Method of predicting characteristic value of material, method of generating trained model, program, and device

Abstract

The present invention improves the accuracy of prediction of a property value of a material. A method according to an embodiment of the present invention acquires an image of a material, and performs a topological data analysis on the image of the material, to thereby extract a feature of the material and predict a property value of the material from the feature of the material.

Description

TITLE OF THE INVENTION: METHOD OF PREDICTING CHARACTERISTIC VALUE OF MATERIAL, METHOD OF GENERATING TRAINED MODEL, PROGRAM, AND DEVICE 5 TECHNICAL FIELD

[0001] The present invention relates to a method of predicting a characteristic value of a material, a 10 method of generating a trained model, programs, and devices. BACKGROUND ART

[0002] 15             Any discussion of the prior art throughout the specification should in no way be considered as an admission that such prior art is widely known or forms part of common general knowledge in the field. [0002a] 20             In material development, an approach that has been taken is such that a material is actually produced and then characteristic values of the produced material are evaluated. Currently, a method of predicting a characteristic value of a material 2023244020   03 Jun 2026 Informatics, is also used. Citation List Patent Document 5

[0003] Patent Document 1: Japanese Unexamined Patent Application Publication No. 2021-111360 SUMMARY OF THE INVENTION 10 Technical Problem

[0004] However, there is a need in material development for predicting a characteristic value of a material with higher accuracy. 15   [0004a] It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative. 20   [0004b] An object of some embodiments of the present invention is to improve accuracy of prediction of a characteristic value of a material. 25 2023244020   03 Jun 2026 Solution to Problem

[0005] A method according to some embodiments of the present invention comprises: 5        acquiring an SEM image of a material and an actual measurement value of a characteristic value of the material; dividing the SEM image into a number of segments selected from two to four, in such a manner that even 10 when an uneven region is present within the image of the material, the uneven region can be extracted by principal component analysis, while avoiding degradation in prediction accuracy due to loss of image information in the segments, and features of 15 the material are extracted from each of the segments; converting the divided SEM image to gray scale and performing standardization or normalization based on brightness of the SEM image; performing a topological data analysis using 20 persistent homology on the standardized or normalized SEM image, thereby generating a persistent diagram that includes a topological feature corresponding to a connected component, ring, or void of the material; dividing the persistent diagram into a grid, 25 generating a feature vector based on distribution 2023244020   03 Jun 2026 density values of points within respective grid section, and weighting the distribution density values according to a distance from a diagonal of the persistent diagram; 5        applying principal component analysis to the feature vector to perform dimensionality reduction; determining parameters for extracting the feature vector by Bayesian optimization; building a regression model using the feature 10 vector and the actual measurement value of the characteristic value, and calculating an acquisition function by calculating a predicted value and a dispersion of the predicted value using the regression model; 15       producing a machine learning model by optimizing hyperparameters of the regression model based on the acquisition function; predicting a characteristic value of the material from the feature vector of the material or 20 the dimension-reduced feature vector, using the produced machine learning model; and outputting the predicted characteristic value to a display device and presenting the predicted characteristic value to a user, wherein 25        the material is a ceramic, a glass-ceramic, a 2023244020   03 Jun 2026 polymer material, a composite resin, or a glass ionomer, and the characteristic value is a biaxial flexural strength. 5   [0005a] A method according to other embodiments of the present invention includes acquiring an image of a material, performing a topological data analysis on the image of the material to extract features of the 10 material, and predicting a characteristic value of the material from the features of the material. [0005b] A method according to further embodiments of the present invention comprises: 15        acquiring an image of a material and an actual measurement value of a characteristic value of the material; performing a topological data analysis on the image of the material to extract features of the 20 material; and producing a machine learning model with the features of the material and the actual measurement value of the characteristic value of the material to generate a trained model for predicting a 2023244020   03 Jun 2026 features of the material wherein parameters for extracting the features of the material are determined through Bayesian optimization, 5        a predicted value of the characteristic value and a dispersion of the predicted value are calculated from the features of the material using a regression model to calculate an acquisition function, and 10       parameters of the machine learning model are optimized based on the acquisition function, and wherein the material is a ceramic, a glass-ceramic, a polymer material, a composite resin, or a glass 15 ionomer the characteristic value is a biaxial flexural strength, the image is an SEM image, and in the performing of the topological data 20 analysis, the image is divided into a number of segments selected from two to four, in such a manner that even when an uneven region is present within the image of the material, the uneven region can be extracted by principal component analysis, while 25 avoiding degradation in prediction accuracy due to 2023244020   03 Jun 2026 loss of image information in the segments, and the features of the material are extracted from each of the segments. [0005c] 5       A device according to some embodiments of the present invention comprises: an acquisition part configured to acquire an SEM image of a material and an actual measurement value of a characteristic 10        value of the material, divide the SEM image into a number of segments selected from two to four, in such a manner that even when an uneven region is present within the image of the material, the 15        uneven region can be extracted by principal component analysis, while avoiding degradation in prediction accuracy due to loss of image information in the segments, and features of the material are extracted from each of the 20        segments, and convert the divided SEM image to gray scale and perform standardization or normalization based on brightness of the SEM image; a feature extraction part configured to 25             perform a topological data analysis using 2023244020   03 Jun 2026 persistent homology on the standardized or normalized SEM image thereby generating a persistent diagram that includes a topological feature corresponding to a connected component, 5 ring, or void of the material, divide the persistent diagram into a grid, generating a feature vector based on distribution density values of points within respective grid section, and weighing the 10 distribution density values according to a distance from a diagonal of the persistent diagram, apply principal component analysis to the feature vector to perform dimensionality 15 reduction, determine parameters for extracting the feature vector by Bayesian optimization, and build a regression model using the feature vector and the actual measurement value of the 20 characteristic value, and calculating an acquisition function by calculating a predicted value and a dispersion of the predicted value using the regression model; and a learning part configured to 25 produce a machine learning model by 2023244020   03 Jun 2026 optimizing hyperparameters of the regression model based on the acquisition function, predict a characteristic value of the material from the feature vector of the material 5        or the dimension-reduced feature vector, using the produced machine learning model, and output the predicted characteristic value to a display device and present the predicted characteristic value to a user; wherein 10        the material is a ceramic, a glass-ceramic, a polymer material, a composite resin, or a glass ionomer, and the characteristic value is a biaxial flexural strength. 15   [0005d] A device according to other embodiments of the present invention comprises: an acquisition part configured to acquire an image of a material and an actual measurement value 20 of a characteristic value of the material; a feature extraction part configured to perform a topological data analysis on the image of the material to extract features of the material; and a learning part configured to produce a machine 25 learning model with the features of the material and 2023244020   03 Jun 2026 an actual measurement value of a characteristic value of the material to generate a trained model for predicting a characteristic value of the material from the features of the material, wherein 5        the learning part is further configured to determine parameters for extracting the features of the material through Bayesian optimization, calculate a predicted value of the characteristic value and a dispersion of the 10 predicted value from the features of the material using a regression model to calculate an acquisition function, and optimize parameters of the machine learning model based on the acquisition function, and wherein 15        the material is a ceramic, a glass-ceramic, a polymer material, a composite resin, or a glass ionomer, the characteristic value is a biaxial flexural strength, 20        the image is an SEM image, and in the performing of the topological data analysis, the image is divided into a number of segments selected from two to four, in such a manner that even when an uneven region is present within the 25 image of the material, the uneven region can be 2023244020   03 Jun 2026 extracted by principal component analysis, while avoiding degradation in prediction accuracy due to loss of image information in the segments, and the features of the material are extracted from each of 5 the segments. Effects of the Invention

[0006] Embodiments of the present invention can 10 improve accuracy of prediction of a characteristic value of a material. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] 15 [Fig. 1] Fig. 1 is a diagram illustrating an overall configuration according to one embodiment of the present invention. [Fig. 2] Fig. 2 is a functional block diagram of a prediction device according to one embodiment of the 20 present invention. [Fig. 3] Fig. 3 is a functional block diagram of a learning device according to one embodiment of the present invention. [Fig. 4] Fig. 4 is a flowchart of a prediction 25 process according to one embodiment of the present 2023244020   03 Jun 2026 invention. [Fig. 5]  Fig. 5 is a flowchart of a learning process according to one embodiment of the present invention. [Fig. 6]  Fig. 6 is a diagram for explaining division 5 of an image according to one embodiment of the present invention. [Fig. 7] Fig. 7 is a diagram for explaining preprocessing of an image according to one embodiment of the present invention. 10 [Fig. 8] Fig. 8 is a diagram for explaining a topological data analysis (persistent homology) according to one embodiment of the present invention. [Fig. 9] Fig. 9 is a diagram for explaining dimensionality reduction of a vector according to one 15 embodiment of the present invention. [Fig. 10] Fig. 10 is a diagram for explaining dimensionality reduction of a vector according to one embodiment of the present invention. [Fig. 11] Fig. 11 is a diagram for explaining machine 20 learning according to one embodiment of the present invention. [Fig. 12] Fig. 12 is a diagram for explaining an inverse analysis according to one embodiment of the present invention. 25 [Fig. 13] Fig. 13 is a diagram for explaining an 2023244020   03 Jun 2026 inverse analysis according to one embodiment of the present invention. [Fig. 14] Fig. 14 is a hardware configuration diagram of a prediction device and a learning device 5 according to one embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0008] Embodiments of the present invention will 10 be described with reference to drawings hereinafter.

[0009] <Explanation of terminologies > • In the present specification, a “material” may be any material. For example, the “material” is a 15 medical material (e.g., a dental material). For example, the “material” is a ceramic, a glassceramic, a polymer material, a composite resin, a glass ionomer, or a metal (e.g., a dental ceramic, a dental glass-ceramic, a dental polymer material, a 20 dental composite resin, a dental glass ionomer, and a dental metal). • In the present specification, a “characteristic value” may be any characteristic value. For example, the “characteristic value” is a mechanical property 25   (e.g., a biaxial flexural strength, abrasion 2023244020   03 Jun 2026 resistance, and the like).

[0010] <Overall configuration> Fig. 1 is a diagram illustrating an overall 5 configuration according to one embodiment of the present invention. A user 30 operates a prediction device 10 and a learning device 20. Although the prediction device 10 and the learning device 20 are explained as separate devices in Fig. 1, the 10 prediction device 10 and the learning device 20 may be implemented as a single device.

[0011] <<Prediction device>> The prediction device 10 is a device 15 configured to predict a characteristic value of a material. The prediction device 10 is composed of one computer or multiple computers. The prediction device 10 can transmit and receive data to and from the learning device 20 via an arbitrary network. 20

[0012] <<Learning device>> The learning device 20 is a device configured to generate a trained model used for predicting a characteristic value of a material. The 25 learning device 20 is composed of one computer or 2023244020   03 Jun 2026 multiple computers. The learning device 20 can transmit and receive data to and from the prediction device 10 via an arbitrary network.

[0013] 5 <Functional blocks> Hereinafter, functional blocks of the prediction device 10 will be explained with reference to Fig. 2, and functional blocks of the learning device 20 will be explained with reference to Fig. 3. 10

[0014] Fig. 2 is a functional block diagram of the prediction device 10 according to one embodiment of the present invention. The prediction device 10 includes an image acquisition part 101, a feature 15 extraction part 102, and a prediction part 103. As a program is executed, the prediction device 10 functions as the image acquisition part 101, the feature extraction part 102, and the prediction part 103. 20

[0015] The image acquisition part (may be merely referred to as an acquisition part) 101 is configured to acquire an image of a material. Note that, the image acquisition part 101 may divide the acquired 25 image and use the divided image. For example, the 2023244020   03 Jun 2026 image is a scanning electron microscopic (SEM) image.

[0016] The feature extraction part 102 performs a topological data analysis on the image of the 5 material (the divided image) acquired by the image acquisition part 101 to extract features of the material. For example, the topological data analysis is persistent homology. Note that, the feature extraction part 102 may perform dimensionality 10 reduction (e.g., a principal component analysis) of the extracted features of the material.

[0017] The prediction part 103 predicts a characteristic value of the material from the 15 features of the material using a trained model generated by the learning device 20.

[0018] Fig. 3 is a functional block diagram of the learning device 20 according to one embodiment of the 20 present invention. The learning device 20 includes a training data acquisition part 201, a feature extraction part 202, a learning part 203, a feature visualization part 204, and an optimization part 205. As a program is executed, the learning device 20 25 functions as the training data acquisition part 201, 2023244020   03 Jun 2026 the feature extraction part 202, a learning part 203, a feature visualization part 204, and an optimization part 205.

[0019] 5             The training data acquisition part (may be merely referred to as an acquisition part) 201 acquires training data used for generating a trained model. Specifically, the training data acquisition part 201 acquires an image of a material, and an 10 actual measurement value of a characteristic value of the material. Note that, the training data acquisition part 201 may divide the acquired image, and use the divided image. For example, the image is a scanning electron microscopic (SEM) image. 15

[0020] The feature extraction part 202 performs a topological data analysis on the image of the material (or the divided image) acquired by the training data acquisition part 201 to extract 20 features of the material. For example, the topological data analysis is persistent homology. Note that, the feature extraction part 202 may perform dimensionality reduction (e.g., a principal component analysis) of the extracted features of the 2023244020   03 Jun 2026

[0021] The learning part 203 produces a machine learning model with the features of the material and the actual measurement value of the characteristic 5 value of the material to generate a trained model for predicting a characteristic value of the material from the features of the material.

[0022] The feature visualization part 204 10 visualizes the features of the material.

[0023] The optimization part 205 determines parameters for extracting the features of the material through Bayesian optimization. 15

[0024] <Processing method> Hereinafter, a prediction process will be explained with reference to Fig. 4, and a learning process will be explained with reference to Fig. 5. 20

[0025] Fig. 4 is a flowchart of a prediction process according to one embodiment of the present invention.

[0026] 25 In step 11 (S11), the image acquisition 2023244020   03 Jun 2026 part 101 of the prediction device 10 acquires an image of a material.

[0027] In step 12 (S12), the image acquisition 5 part 101 of the prediction device 10 divides the image acquired in S11. Note that, S12 can be omitted.

[0028] In step 13 (S13), the feature extraction 10 part 102 of the prediction device 10 performs a topological data analysis on the image of the material acquired in S11 or the image divided in S12 to extract features of the material.

[0029] 15              In step 14 (S14), the feature extraction part 102 of the prediction device 10 performs dimensionality reduction (e.g., a principal component analysis) of the features of the material extracted in S13. Note that, S14 can be omitted. 20

[0030] In step 15 (S15), the prediction part 103 of the prediction device 10 predicts a characteristic value of the material from the features of the material extracted in S13 or the features of the 25  material subjected to dimensionality reduction in S14 2023244020   03 Jun 2026 using the trained model generated by the learning device 20.

[0031] In step 16 (S16), the prediction part 103 5 of the prediction device 10 presents (e.g., by displaying on a screen) the predicted result of S15 to the user 30.

[0032] Fig. 5 is a flowchart of the learning 10 process according to one embodiment of the present invention.

[0033] In step 21 (S21), the training data acquisition part 201 of the learning device 20 15 acquires training data used for generating a trained model. Specifically, the training data acquisition part 201 acquires an image of a material, and an actual measurement value of a characteristic value of the material. 20

[0034] In step 22 (S22), the training data acquisition part 201 of the learning device 20 divides the image acquired in S21. Note that, S22 can be omitted. 2023244020   03 Jun 2026 In step 23 (S23), the optimization part 205 of the learning device 20 determines parameters used for extracting features of the material. For example, the optimization part 205 of the learning 5 device 20 determines parameters used for extracting features of the material through Bayesian optimization.

[0036] In step 24 (S24), the feature extraction 10 part 202 of the learning device 20 performs a topological data analysis on the image of the material acquired in S21 or the image divided in S22 to extract features of the material.

[0037] 15              In step 25 (S25), the feature extraction part 202 of the learning device 20 performs dimensionality reduction (e.g., a principal component analysis) of the features of the material extracted in S24. Note that, S25 can be omitted. 20

[0038] In step 26 (S26), the feature visualization part 204 of the learning device 20 visualizes the features of the material.

[0039] 25 In step 27 (S27), the learning part 203 of 2023244020   03 Jun 2026 the learning device 20 learns the features of the material and the actual measurement value of the characteristic value of the material through machine learning to generate a trained model for predicting a 5 characteristic value of the material from the features of the material.

[0040] Each process will be explained in detail hereinafter. As an example, a case where a dental 10 glass-ceramic is used (note that the glass-ceramic is a glass-ceramic on which alkali etching is performed (i.e., a glass component of the glass-ceramic is dissolved) to expose crystal grains) will be explained. 15

[0041] <<Division of image>> First, the prediction device 10 and the learning device 20 divide an SEM image. Fig. 6 is a diagram for explaining division of an image according 20 to one embodiment of the present invention. The left side of Fig. 6 depicts the SEM image before the division, and the right side of Fig. 6 depicts the SEM image after the division.

[0042] 25 In a case where an unnecessary portion is 2023244020   03 Jun 2026 included in the SEM image, the unnecessary portion is cut out as depicted in <BEFORE DIVISION> on the left side of Fig. 6. Then, the SEM image is divided (divided into four in the example of Fig. 6). 5

[0043] As depicted in <AFTER DIVISION> on the right side of Fig. 6, the single SEM image is divided into two or more images. If the image is excessively divided, information included in the original image 10 may be lost, which may lower the accuracy of the prediction. Therefore, the image is preferably divided into two to four. By dividing the image in the above-described manner, training data for machine learning can be increased. As the image is divided, 15 moreover, when there is an uneven portion in an image of one material, the uneven portion can be extracted by a principal component analysis.

[0044] <<Preprocessing of image>> 20             Next, the prediction device 10 and the learning device 20 perform preprocessing of the image. Fig. 7 is a diagram for explaining preprocessing of the image according to one embodiment of the present invention. 2023244020   03 Jun 2026 After unifying the gray scale of the image in 8 bits, the image is converted into a text format so that the image can be easily handled by a computer. One text-format file is produced for one 5 image, and the files are grouped for each prototype or each product.

[0046] Since brightness of images may vary depending on a day on which an image is captured, a 10 prototype, or a product, images are standardized or normalized.  A calculation for standardization (scaling so that the average value becomes 0 and dispersion (standard deviation) becomes 1) or normalization (scaling so that the minimum value 15 becomes 0 and the maximum value becomes 1) is performed on all the images using the average value, the maximum value, and the minimum value of the brightness of all of the images.

[0047] 20 <<Topological data analysis (persistent homology)>> Next, the prediction device 10 and the learning device 20 performs a topological data analysis (persistent homology) on the image. Fig. 8 is a diagram for explaining the topological data 25 analysis (persistent homology) according to one 2023244020   03 Jun 2026 embodiment of the present invention.

[0048] In one embodiment of the present invention, a calculation of persistent homology is performed on 5 each SEM image (specifically, a text format) to obtain n-dimensional persistence diagrams (e.g., a 0dimensional persistence diagram and a 1-dimensional persistence diagram).  Depending on an image that will be a subject of the analysis, the image is 10 binarized in advance, and the binarized image may be subjected to a topological data analysis.

[0049] The persistent homology will be explained. The persistent homology is one of data analysis 15 methods (topological data analysis) using a mathematical concept of topology, and quantitively represents a shape of data based on a structure of a shape, such as a connected component, ring, void, or the like of a shape.  The persistence diagram 20 represents an appearance (birth) and disappearance (death) of a connected component, ring, void, or the like of a shape.  The 0-dimensional persistent homology computes a linkage between a point and another point, and the 1-dimensional persistent 25 homology computes a relationship of a ring composed 2023244020   03 Jun 2026 of a cluster of points.  As in the above, use of persistent homology can reveal the topological features of the image of the material.

[0050] 5  <<Extraction of features (vectorization)>> Next, the prediction device 10 and the learning device 20 extract (vectorize) features from the persistence diagrams. Specifically, a method of persistence images (PI) (e.g., “Persistent Homology 10 and Its Applications to Materials Science (https: / / www.jim.or.jp / journal / m / pdf3 / 58 / 01 / 17.pdf)”) is used. The persistence diagram is divided into a grid (e.g., 128 x 128 sections), and the frequency (density) of the data points per section of the grid 15 is determined as each element of a vector. It is determined that the frequency (density) conforms to a normal distribution.

[0051] The distribution function p is represented 20 by an equation (1). Dk(X) is a k-dimensional persistence diagram of X, b is birth (i.e., appearance of a connected component, ring, void, or the like of a shape) and d is death (i.e., disappearance of the connected component, ring, void, 25 or the like of the shape). 2023244020   03 Jun 2026

[0052] In accordance with an equation (2), a numerical value is weighed (using an arctangent function) according to a distance from a diagonal 5 line on the persistence diagram. In this manner, an importance of each point on the persistence diagram can be reflected (the importance increases as the point is further from the diagonal line of the persistence diagram). 10

[0053] The o (standard deviation), C, and p are parameters, which need to be preset by a human. As described later, the parameters (o (standard deviation), C, and p) used for extracting features of 15 a material can be determined by Bayesian optimization.

[0054] [Math. 1] , . V ( & - W2 + (y - dty\ p(x,y) =    >    w^, djexp----------- Z_।                    \             zcr            / (bt.dpEDkW              x                       7 ■■■EQUATION (1) 20

[0055] [Math. 2] 2023244020   03 Jun 2026 w( b, d) - arctan(C(d - by?}     ■■ ■ EQUATION (2)

[0056] <<Dimensionality reduction of vector>> Next, the prediction device 10 and the 5 learning device 20 performs dimensionality reduction of the features (vector). Figs. 9 and 10 are diagrams for explaining dimensionality reduction of a vector according to one embodiment of the present invention. As a result of extraction (vectorization) 10 of features from the persistence diagram, one SEM image is converted into a vector having approximately 1,300 elements. Since 1,376 SEM images are used in total, the entire data is composed of a huge matrix of 1,300 x 1,376. If this data is used as it is, 15 confirmation of the features by visualization or highly accurate prediction by machine learning cannot be achieved. Thus, dimensionality reduction of the features (vector) is performed by a principal component analysis. 20

[0057] Fig. 9 illustrates a cumulative contribution rate, where the vertical axis indicates a cumulative contribution rate and the horizontal axis indicates the number of principal components. 2023244020   03 Jun 2026 As a result of the dimensionality reduction of the features (vector), it is confirmed that almost 100% of the original data can be explained with principal components including up to a second principal 5 component.

[0058] In Fig. 10, the data is visualized using the first principal component (horizontal axis) and the second principal component (vertical axis). Each 10 of prototypes or products forms a cluster, and is in a region that is slightly different from one another on the graph, thus it is confirmed that information specific to each material can be extracted.  The feature visualization part 204 visualizes the 15 features of the material by presenting a distribution of each material as in Fig. 10.

[0059] <<Machine learning>> Next, the learning device 20 performs 20 machine learning using the features (vectors). Fig. 11 is a diagram for explaining machine learning according to one embodiment of the present invention.

[0060] The data was condensed to 12 principal 25 components through a principal component analysis 2023244020   03 Jun 2026 (i.e., one SEM image can be expressed by a vector including 12 elements). By determining the 12 principal components as explanatory variables and a biaxial flexural strength (actual measurement value) 5 of a glass-ceramic as an object variable, a regression analysis is performed by machine learning (e.g., support vector regression, random forest regression, etc.), and the accuracy presented in the bottom side of Fig. 11 is obtained (R2 is around 0.9 10 in the test data). Note that, the hyperparameter of the machine learning model may be adjusted by an arbitrary optimizing algorithm. Examples thereof include grid search, random search, Bayesian optimization, and a genetic algorithm. The upper 15 side of Fig. 11 presents actual measurement values (the actual measurement values (MPa) of the horizontal axis) of the biaxial flexural strength and predicted values (the predicted values (MPa) on the vertical axis) of the biaxial flexural strength for 20 the training data (dataset train) and the accuracy _ verification data (dataset_test).

[0061] <<Bayesian optimization>> As described above, the learning device 20 25 can determine parameters (o (standard deviation), C, 2023244020   03 Jun 2026 p of the equations (1) and (2)) used for extracting features of a material by Bayesian optimization. Moreover, the learning device 20 can determine the number of principal components, which is a parameter 5 used for extracting features of a material, by Bayesian optimization. As the Bayesian optimization is performed approximately 50 times, a combination of optimal values is found.

[0062] 10             Specifically, a predicted value of the characteristic value and a dispersion of the predicted value are calculated from the features of the material using the Gaussian process regression model to calculate an acquisition function. Optimum 15 parameters are determined based on the acquisition function. As in the above manner, as a human merely produces and inputs training data, the learning device 20 can automatically learn through machine learning and can generate a trained model using the 20 algorithm of the Bayesian optimization in combination.

[0063] <<Inverse analysis>> An inverse analysis can be performed using 25 the above persistence diagrams and the result of the 2023244020   03 Jun 2026 principal component analysis.

[0064] For example, as depicted in Fig. 12, the points having a longer life time (i.e., a period from 5 birth to death) than a certain period on the persistence diagram (e.g., an upper left portion from the predetermined line of Fig. 12) are assumed to be important points on the image. Therefore, an important structure of crystals can be revealed by 10 analyzing what kind of a structure of crystals corresponds to points having a longer life time than a certain period (e.g., an upper left portion with respect to the predetermined line of Fig. 12).

[0065] 15             For example, as depicted in Fig. 13, what kind of a structure of crystals the points constituting the small cluster in a region being away from the other are derived from can be analyzed.

[0066] 20 <Hardware configuration> Fig. 14 is a diagram illustrating a hardware configuration of the prediction device 10 and the learning device 20 according to one embodiment of the present invention. The prediction 25 device 10 and the learning device 20 include a 2023244020   03 Jun 2026 central processing unit (CPU) 1001, a read-only memory (ROM) 1002, and a random access memory (RAM) 1003. The CPU 1001, the ROM 1002, and the RAM 1003 constitute a so-called computer. Moreover, the 5 prediction device 10 and the learning device 20 may further include an auxiliary memory device 1004, a display device 1005, an operation device 1006, an interface (I / F) device 1007, and a driver 1008. Note that, the hardware components of the prediction 10 device 10 and the learning device 20 are coupled to one another via a bus B.

[0067] The CPU 1001 is a computation device that executes various programs installed in the auxiliary 15 memory device 1004. As the CPU 1001 executes the programs, the processes described in the present specification are performed.

[0068] The ROM 1002 is a non-volatile memory. The 20 ROM 1002 functions as a main storage device that stores various programs, data, etc., necessary for the CPU 1001 to execute various programs installed in the auxiliary memory device 1004. Specifically, the ROM 1002 functions as a main storage device that 25 stores boost programs, etc., such as a basic 2023244020   03 Jun 2026 input / output system (BIOS), an extensible firmware interface (EFI), and the like.

[0069] The RAM 1003 is a volatile memory, such as a 5 dynamic random-access memory (DRAM), a static randomaccess memory (SRAM), or the like. The RAM 1003 functions as a main storage device that provides a work space in which various programs installed in the auxiliary memory device 1004 are expanded when 10 executed by the CPU 1001.

[0070] The auxiliary memory device 1004 is an auxiliary storage device that stores various programs and information used when the various programs are 15 executed.

[0071] The display device 1005 is a display device that displays internal states and the like of the prediction device 10 and the learning device 20. 20

[0072] The operation device 1006 is an input device for a user who operates the prediction device 10 and the learning device 20 to input various instructions to the prediction device 10 and the 2023244020   03 Jun 2026

[0073] The I / F device 1007 is a communication device for connecting to the network to communicate with other devices. 5

[0074] The driver 1008 is a device for setting a storage medium 1009. The storage medium 1009 includes media for optically, electrically, or magnetically recording information, such as compact- 10 disk (CD)-ROM, flexible disks, magneto-optical disks, and the like. The storage medium 1009 may include a semiconductor memory and the like that electrically record information, such as a ROM, a flash memory, and the like. 15

[0075] Note that, various programs to be installed in the auxiliary memory device 1004 are installed, for example, by setting a distributed storage medium 1009 in the driver 1008, and reading the various 20 programs recorded on the storage medium 1009 by the driver 1008. Alternatively, various programs to be installed in the auxiliary memory device 1004 may be installed by downloading the programs from the network via the I / F device 1007. 25

[0076] 2023244020   03 Jun 2026 Although the embodiments of the present invention have been described above in detail, the present invention is not limited to the abovedescribed specific embodiments, and various 5 modifications and variations are possible within the scope of the invention as claimed.

[0077] The present application claims priority to Japanese Patent Application No. 2022-055035, filed 10 with the Japan Patent Office on March 30, 2022, the entire contents of which are incorporated in the present application by reference. [0077a] Unless the context clearly requires 15 otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”. 20 REFERENCE SIGNS LIST

[0078] 10 prediction device 2023244020   03 Jun 2026 30 101 102 user image acquisition part feature extraction part prediction part 103 5 10 15 201 202 203 204 205 1001 1002 1003 1004 1005 1006 1007 1008 training data acquisition part feature extraction part learning part feature visualization part optimization part CPU ROM RAM auxiliary memory device display device operation device I / F device driver 1009 storage medium

Claims

1. 5       A method comprising:acquiring an SEM image of a material and an actual measurement value of a characteristic value ofthe material;dividing the SEM image into a number of segments10 selected from two to four, in such a manner that even when an uneven region is present within the image of the material, the uneven region can be extracted by principal component analysis, while avoiding degradation in prediction accuracy due to loss of15 image information in the segments, and features of the material are extracted from each of the segments;converting the divided SEM image to gray scaleand performing standardization or normalization based on brightness of the SEM image;20       performing a topological data analysis usingpersistent homology on the standardized or normalizedSEM image, thereby generating a persistent diagramthat includes a topological feature corresponding toa connected component, ring, or void of the material;25        dividing the persistent diagram into a grid,2023244020   03 Jun 2026generating a feature vector based on distribution density values of points within respective grid section, and weighting the distribution density values according to a distance from a diagonal of the5 persistent diagram;applying principal component analysis to thefeature vector to perform dimensionality reduction;determining parameters for extracting thefeature vector by Bayesian optimization;10       building a regression model using the featurevector and the actual measurement value of thecharacteristic value, and calculating an acquisitionfunction by calculating a predicted value and adispersion of the predicted value using the15 regression model;producing a machine learning model by optimizinghyperparameters of the regression model based on the acquisition function;predicting a characteristic value of the20 material from the feature vector of the material or the dimension-reduced feature vector, using the produced machine learning model; andoutputting the predicted characteristic value to a display device and presenting the predicted25 characteristic value to a user, wherein2023244020   03 Jun 2026the material is a ceramic, a glass-ceramic, a polymer material, a composite resin, or a glass ionomer, andthe characteristic value is a biaxial flexural5 strength.

2. The method according to claim 1,wherein the topological data analysis is10 persistent homology.

3. The method according to claim 1 or claim 2, further comprising:15       performing dimensionality reduction of thefeatures of the material.

4. The method according to any one of the preceding20 claims, further comprising:visualizing the features of the material.

5. A non-transitory computer readable storage25 medium having stored thereon instructions that cause2023244020   03 Jun 2026a processor to execute the method of any one of the preceding claims.

6. 5       A device comprising:an acquisition part configured toacquire an SEM image of a material and anactual measurement value of a characteristic value of the material,10             divide the SEM image into a number ofsegments selected from two to four, in such a manner that even when an uneven region ispresent within the image of the material, the uneven region can be extracted by principal15        component analysis, while avoiding degradationin prediction accuracy due to loss of imageinformation in the segments, and features of the material are extracted from each of the segments, and20             convert the divided SEM image to gray scaleand perform standardization or normalization based on brightness of the SEM image;a feature extraction part configured to perform a topological data analysis using2023244020   03 Jun 202610152025normalized SEM image thereby generating a persistent diagram that includes a topological feature corresponding to a connected component,ring, or void of the material,divide the persistent diagram into a grid,generating a feature vector based ondistribution density values of points withinrespective grid section, and weighing thedistribution density values according to adistance from a diagonal of the persistentdiagram,apply principal component analysis to the feature vector to perform dimensionalityreduction,determine parameters for extracting thefeature vector by Bayesian optimization, andbuild a regression model using the featurevector and the actual measurement value of thecharacteristic value, and calculating an acquisition function by calculating a predictedvalue and a dispersion of the predicted value using the regression model; anda learning part configured toproduce a machine learning model by optimizing hyperparameters of the regression2023244020   03 Jun 2026model based on the acquisition function, predict a characteristic value of thematerial from the feature vector of the materialor the dimension-reduced feature vector, using5        the produced machine learning model, andoutput the predicted characteristic valueto a display device and present the predictedcharacteristic value to a user; whereinthe material is a ceramic, a glass-ceramic, a10 polymer material, a composite resin, or a glass ionomer, andthe characteristic value is a biaxial flexural strength.15

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