MÉTODO, MEIO DE ARMAZENAMENTO LEGÍVEL POR COMPUTADOR NÃO TRANSITÓRIO E DISPOSITIVO DE PREVISÃO DE CONDIÇÃO

Abstract

The present invention predicts a condition from which a characteristic value of a target material can be obtained. A method according to one embodiment of the present invention comprises: acquiring a characteristic value of a material; inversely analyzing a model for predicting the characteristic value of the material from a feature amount of the material, and thereby predicting the feature amount of the material from the acquired characteristic value of the material; generating phase data analysis results on the basis of the predicted feature amount of the material; and indicating, on an image of a material different from the material, a pixel corresponding to a portion designated in the phase data analysis results.

Description

1 / 29 METHOD, NON-TRANSIENTIAL COMPUTER-READABLE STORAGE MEDIUM AND CONDITION PREDICTION DEVICE TECHNICAL FIELD

[001] The present invention relates to a condition prediction method, a program and a device. PREVIOUS TECHNIQUE

[002] In materials development, a technique of manufacturing real materials and evaluating the values ​​of their properties was adopted. Currently, a technique called materials informatics has also been adopted, which uses machine learning to predict the values ​​of their properties. LIST OF QUOTES Patent Literature

[003] Patent Literature 1: Japanese Patent No. 7188644 SUMMARY OF THE INVENTION Technical Problem

[004] However, in the development of materials, the need arose to predict a condition for obtaining a property value of a target material. An objective of the present invention is to predict a condition for obtaining a property value of a target material. Solution to the Problem

[005] A method according to an embodiment of the present invention includes: acquiring the property value of a material; predicting a material characteristic based on the acquired property value of the material; performing an inverse analysis on a model that predicts a material property value based on a material characteristic; generating a topological data analysis result based on the predicted material characteristic; and displaying, on an image of a material other than the material, a pixel that corresponds Petition 870250099346, dated 10 / 30 / 2025, page 40 / 75 2 / 29 of a designated portion in the result of the topological data analysis. Advantageous Effects of the Invention

[006] According to the present invention, it is possible to predict a condition for obtaining a property value of a target material. BRIEF DESCRIPTION OF THE DRAWINGS

[007] Figure 1 is a diagram illustrating a complete configuration according to an embodiment of the present invention.

[008] Figure 2 is a functional block diagram of an advanced analysis device (property value prediction) according to an embodiment of the present invention.

[009] Figure 3 is a functional block diagram of a learning device according to an embodiment of the present invention.

[0010] Figure 4 is a functional block diagram of an inverse analysis (condition prediction) device according to an embodiment of the present invention.

[0011] Figure 5 is a flowchart of an advanced analysis process (property value prediction) according to an embodiment of the present invention.

[0012] Figure 6 is a flowchart of a learning process according to an embodiment of the present invention.

[0013] Figure 7 is a flowchart of an inverse analysis (condition prediction) process according to an embodiment of the present invention.

[0014] Figure 8 is an explanatory diagram of the correspondence between direct analysis and inverse analysis according to an embodiment of the present invention.

[0015] Figure 9 is an explanatory diagram of the image division according to an embodiment of the present invention. Petition 870250099346, dated 10 / 30 / 2025, page 41 / 75 3 / 29

[0016] Figure 10 is an explanatory diagram of image preprocessing according to an embodiment of the present invention.

[0017] Figure 11 is an explanatory diagram of the topological data analysis (persistent homology) according to an embodiment of the present invention.

[0018] Figure 12 is an explanatory diagram of the reduction of vector dimensionality according to an embodiment of the present invention.

[0019] Figure 13 is an explanatory diagram of the vector dimensionality reduction according to an embodiment of the present invention.

[0020] Figure 14 is an explanatory machine learning diagram according to an embodiment of the present invention.

[0021] Figure 15 is an explanatory diagram of an analysis according to an embodiment of the present invention.

[0022] Figure 16 is an explanatory diagram of an analysis according to an embodiment of the present invention.

[0023] Figure 17 is an explanatory diagram of an inverse analysis (inverse analysis of a regression model) according to an embodiment of the present invention.

[0024] Figure 18 is an explanatory diagram of an inverse analysis (generation of topological data analysis results) according to an embodiment of the present invention.

[0025] Figure 19 is an explanatory diagram of an inverse analysis (display, on an image of a different material, of a pixel that corresponds to a designated portion in the results of the topological data analysis) according to an embodiment of the present invention.

[0026] Figure 20 is a hardware configuration diagram. Petition 870250099346, dated 10 / 30 / 2025, page 42 / 75 4 / 29 of the direct analysis device (property value prediction), the learning device, and the inverse analysis device (condition prediction) according to an embodiment of the present invention. DESCRIPTION OF THE MODALITIES

[0027] The following will describe embodiments of the present invention with reference to the drawings. Explanation of Terms

[0028] As used in this document, a material can be any material. For example, the material is a medical material (e.g., a dental material). For example, the material is any of the following: ceramic, glass-ceramic, polymeric material, composite resin, glass ionomer, or metal (e.g., dental ceramic, dental glass-ceramic, dental polymeric material, dental composite resin, dental glass ionomer, or dental metal).

[0029] As used in this document, a property value can be any property value. For example, the property value is a mechanical property (e.g., biaxial bending strength, abrasion resistance, or similar). Entire Configuration

[0030] Figure 1 is a diagram illustrating a complete configuration according to an embodiment of the present invention. A user 40 operates a direct analysis device (property value prediction) 10, a learning device 20, and an inverse analysis device (condition prediction) 30. Although the direct analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 are described as separate devices in Figure 1, the direct analysis device (property value prediction) 10, the Petition 870250099346, dated 10 / 30 / 2025, page 43 / 75 5 / 29 learning device 20 and inverse analysis device (condition prediction) 30 can be implemented in a single device. Advanced Analysis Device (Property Value Prediction)

[0031] The advanced analysis device (property value prediction) 10 is a device configured to predict the value of a material property. The advanced analysis device (property value prediction) 10 consists of one or more computers. The advanced analysis device (property value prediction) 10 can transmit and receive data to and from the learning device 20 and the inverse analysis device (condition prediction) 30 via any network. Learning Device

[0032] The learning device 20 is a device configured to generate a trained model used to predict the property value of the material. The learning device 20 consists of one or more computers. The learning device 20 can transmit and receive data to and from the forward analysis device (property value prediction) 10 and the inverse analysis device (condition prediction) 30 via any network. Inverse Analysis Device (Condition Prediction)

[0033] The inverse analysis (condition prediction) device 30 is a device configured to predict a condition to obtain a property value of a target material. The inverse analysis (condition prediction) device 30 consists of one or more computers. The inverse analysis (condition prediction) device 30 can transmit and receive data to and from the direct analysis (property value prediction) device 10 and the learning device 20 via any network. Functional Blocks Petition 870250099346, dated 10 / 30 / 2025, page 44 / 75 6 / 29

[0034] Next, the functional blocks of the forward analysis device (property value prediction) 10, the learning device 20 and the inverse analysis device (condition prediction) 30 will be described with reference to Figures 2, 3 and 4, respectively.

[0035] Figure 2 is a functional block diagram of the advanced analysis device (property value prediction) 10 according to an embodiment of the present invention. The advanced analysis device (property value prediction) 10 includes an image acquisition unit 101, a feature extraction unit 102, and a prediction unit 103. Running a program allows the advanced analysis device (property value prediction) 10 to function as the image acquisition unit 101, the feature extraction unit 102, and the prediction unit 103.

[0036] The image acquisition unit (also simply referred to as the acquisition unit) 101 is configured to acquire an image of a material. The image acquisition unit 101 can split the acquired image and use the split images. For example, the image is a scanning electron microscope (SEM) image.

[0037] Feature extraction unit 102 is configured to extract material features by performing topological data analysis on the material image (or split images) acquired by image acquisition unit 101. For example, topological data analysis involves an analysis that uses persistent homology. Feature extraction unit 102 can reduce the dimensionality of the extracted material features (e.g., principal component analysis).

[0038] Prediction unit 103 is configured to predict the material property value from the material characteristics. Petition 870250099346, dated 10 / 30 / 2025, page 45 / 75 7 / 29 using the trained model generated by the learning device 20.

[0039] Figure 3 is a functional block diagram of the learning device 20 according to an embodiment of the present invention. The learning device 20 includes a training data acquisition unit 201, a feature extraction unit 202, a learning unit 203, a feature visualization unit 204, and an optimization unit 205. Running a program allows the learning device 20 to function as the training data acquisition unit 201, the feature extraction unit 202, the learning unit 203, the feature visualization unit 204, and the optimization unit 205.

[0040] The training data acquisition unit (also referred to simply as the acquisition unit) 201 is configured to acquire training data used to generate a trained model. Specifically, the training data acquisition unit 201 is configured to acquire an image of a material and an actual measurement value of a material property value. The training data acquisition unit 201 can split the acquired image and use the split images. For example, the image is a SEM image.

[0041] Feature extraction unit 202 is configured to extract material features by performing topological data analysis on the material image (or split images) acquired by training data acquisition unit 201. For example, topological data analysis involves an analysis that uses persistent homology. Feature extraction unit 202 can reduce the dimensionality of the extracted material features (e.g., principal component analysis). Petition 870250099346, dated 10 / 30 / 2025, page 46 / 75 8 / 29

[0042] Learning unit 203 is configured to create a machine learning model using material characteristics and actual measurement values ​​of material property values ​​and generate a trained model to predict a material property value from a material characteristic.

[0043] For example, learning unit 203 trains the model parameters of the Gaussian Mixture Regression (GMR) algorithm using the Expectation-Maximization (EM) algorithm. Gaussian Mixture Regression is a regression analysis that uses a Gaussian Mixture Model (GMM).

[0044] The feature display unit 204 is configured to display the characteristics of the materials.

[0045] The optimization unit 205 is configured to determine a parameter used to extract the material characteristics through Bayesian optimization.

[0046] Figure 4 is a functional block diagram of the inverse analysis (condition prediction) device 30 according to an embodiment of the present invention. The inverse analysis (condition prediction) device 30 includes a property value acquisition unit 301, a prediction unit 302, a topological data analysis unit 303, and a display unit 304. Running a program allows the inverse analysis (condition prediction) device 30 to function as the property value acquisition unit 301, the prediction unit 302, the topological data analysis unit 303, and the display unit 304.

[0047] The property value acquisition unit (also referred to simply as acquisition unit) 301 is configured to acquire a property value of a material (for example, a property value of a target material entered into the inverse analysis device (condition prediction) 30 by the user 40). Petition 870250099346, dated 10 / 30 / 2025, page 47 / 75 9 / 29

[0048] Prediction unit 302 is configured to perform an inverse analysis on a model (e.g., a model generated by the GMR algorithm) that is generated by learning device 20 and predicts a material property value from the material characteristics and predicts a material characteristic from the material property value acquired by property value acquisition unit 301. An inverse analysis parameter is a model parameter for predicting the material property value from the material characteristics. Gaussian Mixture Regression

[0049] In this document, GMR will be described. As described above, GMR is a regression analysis that uses GMM and is configured to represent a relationship between explanatory variables and objective variables as an overlay of a plurality of normal distributions.

[0050] In GMR, in the case of a model to predict the value of a property (denoted as y) of a material from the characteristics (denoted as x) of the material, a joint distribution (also called a joint probability distribution) p(x,y) is calculated using the GMM and the conditional probability distribution p(y|x) is calculated from p(x,y) using Bayes' theorem. That is, the probability distribution of the material property value is predicted.

[0051] Meanwhile, in the inverse analysis (i.e., in the case of predicting a material characteristic (x) from the material property value (y)), a joint distribution (also called a joint probability distribution) p(y,x) is calculated using the GMM and the conditional probability distribution p(x|y) is calculated from p(y,x) using Bayes' theorem. That is, the probability distribution of the material characteristic is predicted. Petition 870250099346, dated 10 / 30 / 2025, page 48 / 75 10 / 29

[0052] The topological data analysis unit 303 is configured to generate the results of the topological data analysis based on the material characteristics predicted by the prediction unit 302. For example, the topological data analysis unit 303 generates persistence diagrams through persistent homology analysis based on the material characteristic predicted by the prediction unit 302.

[0053] The topological data analysis unit 303 can generate the results of the topological data analysis after conducting an inverse dimensionality reduction transformation (e.g., inverse principal component analysis transformation) on the material feature predicted by the prediction unit 302.

[0054] Display unit 304 displays, over an image of a material (e.g., an existing material) different from the material, a pixel that corresponds to a portion (e.g., a user-designated portion 40) designated in the results of the topological data analysis generated by the topological data analysis unit 303. For example, the image is a SEM image. Processing Method

[0055] Next, an advanced analysis process (property value prediction), a learning process, and an inverse analysis process (condition prediction) will be described with reference to Figures 5, 6, and 7, respectively.

[0056] Figure 5 is a flowchart of the advanced analysis process (property value prediction) according to an embodiment of the present invention.

[0057] In step 11 (S11), the image acquisition unit 101 of the advanced analysis device (property value prediction) 10 acquires an image of a material.

[0058] In Stage 12 (S12), the image acquisition unit 101 Petition 870250099346, dated 10 / 30 / 2025, page 49 / 75 11 / 29 of the direct analysis device (property value prediction) 10 divides the acquired image into S11. S12 can be omitted.

[0059] In Step 13 (S13), the feature extraction unit 102 of the advanced analysis device (property value prediction) 10 extracts material features by conducting topological data analysis on the material image acquired in S11 or on the split images in S12.

[0060] In Step 14 (S14), the feature extraction unit 102 of the advanced analysis device (property value prediction) 10 reduces the dimensionality of the extracted material features in S13 (e.g., principal component analysis). S14 can be omitted.

[0061] In Step 15 (S15), the prediction unit 103 of the advanced analysis device (property value prediction) 10 uses the trained model generated by the learning device 20 to predict a material property value from the material features extracted in S13 or from the material features after dimensionality reduction in S14.

[0062] In Step 16 (S16), the forecasting unit 103 of the advanced analysis device (property value forecasting) 10 presents the forecast results in S15 to the user 40 (e.g., displays the results on a screen).

[0063] Figure 6 is a flowchart of the learning process according to one embodiment of the present invention.

[0064] In Step 21 (S21), the training data acquisition unit 201 of the learning device 20 acquires training data used to generate a trained model. Specifically, the training data acquisition unit 201 acquires the images of the materials and the actual measurement values ​​of the material property values. Petition 870250099346, dated 10 / 30 / 2025, page 50 / 75 12 / 29

[0065] In Step 22 (S22), the training data acquisition unit 201 of the learning device 20 splits the acquired images into S21. S22 can be omitted.

[0066] In Step 23 (S23), optimization unit 205 of learning device 20 determines the parameters used to extract the material characteristics. For example, optimization unit 205 of learning device 20 determines the parameters used to extract the material characteristics through Bayesian optimization.

[0067] In Step 24 (S24), the feature extraction unit 202 of the learning device 20 extracts the features of the materials by conducting topological data analysis on the material images acquired in S21 or on the split images in S22.

[0068] In Step 25 (S25), the feature extraction unit 202 of the learning device 20 reduces the dimensionality of the material features extracted in S24 (e.g., principal component analysis). S25 can be omitted.

[0069] In step 26 (S26), the feature display unit Learning device 204 displays the characteristics of the materials.

[0070] In Step 27 (S27), learning unit 203 of learning device 20 performs machine learning using material characteristics and actual measurement values ​​of material property values ​​to generate a trained model to predict material property values ​​from material characteristics.

[0071] Figure 7 is a flowchart of the inverse analysis (condition prediction) process according to an embodiment of the present invention.

[0072] In Stage 31 (S31), the value acquisition unit of pro Petition 870250099346, dated 10 / 30 / 2025, page 51 / 75 13 / 29 property 301 of the inverse analysis device (condition prediction) 30 acquires a property value of a material.

[0073] In Step 32 (S32), the prediction unit 302 of the inverse analysis device (condition prediction) 30 performs an inverse analysis on the model to predict the material property value from the material characteristics and predicts a material characteristic from the material property value acquired in S31.

[0074] In Step 33 (S33), the topological data analysis unit 303 of the inverse analysis (condition prediction) device 30c performs an inverse dimensionality reduction transformation (e.g., inverse principal component analysis transformation) on the material characteristics predicted in S32. S33 can be omitted.

[0075] In Step 34 (S34), the topological data analysis unit 303 of the inverse analysis device (condition prediction) 30 generates topological data analysis results based on the material characteristics predicted in S32 or the material characteristics after the inverse dimensionality reduction transformation in S33.

[0076] In Step 35 (S35), the display unit 304 of the inverse analysis device (condition prediction) 30 displays, in the image of the different material, a pixel that corresponds to a designated portion in the results of the topological data analysis generated in S34.

[0077] Figure 8 is an explanatory diagram of the correspondence between direct analysis and inverse analysis according to an embodiment of the present invention. Advanced Analysis

[0078] The prospective analysis will be described.

[0079] Firstly, in Step 101 (S101), topological data analysis is performed on the material image. Specifically, the analysis Petition 870250099346, dated 10 / 30 / 2025, page 52 / 75 14 / 29 Topological data analysis is performed on material images using persistent homology to generate persistence diagrams.

[0080] Next, in Step 102 (S102), features are extracted from the results of the topological data analysis of the material images. Specifically, persistence diagrams are vectorized.

[0081] Next, in Step 103 (S103), dimensionality reduction is performed on the features. Specifically, principal component analysis is performed on the features (vectors) to create principal components.

[0082] Next, in Step 104 (S104), regression analysis is performed. Specifically, the principal components are fed into the model generated by the GMR algorithm and the material property value is generated. Inverse Analysis

[0083] The inverse analysis will be described.

[0084] Firstly, in Step 111 (S111), inverse analysis is conducted on the regression model. Specifically, an inverse analysis is conducted on a model (a model in S104 in which a material property value is generated in response to the input of principal components) generated by the GMR algorithm, and the principal components are generated in response to the input of a material property value. In the inverse analysis of Step 111, a parameter used in the regression analysis of Step 104 is employed.

[0085] Next, in Step 112 (S112), an inverse transformation of dimensionality reduction is performed. Specifically, an inverse transformation of principal component analysis (principal component analysis of features (vectors) in S103) is performed, and features (vectors) are generated from the principal components. In the inverse transformation of Step 112, the following is used Petition 870250099346, dated 10 / 30 / 2025, page 53 / 75 15 / 29 the parameter used in the principal component analysis of Step 103.

[0086] Next, in Step 113 (S113), an inverse transformation of the extraction of material features (vectors) is performed. Specifically, the inverse transformation of vectorization (vectorization of persistence diagrams in S102) is performed to generate the persistence diagrams from the material features (vectors). In the inverse transformation of Step 113, a parameter employed in the vectorization of Step 102 is used.

[0087] Next, in Step 114 (S114), a pixel that corresponds to a designated portion in the results of the topological data analysis (e.g., persistence diagrams) is displayed over an image of a different material.

[0088] Next, each process will be described in detail. As an example, a case will be described in which a dental glass-ceramic is used. The glass-ceramic can be subjected to alkaline etching (i.e., the glassy substance is dissolved) to expose the crystal grains or it can be left unprocessed. Alternatively, ionic grinding can be applied. Image Division

[0089] Firstly, the advanced analysis device (property value prediction) 10 and the learning device 20 split a SEM image. Figure 9 is an explanatory diagram of the image splitting according to an embodiment of the present invention. Figure 9 shows a SEM image before splitting on the left and the SEM images after splitting on the right.

[0090] As shown in<ANTES DA DIVISÃO> On the left in Figure 9, an unnecessary portion is removed, if present in the SEM image. Then, the SEM image is split (split into four in the example in Figure 9). Petition 870250099346, dated 10 / 30 / 2025, page 54 / 75 16 / 29

[0091] As shown in<APÓS DIVISÃO> On the right in Figure 9, a SEM image is split into a plurality of images. Excessive splitting causes loss of information contained in the image, leading to inaccurate predictions. Therefore, the image is preferably split into two to four. This image splitting can increase the training data for machine learning. Furthermore, by splitting the image, any non-homogeneities on an image of a material can be extracted using principal component analysis. Image Pre-processing

[0092] Next, the advanced analysis device (property value prediction) 10 and the learning device 20 preprocess the image. Figure 10 is an explanatory diagram of the image preprocessing according to an embodiment of the present invention.

[0093] In the present invention, a grayscale image (i.e., an original SEM image) or a binarized image (in this case, a SEM image is binarized as preprocessing) can be used. Instead of the grayscale image or the binarized image, point cloud data indicating the centroids of the crystal grains included in the image can be used (in this case, the centroids of the crystal grains included in the image are extracted to generate point cloud data as preprocessing). Topological Data Analysis (Persistent Homology)

[0094] Next, the advanced analysis device (property value prediction) 10 and the learning device 20 perform topological data analysis (persistent homology) on the image. Figure 11 is an explanatory diagram of the topological data analysis (persistent homology) according to an embodiment of the present Petition 870250099346, dated 10 / 30 / 2025, page 55 / 75 17 / 29 invention.

[0095] In one embodiment of the present invention, persistent homology is calculated for each SEM image to obtain a persistence diagram of magnitude n (for example, a 0-th magnitude persistence diagram and a 1-magnitude persistence diagram).

[0096] In this document, persistent homology will be described. Persistent homology is a type of data analysis that incorporates the concept of mathematical topology (topological data analysis) and quantitatively displays information about the shape of data based on the structure of connected components, holes, voids, or similar features of a figure. Persistence diagrams show the birth and death of topological features, such as connected components, holes, and voids, or similar features of a figure. 0th magnitude persistent homology calculates the connection between points, and 1st magnitude persistent homology calculates the proportions of loops formed by groupings of points. Thus, using persistent homology, it is possible to find the topological features of the material image. Feature Extraction (Vectorization)

[0097] Next, the advanced analysis device (property value prediction) 10 and the learning device 20 extract (vectorize) the features from the persistence diagrams. Specifically, a persistence image (PI) technique is used (e.g., Basics of Persistent Homology and Application Examples to Materials Engineering (https: / / www.jim.or.jp / journal / m / pdf3 / 58 / 01 / 17.pdf)). The persistence diagrams are sectioned in a grid pattern, and the frequency (density) of the data points in each section serves as each element of the vectors. The frequency (density) follows a distribution. Petition 870250099346, dated 10 / 30 / 2025, page 56 / 75 18 / 29 normal action.

[0098] A distribution function p is expressed by Equation (1). Dk(X) is a persistence diagram of magnitude k of X. b is the birth (i.e., the appearance of a connected component, a hole, a void or something similar of a figure), d is the death (i.e., the disappearance of the connected component, the hole, the void or something similar of the figure).

[0099] According to Equation (2), a numerical value is weighted according to the distance from the diagonal in the persistence diagram (using an arctangent function). In this way, the importance of each point in the persistence diagram can be reflected, with points further from the diagonal in the persistence diagram considered more important.

[00100] Alternatively, the diagonal distance can be calculated using an unweighted Euclidean distance.

[00101] To calculate the diagonal distance, a human must first determine whether to use Euclidean distance or apply weighting based on the arctangent function. Additionally, a human must first determine the (standard deviation), Cp, and Cp, which are parameters. As described later, to calculate the diagonal distance, Bayesian optimization can be used to determine whether to use Euclidean distance or apply weighting based on the arctangent function. Furthermore, Bayesian optimization can also be used to determine the parameters (the (standard deviation), Cp) used for material feature extraction. Mathematical Formula 1 p(x,y) = / d;;exp í-------------v' ... EQUATION (1) Mathematical Formula 2 Petition 870250099346, dated 10 / 30 / 2025, page 57 / 75 19 / 29 w(b, d) = arctan(C(d - ώ)ρ) EQUATION (2) Vector Dimensionality Reduction

[00102] Next, the advanced analysis device (property value prediction) 10 and the learning device 20 perform the dimensionality reduction of the features (vectors). Figures 12 and 13 are explanatory diagrams of the vector dimensionality reduction according to an embodiment of the present invention. As a result of extracting (vectorizing) the features from the persistence diagrams to transform a SEM image into vectors with n elements, all the data is constructed by a very large matrix of the number of elements of the vectors χ number of SEM images. In this state, it is not possible to perform feature confirmation by visualization or highly accurate prediction by machine learning. Thus, the dimensionality reduction of the features (vectors) was performed using principal component analysis.

[00103] Figure 12 shows a cumulative contribution rate. The vertical axis represents the cumulative contribution rate and the horizontal axis represents the number of principal components. As a result of reducing the dimensionality of the features (vectors), it was confirmed that the first two principal components could explain approximately 100% of the original data.

[00104] In Figure 13, the data were visualized using the first principal component (horizontal axis) and the second principal component (vertical axis). It was confirmed that each prototype / product formed a cluster present in a slightly different region on the graph, and specific information for each material could be extracted. The feature visualization unit 204 visualizes the material characteristics, showing the distribution of each material, as shown in Figure 13. Petition 870250099346, dated 10 / 30 / 2025, page 58 / 75 20 / 29 Machine Learning

[00105] Next, the learning device 20 performs machine learning using the features (vectors). Figure 14 is an explanatory diagram of machine learning according to an embodiment of the present invention.

[00106] Figure 14 shows the results of vector extraction from the persistence diagrams, dimensionality reduction through principal component analysis, and regression analysis using the GMR algorithm, with biaxial bending strength serving as the objective variable. In Figure 14, a first-magnitude persistence diagram based on the binarized image was used. The vertical axis in Figure 14 represents a predicted value (MPa) and the horizontal axis in Figure 14 represents an actual measured value (MPa).

[00107] The hyperparameters of a machine learning model can be adjusted by any optimization algorithm such as, for example, grid search, random search, Bayesian optimization or genetic algorithm. Bayesian Optimization

[00108] As described above, learning device 20 can determine whether to use Euclidean distance or weight with the arctangent function for calculating the diagonal distance described above through Bayesian optimization. Furthermore, when the arctangent function is selected, learning device 20 can determine the parameters (σ (standard deviation), C and ep in Equations (1) and (2)) used to extract material characteristics through Bayesian optimization. Additionally, learning device 20 can determine the number of principal components, which is a parameter used to extract material characteristics, through Bayesian optimization. After approximately 50 trials, the ideal combination of values ​​was found. Petition 870250099346, dated 10 / 30 / 2025, page 59 / 75 21 / 29

[00109] Specifically, an acquisition function is calculated by calculating the predicted values ​​of the property values ​​and the variation of the predicted values ​​from the material characteristics using a Gaussian process regression model. Based on this acquisition function, the optimal parameter is determined. Using a Bayesian optimization algorithm in this way, a human only needs to create and input training data so that the learning device 20 can automatically perform machine learning to generate a trained model. Analysis

[00110] Several analyses can be performed using the persistence diagrams and principal component analysis results described above.

[00111] For example, as shown in Figure 15, a point with a lifetime (i.e., a period from birth to death) greater than a given period in the persistence diagram (e.g., a portion in the upper left corner of a predetermined line in Figure 15) is considered an important point in the image. Therefore, an important crystal structure can be found by analyzing which crystal structure corresponds to a point with a lifetime greater than a given period (e.g., a portion in the upper left corner of the predetermined line in Figure 15).

[00112] For example, as shown in Figure 16, it is possible to analyze what type of crystalline structure gives rise to points that form a small cluster in a region distant from the others.

[00113] Next, the inverse analysis (i.e., the prediction of a condition for obtaining a property value of a target material) will be described in detail. Inverse Analysis of the Regression Model Petition 870250099346, dated 10 / 30 / 2025, pp. 60 / 75 22 / 29

[00114] First, the prediction unit 302 of the inverse analysis device (condition prediction) 30 performs an inverse analysis on a model to predict a material property value from the material characteristics (e.g., a model generated by the GMR algorithm) and predicts a material characteristic (main component) from the material property value.

[00115] In the inverse analysis (i.e., in the case of predicting the material characteristics (x) from the material property value (y)), a joint distribution (also called a joint probability distribution) p(y,x) is calculated using a GMM and a conditional probability distribution p(x|y) is calculated from p(y,x) using Bayes' theorem. That is, the probability distribution of the material characteristics is predicted.

[00116] Figure 17 is an explanatory diagram of the inverse analysis (inverse regression model analysis) according to an embodiment of the present invention. Figure 17 shows the results of predicting the characteristics (principal components) of the materials from the property values ​​of the materials when performing an inverse analysis in the regression model. The stars (★) indicate a weighted average (weighted mean) of the predicted characteristic (principal component) scores when the biaxial bending strength (an example of a material property value) is 300 MPa, 350 MPa, 400 MPa, 450 MPa, 500 MPa, 550 MPa, 600 MPa, 650 MPa, 700 MPa, or 750 MPa. Each of the marks from Material 1 to Material 7 indicates an actual value of the characteristic (principal component) score from Material 1 to Material 7. Inverse Transformation of Principal Component Analysis

[00117] Next, the topological data analysis unit 303 of the inverse analysis device (condition prediction) 30 conducts an inverse dimensionality reduction transformation (by Petition 870250099346, dated 10 / 30 / 2025, pp. 61 / 75 23 / 29 example, inverse transformation of principal component analysis) of the material characteristics (principal components) predicted by the prediction unit 302 and generates a characteristic (vector) from the characteristic (principal component). Inverse Vectorization Transformation

[00118] Next, the topological data analysis unit 303 of the inverse analysis device (condition prediction) 30 generates the results of the topological data analysis (e.g., persistent homology persistence diagrams) based on the features (vectors after inverse dimensionality reduction transformation) of the materials predicted by the prediction unit 302.

[00119] Figure 18 is an explanatory diagram of the inverse analysis (generation of the results of the topological data analysis) according to an embodiment of the present invention. Figure 18 shows persistence diagrams in a case where the biaxial bending strength (an example of a material property value) is 300 MPa, 400 MPa, 500 MPa or 600 MPa. Display of the pixel that corresponds to the designated portion in the results of the topological data analysis.

[00120] Next, the display unit 304 of the inverse analysis (condition prediction) device 30 displays, over an image of a material (e.g., an existing material) different from the material, a pixel that corresponds to a portion (e.g., a user-designated portion 40) designated in the topological data analysis results generated by the topological data analysis unit 303.

[00121] Figure 19 is an explanatory diagram of inverse analysis (display of a pixel corresponding to a designated portion in the results of topological data analysis on an image of a different material) according to an embodiment of the present invention. Petition 870250099346, dated 10 / 30 / 2025, page 62 / 75 24 / 29 action.

[00122] The PERSISTENCE DIAGRAM GENERATED BY INVERSE TRANSFORMATION in Figure 19 is a persistence diagram generated by the topological data analysis unit 303 of the inverse analysis device (condition prediction) 30. The user 40 designates a desired part in the persistence diagram displayed in the inverse analysis device (condition prediction) 30. For example, the user can designate a part in the persistence diagram specific to a material with high strength by designating a part of a birth and death pair that occurs only in the 700 MPa persistence diagram (i.e., a part different from other persistence diagrams of 300 MPa, 400 MPa, 500 MPa and 600 MPa).

[00123] The DIFFERENT MATERIAL PERSISTENCE DIAGRAM in Figure 19 is a persistence diagram of a different material (e.g., an existing material designated by user 40).The display unit 304 of the inverse analysis device (condition prediction) 30 identifies a part in the [DIFFERENT MATERIAL PERSISTENCE DIAGRAM] that corresponds to the part designated in the [PERSISTENCE DIAGRAM GENERATED BY INVERSE TRANSFORMATION].

[00124] The DIFFERENT MATERIAL IMAGE in Figure 19 is an image of a different material (e.g., an existing material designated by the user 40). The display unit 304 of the inverse analysis device (condition prediction) 30 clearly indicates, in the different material image, a pixel of a portion in the [DIFFERENT MATERIAL PERSISTENCE DIAGRAM] that corresponds to the portion designated in the [INVERSE TRANSFORMATION GENERATED PERSISTENCE DIAGRAM] (e.g., the pixel is displayed in a different color from that of the other pixels in the image). For example, a pixel that corresponds to the appearance (birth) Petition 870250099346, dated 10 / 30 / 2025, pp. 63 / 75 25 / 29 of a connected component, a hole, a void or similar of a figure in the persistence diagrams and a pixel corresponding to disappearance (death) can be clearly indicated separately (for example, clearly indicated in different colors, clearly indicated with different marks or similar). For example, only the pixel corresponding to appearance (birth) can be displayed, or only the pixel corresponding to disappearance (death) can be displayed, according to a user instruction 40. Not only one image of a different material, but also a plurality of images of different materials can be used.

[00125] Subsequently, user 40 can identify a structure that is assumed to be related to the appearance of a high strength or similar property value, confirming the match with the image of the different material and the structure of the different material. Effects

[00126] As described above, in one embodiment of the present invention, the user 40 can easily recognize the structure, composition, manufacturing conditions and the like of the material to perceive the property value of the target material through inverse analysis. Hardware Configuration

[00127] Figure 20 is a diagram illustrating the hardware configuration of the forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 according to an embodiment of the present invention. The forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 each include a 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 cha Petition 870250099346, dated 10 / 30 / 2025, pp. 64 / 75 26 / 29 computer. The forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 may additionally include an auxiliary storage device 1004, a display device 1005, an operating device 1006, an interface device 1007, and a drive device 1008. The forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 are interconnected via a B-bus at the hardware level. The forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 may include a graphics processing unit (GPU).

[00128] CPU 1001 is a computing device configured to run various programs installed on auxiliary storage device 1004. CPU 1001 runs a program to execute each process described in this document.

[00129] ROM 1002 is non-volatile memory. ROM 1002 functions as a primary storage device configured to store various programs, data, and similar items necessary for CPU 1001 to execute various programs installed on auxiliary storage device 1004. Specifically, ROM 1002 functions as a primary storage device configured to store boot programs and similar items for a basic input / output system (BIOS), an extensible firmware interface (EFI), and similar items.

[00130] RAM 1003 is volatile memory, such as dynamic random access memory (DRAM), static random access memory (SRAM), or similar. RAM 1003 functions as a primary storage device configured to provide an area Petition 870250099346, dated 10 / 30 / 2025, pages 65 / 75 27 / 29 of work where various programs installed on the auxiliary storage device 1004 are loaded and expanded for execution by CPU 1001.

[00131] The auxiliary storage device 1004 is an auxiliary storage device configured to store various programs and information used to run the various programs.

[00132] Display device 1005 is a display device configured to display the internal and similar states of the forward analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30.

[00133] Operational device 1006 is an input device configured for an operator of the direct analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30 to input various instructions into the direct analysis device (property value prediction) 10, the learning device 20, and the inverse analysis device (condition prediction) 30.

[00134] The 1007 interface device is a communication device configured to be connected to a network in order to communicate with other devices.

[00135] The drive device 1008 is a device configured to store and interact with a storage medium 1009. Examples of the storage medium 1009 mentioned herein include a medium that records information optically, electrically, or magnetically, such as a compact disc (-CD)-ROM, a floppy disk, a magneto-optical disk, and the like. Examples of the storage medium 1009 may include a semiconductor memory and the like configured to record information electrically, such as a ROM, a flash memory, and the like. Petition 870250099346, dated 10 / 30 / 2025, pp. 66 / 75 28 / 29

[00136] For example, the various programs installed on the auxiliary storage device 1004 are installed as follows: the drive device 1008 stores and interfaces with the distributed storage medium 1009; and the drive device 1008 reads the various programs stored on the storage medium 1009. Alternatively, the various programs installed on the auxiliary storage device 1004 can be installed by downloading from a network via the interface device 1007.

[00137] Although examples of the present invention have been described in detail above, the present invention is not limited to the specific embodiments described above, and various modifications and alterations may be made within the scope of the essence of the present invention described in the claims.

[00138] This international application claims priority based on Japanese Patent Application No. 2023-050102, filed on March 27, 2023, and the entire content of Japanese Patent Application No. 2023-050102 is incorporated herein by reference. LIST OF REFERENCE SIGNS Future analysis device (property value forecasting) Learning device Inverse analysis device (condition prediction) User 101 Image Acquisition Unit 102 Feature extraction unit 103 Forecast unit 201 Training Data Acquisition Unit 202 Feature Extraction Unit 203 Learning Unit Petition 870250099346, dated 10 / 30 / 2025, pp. 67 / 75 29 / 29 Feature display unit Optimization unit Unit of acquisition of property value Forecast unit Topological data analysis unit Display unit CPU ROM RAM Auxiliary storage device Display device Operating device Interface device Actuating device Storage medium Petition 870250099346, dated 10 / 30 / 2025, pages 68 / 75

Claims

1 / 3 CLAIMS 1. A method, characterized in that it comprises: acquiring a property value of a first material; predicting a feature of the first material based on the acquired property value of the first material by performing an inverse analysis on a model that predicts a property value of the first material based on a feature of the first material; generating a topological data analysis result based on the predicted feature of the first material; and displaying, on an image of a second material different from the first material of the acquired property value, a pixel that corresponds to a designated portion in the topological data analysis result.

2. Method, according to claim 1, characterized in that the inverse analysis is an inverse analysis using Gaussian mixture regression.

3. A method according to claim 1, characterized in that a parameter of the inverse analysis is a parameter of a model for predicting the property value of the first material from the characteristic of the first material.

4. Method, according to claim 1, characterized in that the result of the topological data analysis is a persistence diagram.

5. Method according to claim 1, characterized in that each of the first material and the second material is a ceramic, a glass-ceramic, a polymeric material, a composite resin, a glass ionomer or a metal.

6. Method according to claim 1, characterized in that the property value is the biaxial bending strength.

7. A non-transient, computer-readable storage medium characterized in that it stores instructions which, when executed, cause a computer to: acquire a property value of a first material; predict a feature of the first material based on the acquired property value of the first material by performing an inverse analysis on a model that predicts a property value of the first material based on a feature of the first material; generate a topological data analysis result based on the predicted feature of the first material; and display, on an image of a second material different from the first material of the acquired property value, a pixel that corresponds to a designated portion in the topological data analysis result.

8. Device, characterized in that it comprises: a memory; and a processor coupled to the memory, the processor being configured to: acquire a property value of a first material; predict a feature of the first material based on the acquired property value of the first material by performing an inverse analysis on a model that predicts a property value of the first material based on a feature of the first material; generate a topological data analysis result based on the predicted feature of the first material; and display, on an image of a second material different from the first material of the acquired property value, a pixel that corresponds to a designated portion in the topological data analysis result.

Images