this way, the learning unit 104 obtains an estimated type S e of the atom present at the estimated position P e .
• step S116 the learning unit 104 generates a learned first decoder D1 and a learned second decoder D2 by training the autoencoder AE using unsupervised machine learning so that the estimated atomic position P e obtained in step S112 matches the atomic position data P in the training crystal data, the estimated atomic type S e obtained in step S114 matches the atomic type data S in the training crystal data, and the lattice constant data L e obtained in step S110 matches the lattice constant data L in the training crystal data.
• machine learning termination conditions may include whether the machine learning processing has been performed a predetermined number of times or whether the error between the data output from the autoencoder AE and the training crystal data is below a predetermined threshold. Note that, although the above description has been given using an example in which one training crystal data set is set and training is performed, this is not limiting, and machine learning may be performed at once using multiple training crystal data.
• step S118 the learning unit 104 determines whether the above-mentioned termination conditions are satisfied. If the termination conditions are satisfied, the process proceeds to step S120. On the other hand, if the termination conditions are not satisfied, the process returns to step S102.
• step S120 the learning unit 104 stores the trained autoencoder AE obtained by the machine learning processing in steps S102 to S116 in the trained model storage unit 106.
• the information processing device 10 receives the target vector and the query point, it executes the estimation processing routine shown in FIG. 14.
• step S200 the acquisition unit 108 acquires a target vector and a query point.
• step S202 the processing unit 110 reads out the trained first decoder D1 and the trained second decoder D2 stored in the trained model storage unit 106.
• step S204 the processing unit 110 inputs the target vector and the query point obtained in step S200 to the trained first decoder D1 read out in step S202, thereby obtaining a position field fp corresponding to the target vector and the query point.
• step S206 the processing unit 110 inputs the target vector and the query point acquired in step S200 to the trained second decoder D2 read out in step S202, thereby acquiring a type field fs corresponding to the target vector and the query point.
• step S208 the processing unit 110 outputs the position field fp acquired in step S204 and the type field fs acquired in step S206 as results.
• the information processing device 10 can learn a neural network model that expresses a field that represents the structure of a substance that is composed of a group of atomic points. Furthermore, the information processing device 10 can use the neural network model to express a field that represents the structure of a substance that is composed of a group of atomic points.
• the information processing device 10 acquires training crystal data representing the crystal structure of a training substance, the training crystal data including position data representing the positions of atoms constituting the crystal of the training substance, type data representing the type of atoms constituting the crystal of the training substance, and lattice constant data of the crystal of the training substance, and a training query point which is a focus point within the training substance.
• the information processing device 10 acquires a latent vector representing the crystal structure of the training substance by inputting the training crystal data to an encoder of the autoencoder.
• the information processing device 10 acquires a position field representing the field of the positions of atoms constituting the crystal of the training substance by inputting a combination of the latent vector and the training query point to a first decoder of the autoencoder.
• the information processing device 10 estimates the positions of the atoms constituting the crystal of the training substance based on the position field output from the first decoder.
• the information processing device 10 acquires type field data representing the field of the type of atoms constituting the crystal of the training substance by inputting a combination of the latent vector and the training query point to a second decoder of the autoencoder.
• the information processing device 10 estimates the type of atoms constituting the crystal of the training material based on the type field output from the second decoder.
• the information processing device 10 acquires lattice constant data of the crystal of the training material by inputting a combination of the latent vector and the training query point to a third decoder of the autoencoder.
• the information processing device 10 generates a trained first decoder and a trained second decoder by training the autoencoder using unsupervised machine learning so that a combination of the estimated atomic position, the estimated atomic type, and the lattice constant data output from the third decoder corresponds to a combination of the position data, type data, and lattice constant data of the training crystal data.
• the information processing device 10 also acquires a target vector and a query point, which is a point of interest within the substance, and inputs the target vector and the query point to a first decoder and a second decoder, which are an example of a trained neural network model, to acquire field data corresponding to the query point.
• This field data is represented by a position field representing the field of the position of the atoms constituting the crystal of the substance, and a type field representing the field of the type of atoms constituting the crystal of the substance.
• the second decoder When an arbitrary vector in place of the latent vector and the query point are input, the second decoder outputs a type field corresponding to the query point.
• the information processing device 10 acquires a position field corresponding to the query point by inputting the target vector and the query point to the first decoder.
• the information processing device 10 also acquires a type field corresponding to the query point by inputting the target vector and the query point to the second decoder. For example, when the target vector is a vector representing a desired physical property, field data corresponding to the vector is output.
• the trained first decoder D1 and the trained second decoder D2 are used as pre-trained models.
• the case where the field representing the crystal structure is modeled by a neural field has been described as an example, but the present invention is not limited to this. It is also possible to model the structure of a substance composed of a group of atomic points that does not include a repeating structure, as well as a crystal structure that includes a repeating structure, by a neural field. In this case, it may not be necessary to estimate the lattice constant, and therefore the Lattice Decoder shown in FIG. 1 may not be necessary.
• the vector z input to the decoder is a latent vector output from the encoder, but this is not limited to this.
• a configuration may be used in which random noise is used as the vector z.
• an autoencoder including an encoder and a decoder is used as the neural network model, but the present invention is not limited to this.
• Other models may be used as the neural network model, for example, a generative adversarial network (GAN).
• GAN generative adversarial network
• FIGS 15 to 30 are diagrams for explaining the details of this embodiment.
• processors in this case include PLDs (Programmable Logic Devices) such as FPGAs (Field-Programmable Gate Arrays) whose circuit configuration can be changed after manufacture, and dedicated electric circuits such as ASICs (Application Specific Integrated Circuits), which are processors with circuit configurations designed exclusively to execute specific processes.
• PLDs Programmable Logic Devices
• FPGAs Field-Programmable Gate Arrays
• ASICs Application Specific Integrated Circuits
• each process may be executed by one of these various processors, or may be executed by a combination of two or more processors of the same or different types (for example, multiple FPGAs, or a combination of a CPU and an FPGA, etc.).
• the hardware structure of these various processors is, more specifically, an electric circuit that combines circuit elements such as semiconductor elements.
• the programs are described as being stored (e.g., installed) in advance in a storage device, but this is not limiting.
• the programs may be provided in a form stored in a storage medium such as a CD-ROM, DVD-ROM, Blu-ray disc, or USB memory.
• the programs may also be downloaded from an external device via a network.
• An information processing device including a processing unit that uses a neural network model to represent a field that represents a structure of a substance constituted by a group of atomic points.
• the method further includes an acquisition unit that acquires a target vector and a query point that is a point of interest within the material, the neural network model is a trained neural network model that, when an arbitrary vector and the query point are input, outputs field data representing a field of a structure of the material at the query point; the processing unit inputs the target vector and the query point acquired by the acquisition unit to the trained neural network model, thereby acquiring the field data corresponding to the query point; 2.
• the information processing device according to claim 1.
• the field data is represented by a position field representing a field of a position of an atom constituting the crystal of the substance, and a type field representing a field of a type of an atom constituting the crystal of the substance
• the trained neural network model includes a trained first neural network model and a trained second neural network model; the trained first neural network model, when the arbitrary vector and the query point are input, outputs the position field corresponding to the query point; the second trained neural network model, when the arbitrary vector and the query point are input, outputs the type field corresponding to the query point;
• the processing unit includes: acquiring the position field corresponding to the query point by inputting the target vector and the query point acquired by the acquisition unit into the trained first neural network model; acquiring the type field corresponding to the query point by inputting the target vector and the query point acquired by the acquisition unit into the trained second neural network model; 3.
• the information processing device is represented by a position field representing a field of a position of an atom constituting the crystal of the substance, and a type field
• the trained neural network model is A trained model is generated in advance by machine learning based on training crystal data, the training crystal data including: crystal data representing a crystal structure of the substance, the crystal data including position data representing positions of atoms constituting the crystal of the substance, type data representing types of atoms constituting the crystal of the substance, and lattice constant data of the crystal of the substance. 4.
• the information processing device according to claim 2 or 3.
• the trained neural network model is a trained first decoder and a trained second decoder of a trained autoencoder,
• a trained encoder of the trained autoencoder receives crystal data representing a crystal structure of the substance, the crystal data including position data representing positions of atoms constituting the crystal of the substance, type data representing types of atoms constituting the crystal of the substance, and lattice constant data of the crystal of the substance
• the trained encoder outputs a latent vector representing a crystal of the substance
• the trained first decoder when the arbitrary vector replacing the latent vector and the query point are input, outputs the position field corresponding to the query point
• the trained second decoder when the arbitrary vector replacing the latent vector and the query point are input, outputs the type field corresponding to the query point
• the trained first decoder and the trained second decoder are trained models obtained by performing unsupervised machine learning on an autoencoder including an encoder, a first decoder, and a second decoder based on the
• the autoencoder further comprising a third decoder;
• the trained third decoder is a trained model that outputs lattice constant data of a crystal of the substance when the arbitrary vector instead of the latent vector is input. 5.
• the information processing device according to claim 4.
• a trained model generating device including a learning unit that trains a neural network model that expresses a field that represents the structure of a substance composed of atomic point groups.
• the learning acquisition unit further includes: learning crystal data representing a crystal structure of the learning substance, the learning crystal data including position data representing the positions of atoms constituting the crystal of the learning substance, type data representing the types of atoms constituting the crystal of the learning substance, and lattice constant data of the crystal of the learning substance; and a learning query point which is a point of interest within the learning substance;
• the learning unit is When training an autoencoder using unsupervised machine learning, The training crystal data is input to an encoder of the autoencoder to obtain a latent vector representing a crystal structure of the training substance; A combination of the latent vector and the training query point is input to a first decoder of the autoencoder to obtain a position field representing a position field of atoms constituting a crystal of the training substance; estimating positions of atoms constituting the crystal of the learning material based on the position field output from the first decoder; A combination of the latent vector and the training query point is input to a second decoder of the auto
• Appendix 9 An information processing method in which a computer executes a process to represent a field that represents the structure of a substance composed of a group of atomic points using a neural network model.
• Appendix 10 A trained model generation method in which a computer executes processing to train a neural network model that expresses a field that represents the structure of a substance composed of a group of atomic points.
• Appendix 12 A trained model generation program that trains a neural network model that expresses a field that represents the structure of a substance composed of atomic point groups, and allows a computer to execute processing.

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