Condition prediction method, program, and device

Abstract

And predicting the condition of obtaining the characteristic value of the target material. A method according to one embodiment of the present invention acquires a characteristic value of a material, inversely analyzes a model that predicts the characteristic value of the material from a characteristic quantity of the material, predicts the characteristic quantity of the material from the acquired characteristic value of the material, generates a topological data analysis result on the basis of the predicted characteristic quantity of the material, and generates a topological data analysis result on the basis of the topological data analysis result. And displaying, on an image of a material different from the material, a pixel corresponding to a portion specified in the topological data analysis result.

Description

Technical Field

[0001] This invention relates to a method, procedure, and apparatus for predicting conditions. Background Technology

[0002] Traditionally, materials development involved actually manufacturing materials and then evaluating their properties. The current approach, called materials informatics, uses machine learning to predict these properties.

[0003] [Existing Technical Documents]

[0004] [Patent Documents]

[0005] [Patent Document 1]

[0006] Patent No. 7188644 Summary of the Invention

[0007] [The problem the invention aims to solve]

[0008] However, in materials development, it is necessary to be able to predict the conditions under which the target material's property values ​​can be obtained. The purpose of this invention is to provide such conditions.

[0009] [Methods for solving the problem]

[0010] One embodiment of the present invention relates to a method for obtaining characteristic values ​​of a material, reverse-analyzing a model that predicts the characteristic values ​​of the material from the characteristic quantities of the material, predicting the characteristic quantities of the material from the obtained characteristic values ​​of the material, generating a topology data parsing result based on the predicted characteristic quantities of the material, and displaying pixels corresponding to the portion specified in the topology data parsing result on an image of a material different from the material.

[0011] [The effects of the invention]

[0012] In this invention, the conditions under which the target material property values ​​can be predicted are available. Attached Figure Description

[0013]

【 Figure 1 The diagram shows the overall structure of one embodiment of the present invention.

[0014]

【 Figure 2 A functional block diagram of a forward analysis (characteristic value prediction) device according to one embodiment of the present invention.

[0015]

【 Figure 3 A functional block diagram of a learning device according to one embodiment of the present invention.

[0016]

【 Figure 4A functional block diagram of a reverse analysis (conditional prediction) apparatus according to one embodiment of the present invention.

[0017]

【 Figure 5 A flowchart of a forward parsing (feature value prediction) process according to one embodiment of the present invention.

[0018]

【 Figure 6 A flowchart of a learning process according to one embodiment of the present invention.

[0019]

【 Figure 7 A flowchart of a reverse parsing (conditional prediction) process according to one embodiment of the present invention.

[0020]

【 Figure 8 [A diagram illustrating the correspondence between forward and reverse analysis in one embodiment of the present invention.]

[0021]

【 Figure 9 [A diagram illustrating image segmentation in one embodiment of the present invention.]

[0022]

【 Figure 10 [Image] is used to illustrate an embodiment of the image preprocessing involved in the present invention.

[0023]

【 Figure 11 [A diagram illustrating topology data parsing (persistent coherence) according to one embodiment of the present invention.]

[0024]

【 Figure 12 [A graph used to illustrate a vector dimensionality reduction method according to one embodiment of the present invention.]

[0025]

【 Figure 13 [A graph used to illustrate a vector dimensionality reduction method according to one embodiment of the present invention.]

[0026]

【 Figure 14 [A diagram illustrating machine learning in one embodiment of the present invention.]

[0027]

【 Figure 15 [A diagram illustrating the analysis involved in one embodiment of the present invention.]

[0028]

【 Figure 16 [A diagram illustrating the analysis involved in one embodiment of the present invention.]

[0029]

【 Figure 17 [A diagram illustrating the reverse analysis (reverse analysis of a regression model) involved in one embodiment of the present invention.]

[0030]

【 Figure 18 [A diagram illustrating reverse parsing (generation of topology data parsing results) in accordance with one embodiment of the present invention.]

[0031]

【 Figure 19 [A diagram illustrating a reverse analysis (equivalent to pixel hints on an image of another material for a portion specified in the topology data analysis result) according to one embodiment of the present invention.]

[0032]

【 Figure 20 The present invention relates to a hardware structure diagram of a forward parsing (feature value prediction) device, a learning device, and a reverse parsing (condition prediction) device according to one embodiment of the present invention. Detailed Implementation

[0033] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0034] <Explanation of Terms>

[0035] • In this specification, “material” can be any material. For example, “material” can be a medical material (e.g., dental material). For example, “material” can be any one of ceramics, glass ceramics, polymers, composite resins, glass ionomers, or metals (e.g., dental ceramics, dental glass ceramics, dental polymers, dental composite resins, dental glass ionomers, dental metals).

[0036] • In this specification, “characteristic value” can be any characteristic value. For example, “characteristic value” can be a mechanical property (e.g., biaxial bending strength, wear resistance, etc.).

[0037] <Overall Structure>

[0038] Figure 1 This is a diagram illustrating the overall structure according to one embodiment of the present invention. User 40 operates the forward analysis (feature value prediction) device 10, the learning device 20, and the reverse analysis (conditional prediction) device 30. Furthermore, Figure 1 In this document, the forward analysis (characteristic value prediction) device 10, the learning device 20, and the reverse analysis (conditional prediction) device 30 are described as separate devices, but they can actually be installed as one device.

[0039] <<Forward Analysis (Eigenvalue Prediction) Device>>

[0040] The forward analysis (property value prediction) device 10 is a device for predicting the property values ​​of materials. The forward analysis (property value prediction) device 10 consists of one or more computers. The forward analysis (property value prediction) device 10 can send and receive data with the learning device 20 and the reverse analysis (conditional prediction) device 30 through any network.

[0041] <<Learning Device>>

[0042] The learning device 20 is a device for generating a learned model used when predicting the property values ​​of materials. The learning device 20 consists of one or more computers. The learning device 20 can send and receive data with the forward analysis (property value prediction) device 10 and the reverse analysis (conditional prediction) device 30 via any network.

[0043] <<Reverse Analysis (Conditional Prediction) Device>>

[0044] The reverse analysis (conditional prediction) device 30 is a device for predicting the conditions for obtaining the property values ​​of the target material. The reverse analysis (conditional prediction) device 30 consists of one or more computers. The reverse analysis (conditional prediction) device 30 can send and receive data with the forward analysis (property value prediction) device 10 and the learning device 20 through any network.

[0045] <Function Block>

[0046] The following is for reference Figure 2 This describes the functional blocks of the forward analysis (characteristic value prediction) device 10, referring to... Figure 3 Explain the function blocks of the learning device 20, refer to Figure 4 Explain the function blocks of the reverse analysis (conditional prediction) device 30.

[0047] Figure 2 This is a functional block diagram of a forward parsing (characteristic value prediction) apparatus 10 according to one embodiment of the present invention. The forward parsing (characteristic value prediction) apparatus 10 includes an image acquisition unit 101, a feature extraction unit 102, and a prediction unit 103. Furthermore, the forward parsing (characteristic value prediction) apparatus 10 functions as the image acquisition unit 101, the feature extraction unit 102, and the prediction unit 103 by executing a program.

[0048] The image acquisition unit (or simply acquisition unit) 101 acquires an image of the material. Furthermore, the image acquisition unit 101 can segment the acquired image and use the segmented image. For example, the image is a scanning electron microscope (SEM) image.

[0049] The feature extraction unit 102 performs topological data parsing on the material image (or segmented image) acquired by the image acquisition unit 101, thereby extracting material features. For example, the topological data parsing is a persistent homology parsing. Furthermore, the feature extraction unit 102 can reduce the dimensionality of the extracted material features (e.g., principal component analysis).

[0050] The prediction unit 103 uses the learned model generated by the learning device 20 to predict the material's property values ​​based on the material's characteristic quantities.

[0051] Figure 3This is a functional block diagram of a learning device 20 according to one embodiment of the present invention. The learning device 20 includes a learning data acquisition unit 201, a feature extraction unit 202, a learning unit 203, a feature visualization unit 204, and an optimization unit 205. Furthermore, the learning device 20 functions as the learning data acquisition unit 201, the feature extraction unit 202, the learning unit 203, the feature visualization unit 204, and the optimization unit 205 by executing a program.

[0052] The learning data acquisition unit (or simply acquisition unit) 201 acquires the learning data used when generating the learned model. Specifically, the learning data acquisition unit 201 acquires images of materials and measured values ​​of the material's properties. Furthermore, the learning data acquisition unit 201 can segment the acquired images and use the segmented images. For example, the image is an SEM image.

[0053] The feature extraction unit 202 performs topological data parsing on the material image (or segmented image) acquired by the learning data acquisition unit 201, thereby extracting material features. For example, the topological data parsing is a persistent homology parsing. Furthermore, the feature extraction unit 202 can reduce the dimensionality of the extracted material features (e.g., principal component analysis).

[0054] Learning Unit 203 uses the material's characteristic quantities and measured values ​​of the material's properties to create a machine learning model, generating a fully learned model for predicting the material's property values ​​from the material's characteristic quantities.

[0055] For example, the learning section 203 uses the Gaussian Mixture Regression (GMR) algorithm, training the model parameters using the EM (expectation-maximization) algorithm. Furthermore, Gaussian Mixture Regression is a regression analysis using a Gaussian Mixture Model (GMM).

[0056] The feature visualization unit 204 visualizes the feature quantities of the material.

[0057] The optimization unit 205 determines the parameters used for extracting material features through Bayesian optimization.

[0058] Figure 4 This is a functional block diagram of a reverse analysis (conditional prediction) apparatus 30 according to one embodiment of the present invention. The reverse analysis (conditional prediction) apparatus 30 includes a characteristic value acquisition unit 301, a prediction unit 302, a topology data parsing unit 303, and a prompting unit 304. Furthermore, the reverse analysis (conditional prediction) apparatus 30 functions as the characteristic value acquisition unit 301, the prediction unit 302, the topology data parsing unit 303, and the prompting unit 304 by executing a program.

[0059] The characteristic value acquisition unit (or simply acquisition unit) 301 acquires the characteristic values ​​of the material (e.g., the characteristic values ​​of the target material input by the user 40 to the reverse analysis (conditional prediction) device 30).

[0060] The prediction unit 302 uses the reverse analysis learning device 20 to generate a model that predicts the material's characteristic values ​​from its characteristic quantities (e.g., a model generated by the GMR algorithm), and the characteristic value acquisition unit 301 acquires the material's characteristic values ​​to predict the material's characteristic quantities. The parameters for reverse analysis are the model parameters for predicting the material's characteristic values ​​from its characteristic quantities.

[0061] Gaussian Mixture Regression

[0062] This section explains GMR. As mentioned above, GMR is a regression analysis using GMM, which represents the relationship between explanatory variables and the target variable as a superposition of multiple normal distributions. GMR is a regression analysis that can be reversed.

[0063] In GMR, in a model that predicts the material's property values ​​(denoted as y) from its characteristic quantities (let's call them x), the joint distribution (also called the joint probability distribution) is calculated by the GMM: p(x,y), and the conditional probability distribution is calculated by p(x,y) and Bayes' theorem: p(y|x). That is, the probability distribution for predicting the material's property values.

[0064] On the other hand, in reverse analysis (i.e., predicting the material's characteristic quantity (x) from its property value (y), the joint distribution (also called the joint probability distribution) is calculated by the GMM: p(y,x), and the conditional probability distribution is calculated by p(y,x) and Bayes' theorem: p(x|y). That is, the probability distribution for predicting the material's characteristic quantity.

[0065] The topology data parsing unit 303 generates topology data parsing results based on the material feature quantities predicted by the prediction unit 302. For example, the topology data parsing unit 303 generates a persistence graph through persistence coherence parsing based on the material feature quantities predicted by the prediction unit 302.

[0066] Furthermore, the topology data parsing unit 303 can generate topology data parsing results based on the inverse dimensionality reduction transformation (e.g., the inverse transformation of principal component analysis) performed on the material characteristic quantities predicted by the prediction unit 302.

[0067] The prompting unit 304 displays pixels on an image of a material different from the material itself (e.g., an existing material), corresponding to the portion specified in the topology data parsing result generated by the topology data parsing unit 303 (e.g., the portion specified by the user 40). For example, the image is an SEM image.

[0068] <Processing Method>

[0069] The following is for reference Figure 5 Explanation of forward analysis (characteristic value prediction) processing, refer to... Figure 6 Explanation of learning and processing, refer to Figure 7 Explain the reverse parsing (conditional prediction) process.

[0070] Figure 5 This is a flowchart of a forward parsing (feature value prediction) process according to one embodiment of the present invention.

[0071] In step 11 (S11), the image acquisition unit 101 of the forward analysis (characteristic value prediction) device 10 acquires an image of the material.

[0072] In step 12 (S12), the image acquisition unit 101 of the forward parsing (characteristic value prediction) device 10 segments the image acquired in S11. Furthermore, S12 can be omitted.

[0073] In step 13 (S13), the feature extraction unit 102 of the forward analysis (characteristic value prediction) device 10 performs topological data analysis on the material image obtained in S11 or the segmented image in S12, thereby extracting the feature quantities of the material.

[0074] In step 14 (S14), the feature extraction unit 102 of the forward analysis (characteristic value prediction) device 10 reduces the dimensionality of the material feature quantities extracted in S13 (e.g., principal component analysis). Furthermore, S14 can be omitted.

[0075] In step 15 (S15), the prediction unit 103 of the forward analysis (characteristic value prediction) device 10 uses the learned model generated by the learning device 20 to predict the characteristic value of the material from the material feature quantities extracted in S13 or the material feature quantities reduced in S14.

[0076] In step 16 (S16), the prediction unit 103 of the forward analysis (characteristic value prediction) device 10 prompts the user 40 with the prediction result of S15 (for example, displayed on an image).

[0077] Figure 6 This is a flowchart of a learning process according to one embodiment of the present invention.

[0078] In step 21 (S21), the learning data acquisition unit 201 of the learning device 20 acquires the learning data used when generating the learned model. Specifically, the learning data acquisition unit 201 acquires an image of the material and measured values ​​of the material's properties.

[0079] In step 22 (S22), the learning data acquisition unit 201 of the learning device 20 segments the image acquired in S21. Furthermore, S22 can be omitted.

[0080] In step 23 (S23), the optimization unit 205 of the learning device 20 determines the parameters used for extracting material feature quantities. For example, the optimization unit 205 of the learning device 20 determines the parameters used for extracting material feature quantities through Bayesian optimization.

[0081] In step 24 (S24), the feature extraction unit 202 of the learning device 20 performs topological data parsing on the material image acquired in S21 or the segmented image in S22, thereby extracting the material features.

[0082] 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). Furthermore, S25 can be omitted.

[0083] In step 26 (S26), the feature quantity visualization unit 204 of the learning device 20 visualizes the feature quantities of the material.

[0084] In step 27 (S27), the learning unit 203 of the learning device 20 performs machine learning using the measured values ​​of the material's characteristic quantities and material property values ​​to generate a learned model for predicting material property values ​​from the material's characteristic quantities.

[0085] Figure 7 This is a flowchart of a reverse parsing (conditional prediction) process according to one embodiment of the present invention.

[0086] In step 31 (S31), the characteristic value acquisition unit 301 of the reverse analysis (conditional prediction) device 30 acquires the characteristic value of the material.

[0087] In step 32 (S32), the prediction unit 302 of the reverse analysis (conditional prediction) device 30 reverse analyzes the model that predicts the characteristic value of the material from the characteristic quantity of the material, and predicts the characteristic quantity of the material from the material characteristic value obtained in S31.

[0088] In step 33 (S33), the topology data parsing unit 303 of the inverse analysis (conditional prediction) device 30 performs an inverse dimensionality reduction transformation (e.g., inverse transformation of principal component analysis) on the material characteristic quantities predicted in S32. Furthermore, S33 can be omitted.

[0089] In step 34 (S34), the topology data parsing unit 303 of the reverse parsing (conditional prediction) device 30 generates a topology data parsing result based on the material feature quantity predicted in S32 or the material feature quantity that has undergone inverse dimensionality reduction transformation in S33.

[0090] In step 35 (S35), the prompting unit 304 of the reverse analysis (conditional prediction) device 30 displays pixels on the image of another material that correspond to the portion specified in the topology data analysis result generated in S34.

[0091] Figure 8 This is a diagram illustrating the correspondence between forward and reverse analysis in one embodiment of the present invention.

[0092] <Forward Analysis>

[0093] This illustrates positive parsing.

[0094] First, in step 101 (S101), topological data parsing of the material image is performed. Specifically, the material image is parsed using persistent coherence to generate a persistence graph.

[0095] Next, in step 102 (S102), feature quantities are extracted from the topological data parsing results of the material image. Specifically, the persistence graph is vectorized.

[0096] Next, in step 103 (S103), dimensionality reduction of the feature quantities is performed. Specifically, principal component analysis of the feature quantities (vectors) is performed to generate principal components.

[0097] Next, in step 104 (S104), regression analysis is performed. Specifically, principal components are input into the model generated by the GMR algorithm, and the material property values ​​are output.

[0098] <Reverse Analysis>

[0099] This explains reverse engineering.

[0100] First, in step 111 (S111), the inverse analysis of the regression model is performed. Specifically, the inverse analysis of the model generated by the GMR algorithm (the model that outputs material property values ​​when the principal components of S104 are input) is performed, and the principal components are output when the material property values ​​are input. In this inverse analysis of step 111, the parameters used in the regression analysis of step 104 are used.

[0101] Next, in step 112 (S112), an inverse dimensionality reduction transformation is performed. Specifically, an inverse transformation of principal component analysis (principal component analysis of the feature quantities (vectors) in S103) is performed to generate feature quantities (vectors) from the principal components. In this inverse transformation of step 112, the parameters used in the principal component analysis in step 103 are used.

[0102] Next, in step 113 (S113), an inverse transformation for extracting the material's feature quantities (vectors) is performed. Specifically, an inverse transformation of vectorization (vectorization of the persistence graph in S102) is performed to generate a persistence graph from the material's feature quantities (vectors). In this inverse transformation of step 113, the parameters used in the vectorization in step 102 are employed.

[0103] Next, in step 114 (S114), pixels corresponding to the portion specified in the topology data parsing result (e.g., persistence map) are displayed on the image of other materials.

[0104] The following details each process. As an example, the use of dental glass-ceramics will be explained. Furthermore, the glass-ceramics can be etched with alkaline etching (i.e., dissolving the vitreous material) to expose the crystalline grains, or they can be left unprocessed. Additionally, ion milling-based processing can be performed.

[0105] Image Segmentation

[0106] First, the forward parsing (characteristic value prediction) device 10 and the learning device 20 segment the SEM image. Figure 9 This is a diagram illustrating image segmentation in one embodiment of the present invention. Figure 9 The left side represents the SEM image before segmentation. Figure 9 The right side represents the segmented SEM image.

[0107] like Figure 9 As shown on the left side of the image (before segmentation), if there are unwanted parts in the SEM image, those unwanted parts are cut off. Then the SEM image is segmented. Figure 9 In the example, it is divided into 4 parts.

[0108] like Figure 9 As shown in the "Segmented" section on the right, one SEM image is segmented into multiple images. Furthermore, over-segmentation leads to information loss and decreased prediction accuracy; therefore, 2 to 4 segmentations are preferred. This image segmentation increases the amount of learning data available for machine learning. Additionally, when non-uniform areas are found within the image of a particular material, principal component analysis can be used for extraction.

[0109] <<Image Preprocessing>>

[0110] Next, the forward analysis (characteristic value prediction) device 10 and the learning device 20 preprocess the image. Figure 10 This is a diagram illustrating image preprocessing involved in one embodiment of the present invention.

[0111] In this invention, grayscale images (i.e., the original SEM image) or binarized images can be used (in this case, the SEM image is binarized as a preprocessing step). In addition to grayscale images and binarized images, point cloud data representing the centroids of the crystal grains contained in the image can also be used (in this case, the centroids of the crystal grains contained in the image are extracted as a preprocessing step to generate point cloud data).

[0112] <<Topology Data Parsing (Persistent Homology)>>

[0113] Next, the forward parsing (feature value prediction) device 10 and the learning device 20 perform topological data parsing (persistent coherence) of the image. Figure 11 This is a diagram illustrating topology data parsing (persistent coherence) in one embodiment of the present invention.

[0114] In one embodiment of the present invention, the persistence coherence of each SEM image is calculated to obtain an n-dimensional persistence map (e.g., a 0-dimensional persistence map and a 1-dimensional persistence map).

[0115] This section explains persistent coherence. Persistent coherence is a type of data analysis (topological data analysis) that uses mathematical topological concepts to quantitatively display information about the data's morphology based on the structure of connections, holes, voids, etc., in a graph. In a persistence graph, the birth and death of connections, holes, voids, etc., are displayed. 0-dimensional persistent coherence calculates the connections between points, while 1-dimensional persistent coherence calculates the relationships between loops formed by sets of points. Thus, by using persistent coherence, the topological features of a material image can be identified.

[0116] <<Feature Extraction (Vectorization)>>

[0117] Next, the forward analytical (characteristic value prediction) device 10 and the learning device 20 extract feature quantities (vectorization) from the persistence map. Specifically, the PI (Persistence Image) technique is used (e.g., "Fundamentals of Persistent Homogeneity and Applicability in Materials Engineering (https: / / www.jim.or.jp / journal / m / pdf3 / 58 / 01 / 17.pdf)"). The persistence map is divided into a grid, and the frequency (density) of the data points in each region is used as the elements of the vector. The frequency (density) is assumed to follow a normal distribution.

[0118] The distribution function ρ is shown in equation (1). Dk(X) is the k-dimensional persistence graph of X, b is birth (i.e., the generation of connecting parts, holes, gaps, etc. of the graph), and d is death (i.e., the elimination of connecting parts, holes, gaps, etc. of the graph).

[0119] Equation (2) uses the arctangent function to weight the values ​​based on their distance from the diagonal of the persistence graph. This reflects the importance of each point on the persistence graph (and the further away from the diagonal of the persistence graph, the higher the importance).

[0120] In addition, the distance from the diagonal can be calculated using unweighted Euclidean distance.

[0121] Whether to use Euclidean distance or arctangent weighting for calculating the distance from the diagonal, along with parameters such as σ (standard deviation), C, and p, needs to be decided beforehand. As discussed later, whether to use Euclidean distance or arctangent weighting for calculating the distance from the diagonal, and the parameters (σ (standard deviation), C, p) used for extracting material characteristics, can be determined through Bayesian optimization.

[0122]

Number 1

[0123]

[0124]

Number 2

[0125] w(b, d) = arctan(C(db)) p ...Equation (2)

[0126] <<Vector Dimensionality Reduction>>

[0127] Next, the forward parsing (feature value prediction) device 10 and the learning device 20 reduce the dimensionality of the feature quantity (vector). Figure 12 and Figure 13 This is a diagram illustrating vector dimensionality reduction in one embodiment of the present invention. When extracting (vectorizing) features from a persistent graph, transforming a single SEM image into a vector with n elements results in a massive matrix consisting of the number of vector elements multiplied by the number of SEM image slices. This makes feature-based visualization and high-precision machine learning-based prediction impossible; therefore, principal component analysis is used to reduce the dimensionality of the feature vectors.

[0128] Figure 12 The cumulative contribution rate is displayed on the vertical axis, and the number of principal components is displayed on the horizontal axis. Dimensionality reduction of the feature vectors confirms that by the second principal component, almost 100% of the original data can be explained.

[0129] Figure 13 In the diagram, the data is visualized using the first principal component (horizontal axis) and the second principal component (vertical axis). It can be confirmed that each sample / product clusters together and exists in slightly different areas on the chart, allowing for the extraction of information specific to each material. The feature visualization unit 204 displays, for example... Figure 13 The distribution of each material is visualized, and the characteristic quantities of the materials are visualized.

[0130] Machine Learning

[0131] Next, the learning device 20 uses feature vectors to perform machine learning. Figure 14 This is a diagram illustrating machine learning in one embodiment of the present invention.

[0132] Figure 14 The results show the results of a GMR-based regression analysis with biaxial bending strength as the objective variable, performed after extracting vectors from the durability graph, using principal component analysis for dimensionality reduction. Furthermore, Figure 14 In this context, a 1-dimensional persistent graph is used to represent the binarized image. Figure 14 The vertical axis represents the predicted value (MPa). Figure 14 The horizontal axis represents the measured value (MPa).

[0133] Furthermore, the hyperparameters of machine learning models can be tuned using any optimization algorithm, such as grid search, random search, Bayesian optimization, and genetic algorithms.

[0134] Bayesian Optimization

[0135] As described above, the learning device 20 can be determined through Bayesian optimization, and the calculation of the distance from the diagonal uses Euclidean distance or weighted by the arctangent function. Furthermore, when selecting the arctangent function, the learning device 20 can determine the parameters used for material feature extraction (σ (standard deviation), C, p in equations (1) and (2)) through Bayesian optimization. Furthermore, the learning device 20 can determine the number of principal components used as parameters for material feature extraction through Bayesian optimization. In addition, after approximately 50 trials, the optimal combination of values ​​is found.

[0136] Specifically, a Gaussian process regression model is used to calculate the predicted values ​​of the material's characteristic values ​​and the deviations from these predicted values, thereby calculating the acquisition function. Based on this acquisition function, the optimal parameters are determined. Thus, by combining a Bayesian optimization algorithm, the learning device 20 can automatically perform machine learning and generate a learned model using only human-made and input learning data.

[0137] <<Analysis>>

[0138] Various analyses can be performed using the persistence plot and principal component analysis results described above.

[0139] For example, such as Figure 15 Points on the persistence graph that have a lifetime longer than a certain period (i.e., the period from birth to death) (e.g., Figure 15The upper left portion of the designated line is assumed to be an important point on the image. Therefore, by analyzing points with a lifespan longer than a certain period (e.g., ...), Figure 15 The upper left part of the specified line corresponds to which structure of the crystal, and the important structure of the crystal can be found.

[0140] For example, such as Figure 16 It can be analyzed what crystal structure the points that form small clusters in areas far from other parts originate from.

[0141] The following details reverse analysis (i.e., the prediction of the conditions for obtaining the target material property values).

[0142] <<Inverse Analysis of Regression Models>>

[0143] First, the prediction unit 302 of the reverse analysis (conditional prediction) device 30 reverse analyzes the model that predicts the characteristic value of the material from the characteristic quantity of the material (e.g., the model generated by the GMR algorithm), and predicts the characteristic quantity (principal component) of the material from the characteristic value of the material.

[0144] In reverse analysis (i.e., predicting the material's characteristic quantity (x) from its property value (y), the joint distribution (also called the joint probability distribution) is calculated by the GMM: p(y,x), and the conditional probability distribution is calculated by p(y,x) and Bayes' theorem: p(x|y). That is, the probability distribution for predicting the material's characteristic quantity.

[0145] Figure 17 This is a diagram illustrating the reverse analysis (reverse analysis of a regression model) involved in one embodiment of the present invention. Figure 17 This displays the results of the inverse analytical regression model, predicting the material's characteristic quantities (principal components) from its property values. The star-shaped markers (★) show the weighted average of the predicted characteristic quantity (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, and 750 MPa. Furthermore, the markers for materials 1 through 7 show the actual values ​​of the characteristic quantity (principal component) scores for materials 1 through 7.

[0146] Inverse Transformation of Principal Component Analysis

[0147] Next, the topology data parsing unit 303 of the inverse analysis (conditional prediction) device 30 performs an inverse dimension reduction transformation (e.g., inverse transformation of principal component analysis) on the material characteristic quantities (principal components) predicted by the prediction unit 302, and generates characteristic quantities (vectors) from the characteristic quantities (principal components).

[0148] <<Vectorized Inverse Transform>>

[0149] Next, the topology data parsing unit 303 of the inverse parsing (conditional prediction) device 30 generates topology data parsing results (e.g., a persistence graph of persistence coherence) based on the material feature quantities (vectors that have undergone inverse dimension reduction transformation) predicted by the prediction unit 302.

[0150] Figure 18 This is a diagram illustrating a reverse parsing (generation of topology data parsing results) involved in one embodiment of the present invention. Figure 18 This shows the durability graphs when the biaxial bending strength (an example of a material property value) is 300 MPa, 400 MPa, 500 MPa, and 600 MPa.

[0151] <<Equivalent to a hint about the specified portion of pixels in the topology data parsing result>>

[0152] Next, the prompting unit 304 of the reverse analysis (conditional prediction) device 30 displays on the image of a material different from the material (e.g., an existing material) the pixels corresponding to the portion specified in the topology data analysis result generated by the topology data analysis unit 303 (e.g., the portion specified by the user 40).

[0153] Figure 19 This is a diagram illustrating a reverse analysis (a hint of pixels on an image of another material, corresponding to a portion specified in the topological data analysis result) involving one embodiment of the present invention.

[0154] Figure 19 The [persistence map generated by inverse transformation] is a persistence map generated by the topology data parsing unit 303 of the inverse analysis (conditional prediction) device 30. The user 40 specifies the desired portion on the persistence map displayed by the inverse analysis (conditional prediction) device 30. For example, the user specifies only the paired portions of Birth and Death generated in the persistence map of 700 MPa (i.e., portions different from other persistence maps such as 300 MPa, 400 MPa, 500 MPa, 600 MPa), thereby specifying portions on the persistence map specific to high-strength materials.

[0155] Figure 19 The [Persistence Map of Other Materials] is a persistence map of other materials (e.g., an existing material specified by user 40). The prompting unit 304 of the reverse analysis (conditional prediction) device 30 determines the portion on the [Persistence Map of Other Materials] corresponding to the portion specified in the [Persistence Map Generated by Inverse Transformation].

[0156] Figure 19The [image of other materials] is an image of other materials (e.g., an existing material specified by user 40). The prompting unit 304 of the reverse analysis (conditional prediction) device 30 displays on the image of other materials the pixels of the portion on the [persistence map of other materials] corresponding to the portion specified in the [persistence map generated by inverse transformation] (e.g., the pixel is represented on the image with a different color than other pixels). For example, pixels representing the birth of the connection portion, hole, gap, etc., corresponding to the graphics of the persistence map, and pixels representing the death can be displayed separately (e.g., each is displayed with a different color, each is displayed with a different mark, etc.). For example, according to the instruction from user 40, only pixels corresponding to the birth can be displayed, or only pixels corresponding to the death can be displayed. Furthermore, not only one image of a single material, but also multiple images of other materials can be used.

[0157] Then, by confirming the correspondence between the image of another material and the structure of that other material, user 40 can find the structure that is related to the discovery of properties such as high strength.

[0158] <Effect>

[0159] Thus, in one embodiment of the present invention, the user 40 can easily learn, through reverse analysis, the structure, composition, manufacturing conditions, etc. of the material used to achieve the target material property value.

[0160] <Hardware Structure>

[0161] Figure 20 This diagram illustrates the hardware structure of a forward parsing (feature value prediction) device 10, a learning device 20, and a reverse parsing (conditional prediction) device 30 according to one embodiment of the present invention. The forward parsing (feature value prediction) device 10, the learning device 20, and the reverse parsing (conditional prediction) device 30 include a CPU (Central Processing Unit) 1001, a ROM (Read-Only Memory) 1002, and a RAM (Random Access Memory) 1003. The CPU 1001, ROM 1002, and RAM 1003 form a so-called computer. Furthermore, the forward parsing (feature value prediction) device 10, the learning device 20, and the reverse parsing (conditional prediction) device 30 may include an auxiliary storage device 1004, a display device 1005, an operation device 1006, an I / F (interface) device 1007, and a drive device 1008. Moreover, the hardware components of the forward parsing (feature value prediction) device 10, the learning device 20, and the reverse parsing (conditional prediction) device 30 are interconnected via a bus B. Furthermore, the forward parsing (feature value prediction) device 10, the learning device 20, and the reverse parsing (conditional prediction) device 30 are equipped with GPUs (graphics processing units).

[0162] CPU 1001 is a computing device that executes various programs installed in auxiliary storage device 1004. CPU 1001 performs the various processes described in this specification by executing programs.

[0163] ROM1002 is a non-volatile memory. ROM1002 functions as a main storage device, storing various programs and data required for CPU1001 to execute various programs installed in auxiliary storage device 1004. Specifically, ROM1002 functions as a main storage device storing boot programs such as BIOS (Basic Input / Output System) and EFI (Extensible Firmware Interface).

[0164] RAM1003 is a volatile memory such as DRAM (Dynamic Random Access Memory) or SRAM (Static Random Access Memory). RAM1003 functions as the main storage device, providing the operating area for various programs installed on the auxiliary storage device 1004 when executed by the CPU 1001.

[0165] Auxiliary storage device 1004 is an auxiliary storage device for storing various programs and information used when executing various programs.

[0166] Display device 1005 is a display device that displays the internal states of forward analysis (characteristic value prediction) device 10, learning device 20, and reverse analysis (conditional prediction) device 30.

[0167] The operating device 1006 is an input device for the operator of the forward analysis (characteristic value prediction) device 10, learning device 20, and reverse analysis (condition prediction) device 30 to input various instructions to the forward analysis (characteristic value prediction) device 10, learning device 20, and reverse analysis (condition prediction) device 30.

[0168] I / F device 1007 is a communication device used to connect to a network and communicate with other devices.

[0169] The drive device 1008 is a device for setting the storage medium 1009. The storage medium 1009 described herein includes media such as CD-ROMs, floppy disks, and magneto-optical disks, which record information optically, electrically, or magnetically. Furthermore, the storage medium 1009 may include semiconductor memory such as ROMs or flash memory, which record information electrically.

[0170] Furthermore, various programs installed on the auxiliary storage device 1004 can be installed, for example, by placing a distributed storage medium 1009 on the drive device 1008, and reading the various programs recorded on the storage medium 1009 via the drive device 1008. Alternatively, various programs installed on the auxiliary storage device 1004 can be downloaded from a network via the I / F device 1007.

[0171] The embodiments of the present invention have been described in detail above, but the present invention is not limited to the specific embodiments described above. Various modifications and alterations can be made within the scope of the spirit of the present invention as described in the patent claims.

[0172] This international application claims priority based on Japanese Patent Application No. 2023-050102, filed on March 27, 2023, the entire contents of which are incorporated herein by reference.

[0173] [Attached image labels]

[0174] 10 Forward Analysis (Characteristic Value Prediction) Device

[0175] 20 learning devices

[0176] 30 Reverse Analysis (Conditional Prediction) Device

[0177] 40 users

[0178] 101 Image Acquisition Department

[0179] 102 Feature Extraction Section

[0180] 103 Forecasting Department

[0181] 201 Learning Data Acquisition Department

[0182] 202 Feature Extraction Section

[0183] 203 Study Department

[0184] 204 Feature Visualization Section

[0185] 205 Optimization Department

[0186] 301 Characteristic Value Acquisition Department

[0187] 302 Forecasting Department

[0188] 303 Topology Data Parsing Department

[0189] 304 Notification Department

[0190] 1001CPU

[0191] 1002ROM

[0192] 1003 RAM

[0193] 1004 Auxiliary storage device

[0194] 1005 Display Device

[0195] 1006 Operating Device

[0196] 1007I / F device

[0197] 1008 drive unit

[0198] 1009 Storage Media

Claims

1. A method, Obtain the material's property values. The model for predicting the material's characteristic values ​​from its characteristic quantities is analyzed in reverse; the characteristic quantities of the material are predicted from the obtained characteristic values ​​of the material. Based on the predicted characteristic quantities of the material, topological data parsing results are generated. On an image of a material different from the stated material, pixels corresponding to the portion specified in the topology data parsing result are displayed.

2. The method according to claim 1, wherein the reverse analysis is based on Gaussian mixture regression.

3. The method according to claim 1, wherein the parameters of the reverse analysis are the parameters of the model that predicts the characteristic values ​​of the material from the characteristic quantities of the material.

4. The method according to claim 1, wherein the topology data parsing result is a persistent graph.

5. The method according to any one of claims 1 to 4, wherein the material is any one of ceramics, glass ceramics, polymer materials, composite resins, glass ionomers, and metals.

6. The method according to any one of claims 1 to 4, wherein the characteristic value is biaxial bending strength.

7. A program for causing a computer to execute: The steps to obtain the property values ​​of a material. The reverse engineering process involves reversing the model to predict the material's characteristic values ​​from its characteristic quantities, and using the obtained characteristic values ​​of the material to predict its characteristic quantities. The step of generating topological data parsing results based on the predicted characteristic quantities of the material. The step of displaying pixels corresponding to the portion specified in the topology data parsing result on an image of a material different from the material stated therein.

8. An apparatus comprising: The acquisition department acquires the property values ​​of the materials. The prediction unit reverse-engineers a model that predicts the material's characteristic values ​​from its characteristic quantities, and predicts the material's characteristic quantities from the acquired characteristic values. A topology data parsing unit generates topology data parsing results based on the predicted characteristic quantities of the material, and The prompt section displays pixels corresponding to the portion specified in the topology data parsing result on an image of a material different from the material stated therein.

Images