Information processing method, information processing device, and program

Abstract

This invention provides a mathematical model for predicting material properties, and offers techniques for obtaining highly interpretable mathematical models. [Solution] The information processing device 10 includes a formula generation unit 130. The formula generation unit 130 generates a first formula and a second formula. The first formula is a formula that shows the relationship between a first group of explanatory variables and a first target variable. The second formula is a formula that shows the relationship between a second group of explanatory variables and a second target variable. The second group of explanatory variables includes the first target variable. One or more variables included in the first group of explanatory variables and one or more variables included in the second group of explanatory variables are variables relating to physical properties. The second target variable is a variable relating to physical properties on a larger scale than the first target variable.

Description

Technical Field

[0001] The present invention relates to an information processing method, an information processing apparatus, and a program.

Background Art

[0002] In material design, attempts have been made to predict the properties of materials obtained from a plurality of raw materials.

[0003] Patent Document 1 describes symbolic regression based on genetic programming. It is described that symbolic regression can obtain a mathematical equation that gives the value of a dependent variable based on the input values of one or more independent variables.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, when trying to obtain a mathematical formula for obtaining parameters related to macroscale physical properties from parameters related to nanoscale physical properties, etc., the generation of the mathematical formula may not succeed well, or even if obtained, the interpretability of the mathematical formula may be low.

[0006] One aspect of the present invention provides a technique for obtaining a mathematical model for predicting material properties and having high interpretability.

Means for Solving the Problems

[0007] According to one form of the present invention, the following information processing method, information processing apparatus, and program are provided.

[0008] (1) An information processing method performed by one or more computers, A first equation generation step generates a first equation that shows the relationship between the first group of explanatory variables and the first dependent variable, The process includes a second equation generation step of generating a second equation that shows the relationship between the second group of explanatory variables, including the first dependent variable, and the second dependent variable, The first group of explanatory variables and the second group of explanatory variables each contain one or more variables relating to physical properties. The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. Information processing methods. (2) In the information processing method described in (1), The first objective variable is a variable relating to at least one of the following: within a particle, between particles, in a particle aggregate, and in a substance containing particles. Information processing methods. (3) In the information processing method described in (1), The first objective variable described above is a variable relating to particles, The second objective variable is a variable relating to the substance containing the particles. Information processing methods. (4) In the information processing method described in (1), The first objective variable described above is a variable relating to particles, The second objective variable is a variable relating to the set of particles. Information processing methods. (5) In the information processing method described in (1), The first objective variable is a variable relating to a first object containing one or more particles, The second objective variable is a variable relating to the second object which contains more of the particles than the first object. Information processing methods. (6) In the information processing method described in any one of (2) to (5), The particles are atoms, molecules, or solid particles. Information processing methods. (7) In the information processing method described in any one of (1) to (6), In the first mathematical formula generation step, the first mathematical formula is generated by symbolic regression, and in the second mathematical formula generation step, the second mathematical formula is generated by symbolic regression. Information processing method. (8) In the information processing method according to any one of (1) to (7), the method further includes an integration step of generating an integrated mathematical formula using the first mathematical formula and the second mathematical formula. Information processing method. (9) In the information processing method according to any one of (1) to (8), the method further includes a third mathematical formula generation step of generating a third mathematical formula indicating the relationship between a third explanatory variable group including the second target variable and a third target variable, one or more variables included in the third explanatory variable group are variables related to physical properties, and the third target variable is a variable related to physical properties on a scale larger than either the first target variable or the second target variable. Information processing method. (10) An information processing apparatus including a mathematical formula generation unit that generates a first mathematical formula indicating the relationship between a first explanatory variable group and a first target variable, and a second mathematical formula indicating the relationship between a second explanatory variable group including the first target variable and a second target variable, where one or more variables included in the first explanatory variable group and one or more variables included in the second explanatory variable group are variables related to physical properties, and the second target variable is a variable related to physical properties on a scale larger than the first target variable. Information processing apparatus. (11) A program that causes a computer to function as a mathematical formula generation means for generating a first mathematical formula indicating the relationship between a first explanatory variable group and a first target variable, and a second mathematical formula indicating the relationship between a second explanatory variable group including the first target variable and a second target variable, where one or more variables included in the first explanatory variable group and one or more variables included in the second explanatory variable group are variables related to physical properties, and the second target variable is a variable related to physical properties on a scale larger than the first target variable. Program.

Advantages of the Invention

[0009] According to one aspect of the present invention, a mathematical model for predicting material properties can provide a technique for obtaining a highly interpretable mathematical model.

Brief Description of the Drawings

[0010] [Figure 1] It is a diagram showing an overview of an information processing apparatus according to the first embodiment. [Figure 2] It is a diagram showing an overview of an information processing method according to the first embodiment. [Figure 3] It is a diagram for explaining the concept of an information processing method according to the first embodiment. [Figure 4] It is a diagram exemplifying the functional configuration of an information processing apparatus according to the first embodiment. [Figure 5] It is a diagram exemplifying the flow of processing executed by an information processing apparatus according to the first embodiment. [Figure 6] It is a diagram for explaining the first mathematical formula generation step. [Figure 7] It is a diagram for explaining the second mathematical formula generation step. [Figure 8] It is a diagram exemplifying a computer for realizing an information processing apparatus. [Figure 9] It is a diagram exemplifying the flow of processing executed by an information processing apparatus according to the second embodiment. [Figure 10] It is a diagram exemplifying the functional configuration of an information processing apparatus according to the third embodiment. [Figure 11] It is a diagram exemplifying the flow of processing executed by an information processing apparatus according to the third embodiment.

Modes for Carrying Out the Invention

[0011] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In all the drawings, the same components are denoted by the same reference numerals, and the description thereof will be omitted as appropriate.

[0012] (First Embodiment) Figure 1 is a diagram showing an overview of an information processing device 10 according to the first embodiment. The information processing device 10 includes a formula generation unit 130. The formula generation unit 130 generates a first formula and a second formula. The first formula is a formula that shows the relationship between a first group of explanatory variables and a first target variable. The second formula is a formula that shows the relationship between a second group of explanatory variables and a second target variable. The second group of explanatory variables includes the first target variable. One or more variables included in the first group of explanatory variables and one or more variables included in the second group of explanatory variables are variables relating to physical properties. The second target variable is a variable relating to physical properties on a larger scale than the first target variable.

[0013] Figure 2 is a diagram illustrating an overview of the information processing method according to the first embodiment. The information processing method according to this embodiment is executed by one or more computers. The information processing method according to this embodiment includes a first formula generation step S10 and a second formula generation step S20. In the first formula generation step S10, one or more computers generate a first formula. The first formula is a formula that shows the relationship between a first group of explanatory variables and a first target variable. In the second formula generation step S20, one or more computers generate a second formula. The second formula is a formula that shows the relationship between a second group of explanatory variables and a second target variable. The second group of explanatory variables includes the first target variable. One or more variables included in the first group of explanatory variables and one or more variables included in the second group of explanatory variables are variables relating to physical properties. The second target variable is a variable relating to physical properties on a larger scale than the first target variable.

[0014] When attempting to obtain a desired material using multiple raw materials, the state, phenomena, and structure at multiple scales, from nanoscale to macroscale, are crucial for the manifestation of the material's properties. On the other hand, when attempting to directly obtain mathematical formulas that show the relationships between physical properties at vastly different scales, multiple complexly related elements are combined into a single formula, which can lead to calculation failures and the inability to obtain a practical mathematical model. Furthermore, even if a mathematical model is obtained, there is a problem in that the interpretability of the formula is low, making it difficult to obtain design insights that can be applied in various ways.

[0015] In contrast, the information processing apparatus 10 and information processing method according to this embodiment divide the relationships between physical properties into multiple mathematical formulas, that is, perform hierarchical modeling, thereby obtaining a highly interpretable mathematical model and improving prediction accuracy.

[0016] Figure 3 is a diagram illustrating the concept of the information processing method according to this embodiment. However, the formulas shown in Figure 3 are illustrative, and the formulas generated by the information processing device 10 according to this embodiment are not limited to these examples. Figure 3 shows formulas (1) to (4). The meanings of the symbols used in these formulas are as follows. k bond : Intermolecular bonding stiffness C: coefficient ε: Depth of the bond energy σ: Constant indicating the equilibrium distance between molecules E micro Effective modulus of elasticity at the microscale η: Number of valid bonds V a :Average volume occupied by molecules E meso Effective modulus of elasticity at the mesoscale γ: coefficient λ: Defect density σ macro : Breaking strength at the macroscale σ0: Breaking strength in the ideal state β: Correction coefficient λ0: Reference defect density α: Correction coefficient E0: Reference modulus of elasticity

[0017] Equation (1) is a formula for deriving the intermolecular bond stiffness from the relationships between molecules. Equation (2) is a formula for deriving the effective modulus of elasticity at the microscale from the intermolecular bond stiffness and information about the molecular assembly. Equation (3) is a formula for deriving the effective modulus of elasticity at the mesoscale from the effective modulus of elasticity at the microscale and the material characteristics at the mesoscale. Equation (4) is a formula for deriving the fracture strength at the macroscale from the effective modulus of elasticity at the mesoscale and the material characteristics.

[0018] Thus, there are specific formulas that can be used to identify materials at different scales, and these are connected through variables. These formulas can also be integrated through variables. When this is done, as shown in Figure 3, equations (1) through (4) are integrated to show the material properties at the macroscale σ macro ε, σ, η, V a A formula can be derived using material properties on a smaller scale, such as λ.

[0019] For example, when attempting to derive a mathematical formula from macro-scale material properties using molecular-scale material properties, it is effective to formulate the phenomena at each scale by establishing connections through variables, as shown in equations (1) through (4). By doing so, a mathematical model with superior interpretability and higher predictive accuracy can be obtained compared to directly attempting to derive an integrated formula as described above.

[0020] Figure 4 is a diagram illustrating the functional configuration of the information processing device 10 according to this embodiment. Figure 5 is a diagram illustrating the processing flow executed by the information processing device 10 according to this embodiment. Figure 6 is a diagram illustrating the first formula generation step. Figure 7 is a diagram illustrating the second formula generation step. However, Figures 6 and 7 are illustrative, and the configuration of variables and formulas according to this embodiment is not limited to these examples. The information processing device 10 according to this embodiment further comprises an acquisition unit 110 and an output unit 190.

[0021] The acquisition unit 110 acquires data that the formula generation unit 130 uses to generate formulas. The data acquired by the acquisition unit 110 is a combination of multiple values ​​related to physical properties. The data acquired by the acquisition unit 110 can also be described as a vector whose elements are values ​​related to physical properties.

[0022] The data used by the formula generation unit 130 to generate the first formula is called the first acquired data, and the data used by the formula generation unit 130 to generate the second formula is called the second acquired data. The variables included in the first explanatory variable group are also called the first explanatory variables. The first explanatory variable group includes one or more first explanatory variables. The variables included in the second explanatory variable group are also called the second explanatory variables. The second explanatory variable group includes one or more second explanatory variables.

[0023] The first acquired data includes values ​​for at least one variable (x1 and x4 in Figure 6) included in the first explanatory variable group. The first acquired data also includes values ​​for at least the first dependent variable (y1 in Figure 6). The first acquired data may further include values ​​for variables not included in the first explanatory variable group (x2 and x3 in Figure 6). The first acquired data contains multiple vectors, which are combinations of values ​​for multiple variables. These vectors represent the relationship between the value of the first dependent variable and the values ​​of multiple candidate first explanatory variables (x1, x2, x3, and x4 in Figure 6). In other words, these vectors associate the value of the first dependent variable with the values ​​of other variables that are candidates for the first explanatory variable. These multiple vectors may, for example, represent data for multiple materials. The variables that are candidates for the first explanatory variable are exemplified in the same way as the first explanatory variable, which will be described in detail later.

[0024] Some or all of the values ​​included in the first acquired data may be experimental values. Some or all of the values ​​included in the first acquired data may be theoretical values. Some or all of the values ​​included in the first acquired data may be values ​​obtained through simulation.

[0025] The formula generation unit 130 generates a first formula using the first acquired data and an existing method. In the first formula generation step, the formula generation unit 130 can generate the first formula, for example, by symbolic regression. In the process of generating the first formula, the formula generation unit 130 can extract the first explanatory variable to be used in the first formula from multiple candidates for the first explanatory variable included in the first acquired data. In symbolic regression, the form of the formula and the constants included in the formula are specified. In this way, a first formula (y1=f1(x1,x4) in Figure 6) is obtained that shows the relationship between the group of first explanatory variables consisting of one or more first explanatory variables and the first dependent variable. By substituting the values ​​of one or more first explanatory variables into the first formula, the value of the first dependent variable can be derived.

[0026] The second set of acquired data includes values ​​for at least one variable (y1, y3, and y4 in Figure 7) included in the second group of explanatory variables. The second set of acquired data also includes values ​​for at least the second dependent variable (z1 in Figure 7). The second set of acquired data may further include values ​​for variables not included in the second group of explanatory variables (y2 in Figure 7). The second set of acquired data includes multiple vectors, which are combinations of values ​​for multiple variables. These vectors represent the relationship between the values ​​of the second dependent variable and the values ​​of multiple candidate second explanatory variables (y1, y2, y3, and y4 in Figure 7). In other words, these vectors associate the values ​​for the second dependent variable with the values ​​for other variables that are candidates for the second explanatory variable. These multiple vectors are, for example, data related to multiple materials. Here, the second set of acquired data includes values ​​for the first dependent variable, and the multiple candidate second explanatory variables include values ​​for the first dependent variable.

[0027] The variables that are candidates for the second explanatory variable are exemplified in the same way as the second explanatory variable, which will be described in detail later. Note that the number of variables shown in the second set of acquired data does not have to be the same as the number of variables shown in the first set of acquired data.

[0028] Some or all of the values ​​included in the second set of acquired data may be experimental values. Some or all of the values ​​included in the second set of acquired data may be theoretical values. Some or all of the values ​​included in the second set of acquired data may be values ​​obtained through simulation.

[0029] The formula generation unit 130 generates a second formula using the second acquired data and an existing method. In the second formula generation step, the formula generation unit 130 can generate the second formula, for example, by symbolic regression. In the process of generating the second formula, the formula generation unit 130 can extract the second explanatory variables to be used in the second formula from multiple candidates for the second explanatory variables included in the second acquired data. However, the formula generation unit 130 includes at least the first dependent variable in the group of second explanatory variables. For example, the formula generation unit 130 performs a restricted symbolic regression so that at least the first dependent variable is included in the group of second explanatory variables. In this way, a second formula (z1=f2(y1,y3,y4) in Figure 7) is obtained that shows the relationship between the group of second explanatory variables, consisting of one or more second explanatory variables, and the second dependent variable. The value of the second dependent variable can be derived by substituting the values ​​of one or more second explanatory variables into the second formula.

[0030] The second group of explanatory variables includes at least the first dependent variable as a second explanatory variable. That is, the second group of explanatory variables includes at least a variable that exhibits the same physical properties as the first dependent variable as a second explanatory variable. In this way, the relationship between the first and second equations can be interpreted. In the examples in Figures 6 and 7, the variable y1 is both the first dependent variable and the second explanatory variable.

[0031] The first objective variable may be a variable relating to at least one of the following: within particles, between particles, aggregates of particles, and substances containing particles. The second objective variable may also be a variable relating to at least one of the following: within particles, between particles, aggregates of particles, and substances containing particles. Particles are, for example, atoms, molecules, or solid particles. Solid particles may be, for example, individual particles in a filler or powder in a resin composition. Solid particles are aggregates of at least one of atoms and molecules.

[0032] The collection of particles may consist of a single type of particle or multiple types of particles. The collection of particles may be a liquid or a solid.

[0033] A substance containing particles may be a liquid, a solid, or a mixture of liquid and solid. The substance may also be a composition containing resins, etc. Variables relating to a substance containing particles may be physical properties measured or defined for the substance, physical properties measured during the process of the substance's formation, or physical properties defined for the state of the substance's formation process. Examples of variables relating to a substance containing particles include variables relating within the substance, variables relating between substances, and variables relating to interfaces present within the substance.

[0034] Examples of properties represented by variables include mechanical properties, thermal properties, optical properties, chemical properties, and physical properties. Examples of mechanical properties include hardness, strength, modulus of elasticity, defect density, coefficient of friction, wear resistance, and interface roughness. Examples of thermal properties include melting point, boiling point, glass transition temperature, coefficient of thermal expansion, specific heat, heat capacity, thermal decomposition temperature, thermal diffusivity, and thermal conductivity. Examples of optical properties include light transmittance, reflectance, refractive index, and absorbance. Examples of chemical properties include solubility, oxidation-reduction potential, acid resistance, and alkali resistance. Examples of physical properties include electron number, mass number, ionization energy, electronegativity, energy levels, number of interparticle bonds, magnitude of interparticle forces, particle size, particle size distribution, specific surface area, average interparticle distance, interparticle equilibrium distance, molecular weight, interparticle bond strength, volume, density, electrical resistivity, dielectric constant, polarizability, permeability, and specific gravity.

[0035] As described above, one or more variables in the first explanatory variable group and one or more variables in the second explanatory variable group are variables relating to physical properties. The first and second explanatory variables are exemplified in the same way as the first and second objective variables described above. That is, the first and second explanatory variables may be variables relating to at least one of the following: within particles, between particles, aggregates of particles, and substances containing particles.

[0036] As mentioned above, the second objective variable is a variable relating to physical properties on a larger scale than the first objective variable. The physical properties of solid particles, molecules, and atoms can be said to increase in scale in that order. That is, of these, the scale of physical properties relating to solid particles is the largest, and the scale of physical properties relating to atoms is the smallest. The physical properties relating to a substance or a collection of particles containing particles, the physical properties between those particles, and the physical properties within those particles can be said to increase in scale in that order. That is, of these, the scale of physical properties relating to a substance or a collection of particles containing particles is the largest, and the scale of physical properties within those particles is the smallest. For physical properties relating to a substance containing particles and physical properties relating to a collection of particles, the larger the number of particles contained, or the larger the volume of the object, the larger the scale. Specifically, the larger the size of the sample used to measure the value of that physical property, the larger the scale of the physical property. The larger the size of the real-world unit structure corresponding to the model used in theoretical calculations or simulations of that physical property, the larger the scale of the physical property. For example, the sample used to measure the value of the material property indicated by the second objective variable is larger than the sample used to measure the value of the material property indicated by the first objective variable. Alternatively, the real-world unit structure corresponding to the model used in theoretical calculations or simulations to determine the value of the material property indicated by the second objective variable is larger than the real-world unit structure corresponding to the model used in theoretical calculations or simulations to determine the value of the material property indicated by the first objective variable.

[0037] For example, if the first objective variable is a variable relating to a particle, the second objective variable may be a variable relating to a substance containing that particle. If the first objective variable is a variable relating to a particle, the second objective variable may be a variable relating to a collection of those particles. If the first objective variable is a variable relating to a first object containing one or more particles, the second objective variable may be a variable relating to a second object containing more of those particles than the first object. If both the first and second objects are collections of particles, the second object can be said to be a larger collection than the first object.

[0038] The relationship between the scale of the first explanatory variable and the second objective variable is not particularly limited, but it is preferable that all variables included in the first explanatory variable group are variables relating to physical properties on a smaller scale than the second objective variable.

[0039] The hardware configuration of the information processing device 10 is described below. Each functional component of the information processing device 10 (acquisition unit 110, formula generation unit 130, and output unit 190) is realized through a combination of hardware and software (e.g., a combination of an electronic circuit and a program to control it).

[0040] Figure 8 illustrates a computer 1000 for implementing the information processing device 10. Computer 1000 is any computer. For example, computer 1000 could be an SoC (System on Chip), a Personal Computer (PC), a server machine, a tablet terminal, or a smartphone. Computer 1000 may be a dedicated computer designed to implement the information processing device 10, or it may be a general-purpose computer. Furthermore, the information processing device 10 may be implemented by a single computer 1000, or by a combination of multiple computers 1000.

[0041] Computer 1000 includes a bus 1020, a processor 1040, memory 1060, a storage device 1080, an input / output interface 1100, and a network interface 1120. Bus 1020 is a data transmission path for the processor 1040, memory 1060, storage device 1080, input / output interface 1100, and network interface 1120 to send and receive data to and from each other. However, the method of connecting the processor 1040 and the other components is not limited to bus connection. Examples of the processor 1040 include various processors such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), and an FPGA (Field-Programmable Gate Array). Memory 1060 is a main memory device implemented using RAM (Random Access Memory), etc. Storage device 1080 is an auxiliary storage device implemented using a hard disk, SSD (Solid State Drive), memory card, or ROM (Read Only Memory), etc.

[0042] The input / output interface 1100 is an interface for connecting the computer 1000 with input / output devices. For example, input devices such as a keyboard and output devices such as a display are connected to the input / output interface 1100. The method by which the input / output interface 1100 connects to the input and output devices may be wireless or wired.

[0043] The network interface 1120 is an interface for connecting the computer 1000 to a network. Examples of such networks include LANs (Local Area Networks) and WANs (Wide Area Networks). The network interface 1120 may connect to the network via a wireless connection or a wired connection.

[0044] The storage device 1080 stores program modules that realize each functional component of the information processing device 10. The processor 1040 reads these program modules into the memory 1060 and executes them to realize the functions corresponding to each program module.

[0045] Referring to Figure 5, the processing flow executed by the information processing device 10 is described below. In step S101, the acquisition unit 110 acquires first acquired data and second acquired data. The acquisition unit 110 may acquire data input by the user using a keyboard or the like connected to the information processing device 10 as first acquired data and second acquired data. The acquisition unit 110 may acquire first acquired data and second acquired data from other devices. Alternatively, the acquisition unit 110 may output data previously held in a storage unit as first acquired data and second acquired data. This storage unit may be provided in the information processing device 10, or it may be a storage device provided outside the information processing device 10. If the storage unit is provided in the information processing device 10, this storage unit is realized by the storage device 1080 of the computer 1000.

[0046] The timing at which the acquisition unit 110 acquires the second acquisition data is not particularly limited, as long as it is before the formula generation unit 130 generates the second formula.

[0047] In step S102, the formula generation unit 130 generates a first formula using the first acquired data. In step S103, the formula generation unit 130 generates a second formula using the second acquired data. The order in which the formula generation unit 130 generates the first and second formulas is not particularly limited.

[0048] In step S104, the output unit 190 outputs the generated first and second equations. The user can use these equations to, for example, understand the relationship between the first group of explanatory variables and the second objective variable, or to predict the value of the second objective variable in material design.

[0049] The output unit 190 may display the first and second mathematical formulas on a display connected to the information processing device 10, transmit them to another device, or store them in a storage unit accessible to the output unit 190.

[0050] According to this embodiment, the formula generation unit 130 generates a first formula and a second formula. The second explanatory variable group includes the first objective variable, and the second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. Therefore, a highly interpretable mathematical model can be obtained that predicts material properties.

[0051] (Second embodiment) Figure 9 is a diagram illustrating the processing flow executed by the information processing device 10 according to the second embodiment. The functional configuration of the information processing device 10 according to this embodiment is illustrated by Figure 4, similar to the first embodiment. The information processing device 10 and information processing method according to this embodiment are the same as those of the information processing device 10 and information processing method according to the first embodiment, except for the points described below.

[0052] The information processing method according to this embodiment further includes a third formula generation step (step S204). In the third formula generation step, the formula generation unit 130 generates a third formula. The third formula is a formula that shows the relationship between the third group of explanatory variables, which includes the second objective variable, and the third objective variable. One or more variables included in the third group of explanatory variables are variables relating to physical properties. The third objective variable is a variable relating to physical properties on a larger scale than either the first or second objective variable.

[0053] The data used by the formula generation unit 130 to generate the third formula is called the third acquired data. The variables included in the third explanatory variable group are also called the third explanatory variables. The third explanatory variable group includes one or more third explanatory variables.

[0054] The third set of acquired data includes values ​​for at least one variable included in the third group of explanatory variables. Furthermore, the third set of acquired data includes values ​​for at least the third dependent variable. The third set of acquired data may also include values ​​for variables not included in the third group of explanatory variables. The third set of acquired data includes multiple vectors, which are combinations of values ​​for multiple variables. These vectors can be said to represent the relationship between the values ​​of the third dependent variable and multiple candidate values ​​for the third explanatory variable. In other words, these vectors associate the values ​​for the third dependent variable with the values ​​for other variables that are candidates for the third explanatory variable. These multiple vectors are, for example, data related to multiple materials. Here, the third set of acquired data includes values ​​for the second dependent variable, and the multiple candidates for the third explanatory variable include values ​​for the second dependent variable.

[0055] The variables that are candidates for the third explanatory variable are exemplified in the same way as the third explanatory variable described in detail later. Note that the number of variables shown in the third acquired data does not have to be the same as the number of variables shown in the second acquired data. Similarly, the number of variables shown in the third acquired data does not have to be the same as the number of variables shown in the first acquired data.

[0056] Some or all of the values ​​included in the third acquisition data may be experimental values. Some or all of the values ​​included in the third acquisition data may be theoretical values. Some or all of the values ​​included in the third acquisition data may be values ​​obtained from simulations.

[0057] The formula generation unit 130 generates a third formula using the third acquired data and an existing method. In the third formula generation step, the formula generation unit 130 can generate the third formula, for example, by symbolic regression. In the process of generating the third formula, the formula generation unit 130 can extract the third explanatory variables to be used in the third formula from a plurality of candidates for the third explanatory variables included in the third acquired data. However, the formula generation unit 130 includes at least the second dependent variable in the group of third explanatory variables. For example, the formula generation unit 130 performs a restricted symbolic regression so that the group of third explanatory variables includes at least the second dependent variable. In this way, a third formula is obtained that shows the relationship between the group of third explanatory variables, consisting of one or more third explanatory variables, and the third dependent variable. The value of the third dependent variable can be derived by substituting the values ​​of one or more third explanatory variables into the third formula.

[0058] The third group of explanatory variables includes at least the second dependent variable as a third explanatory variable. That is, the third group of explanatory variables includes at least a variable that exhibits the same physical properties as the second dependent variable as a third explanatory variable. In this way, the relationship between the second and third equations can be interpreted. Furthermore, the relationship between the first and third equations can be interpreted through the second equation.

[0059] The third dependent variable and third explanatory variables are exemplified in the same way as the first and second dependent variables. That is, the third dependent variable and one or more third explanatory variables may each be variables relating to at least one of the following: within a particle, between particles, in a particle aggregate, and in a substance containing particles.

[0060] As described above, the third objective variable is a variable relating to a physical property on a larger scale than either the first or second objective variable. The scale of the physical property is as described in the first embodiment.

[0061] If the second objective variable is a variable relating to a particle, the third objective variable may be a variable relating to a substance containing that particle. If the second objective variable is a variable relating to a particle, the third objective variable may be a variable relating to a collection of that particle. If the second objective variable is a variable relating to a second object containing one or more particles, the third objective variable may be a variable relating to a third object containing more of those particles than the second object. If both the second and third objects are collections of particles, the third object can be said to be a larger collection than the second object.

[0062] The relationship between the scale of the second explanatory variable and the third objective variable is not particularly limited, but it is preferable that all variables included in the second explanatory variable group are variables relating to physical properties on a smaller scale than the third objective variable.

[0063] In step S201 of Figure 9, the acquisition unit 110 acquires the first acquired data, the second acquired data, and the third acquired data. The method by which the acquisition unit 110 acquires the third acquired data will be described in the same way as the method for acquiring the first acquired data.

[0064] The timing at which the acquisition unit 110 acquires the third acquisition data is not particularly limited, as long as it is before the formula generation unit 130 generates the third formula.

[0065] Steps S202 and S203 are the same as steps S102 and S103 described in the first embodiment, respectively. In step S204, the formula generation unit 130 generates a third formula using the third acquired data. The order in which the formula generation unit 130 generates the first formula, the second formula, and the third formula is not particularly limited.

[0066] In step S205, the output unit 190 outputs the generated first equation, second equation, and third equation. The method by which the output unit 190 outputs the equations is as described in the first embodiment. The user can use these equations to, for example, understand the relationship between the first group of explanatory variables and the third objective variable, or to predict the value of the third objective variable in material design.

[0067] Furthermore, the information processing device 10 may generate one or more additional mathematical formulas, similar to the first to third formulas. Doing so will allow for the interpretation of relationships between physical properties that are on a much larger scale.

[0068] According to this embodiment, the same functions and effects as in the first embodiment can be obtained. In addition, according to this embodiment, the formula generation unit 130 generates a third formula. Therefore, formulaization is performed in multiple stages, and a highly interpretable formula model can be obtained.

[0069] (Third embodiment) Figure 10 is a diagram illustrating the functional configuration of the information processing device 10 according to the third embodiment. Figure 11 is a diagram illustrating the processing flow executed by the information processing device 10 according to the third embodiment. The information processing device 10 according to this embodiment is the same as the information processing device 10 according to at least one of the first and second embodiments, except for the points described below. The information processing method according to this embodiment is the same as the information processing method according to at least one of the first and second embodiments, except for the points described below.

[0070] The information processing method according to this embodiment further includes an integration step (step S304) for generating an integrated formula using a first formula and a second formula. The information processing device 10 according to this embodiment further includes an integration unit 170 for integrating the first formula and the second formula.

[0071] Steps S301, S302, and S303 are the same as steps S101, S102, and S103 described above, respectively.

[0072] In step S304, the integration unit 170 generates an integrated formula by integrating the generated first formula and the second formula. Specifically, the integration unit 170 integrates the first and second formulas by substituting the first formula into the part of the second formula where one or more second explanatory variables are the same as the first dependent variable. Specifically, in the example in Figure 3, the k of formula (2) bond By substituting this into the right-hand side of equation (1), equations (1) and (2) can be combined.

[0073] In step S305, the output unit 190 outputs at least the integrated formula. The user can use the integrated formula to calculate the value of the second objective variable relating to a relatively large-scale physical property using the values ​​of the first explanatory variable group. The output unit 190 may also output the first and second formulas before integration. Doing so improves the interpretability of the integrated formula for the user. The method by which the output unit 190 outputs the formula is as described in the first embodiment.

[0074] In this embodiment, the formula generation unit 130 may further generate the third formula described in the second embodiment, or it may generate one or more formulas in addition to that. In that case, the integration unit 170 may further integrate those formulas to generate an integrated formula. For example, by substituting the formula obtained by integrating the first and second formulas into the part of the third formula where one or more third explanatory variables are the same as the second objective variable, an integrated formula of the first, second, and third formulas can be obtained.

[0075] The hardware configuration of the computer implementing the information processing device 10 according to this embodiment is shown, for example, in Figure 8, similar to the first embodiment. However, the storage device 1080 of the computer 1000 implementing the information processing device 10 according to this embodiment further stores program modules that realize the functions of the integration unit 170.

[0076] According to this embodiment, the same operation and effects as in the first embodiment can be obtained. In addition, according to this embodiment, the integration unit 170 generates an integrated formula using the first formula and the second formula. Therefore, a formula can be obtained that can calculate the value of the second objective variable relating to relatively large-scale physical properties using the values ​​of the first group of explanatory variables.

[0077] The embodiments of the present invention have been described above with reference to the drawings, but these are merely examples of the present invention, and various other configurations can also be adopted.

[0078] Furthermore, while the flowcharts used in the above description show multiple steps (processes) in sequence, the execution order of the steps performed in each embodiment is not limited to the order in which they are described. In each embodiment, the order of the illustrated steps can be changed to the extent that it does not impede the content. Also, the above embodiments can be combined to the extent that their contents do not conflict. [Explanation of Symbols]

[0079] 10 Information Processing Devices 110 Acquisition Department 130 Formula Generation Unit 170 Integration Department 190 Output section 1000 calculator 1020 Bus 1040 processor 1060 memory 1080 storage devices 1100 Input / Output Interface 1120 Network Interface

Claims

1. An information processing method performed by one or more computers, A first equation generation step generates a first equation that shows the relationship between the first group of explanatory variables and the first dependent variable, The process includes a second equation generation step of generating a second equation that shows the relationship between the second group of explanatory variables, which includes the first dependent variable, and the second dependent variable, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. In the first formula generation step, the first formula is generated by symbolic regression, In the second formula generation step, the second formula is generated by symbolic regression. Information processing methods.

2. An information processing method performed by one or more computers, A first equation generation step generates a first equation that shows the relationship between the first group of explanatory variables and the first dependent variable, The process includes a second equation generation step of generating a second equation that shows the relationship between the second group of explanatory variables, which includes the first dependent variable, and the second dependent variable, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The process further includes an integration step of generating an integrated formula using the first and second formulas. Information processing methods.

3. An information processing method performed by one or more computers, A first equation generation step generates a first equation that shows the relationship between the first group of explanatory variables and the first dependent variable, The process includes a second equation generation step of generating a second equation that shows the relationship between the second group of explanatory variables, which includes the first dependent variable, and the second dependent variable, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The method further includes a third equation generation step of generating a third equation that shows the relationship between the third group of explanatory variables, including the second dependent variable, and the third dependent variable, One or more variables included in the third group of explanatory variables are variables relating to physical properties, The third objective variable is a variable relating to a physical property on a larger scale than either the first or second objective variable. Information processing methods.

4. In the information processing method according to any one of claims 1 to 3, The first objective variable is a variable relating to at least one of the following: within a particle, between particles, in a particle aggregate, and in a substance containing particles. Information processing methods.

5. In the information processing method according to any one of claims 1 to 3, The first objective variable is a variable relating to particles, The second objective variable is a variable relating to the substance containing the particles. Information processing methods.

6. In the information processing method according to any one of claims 1 to 3, The first objective variable is a variable relating to particles, The second objective variable is a variable relating to the set of particles. Information processing methods.

7. In the information processing method according to any one of claims 1 to 3, The first objective variable is a variable relating to a first object containing one or more particles, The second objective variable is a variable relating to the second object which contains more of the particles than the first object. Information processing methods.

8. In the information processing method described in claim 4, The particles are atoms, molecules, or solid particles. Information processing methods.

9. In the information processing method described in claim 3, In the first formula generation step, the first formula is generated by symbolic regression, In the second formula generation step, the second formula is generated by symbolic regression. Information processing methods.

10. In the information processing method according to any one of claims 1, 3, and 9, The process further includes an integration step of generating an integrated formula using the first and second formulas. Information processing methods.

11. The system includes a formula generation unit that generates a first formula showing the relationship between a first group of explanatory variables and a first dependent variable, and a second formula showing the relationship between a second group of explanatory variables, including the first dependent variable, and a second dependent variable. The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The formula generation unit generates the first and second formulas by symbolic regression. Information processing device.

12. A formula generation unit that generates a first formula showing the relationship between a first group of explanatory variables and a first dependent variable, and a second formula showing the relationship between a second group of explanatory variables including the first dependent variable and a second dependent variable, The system comprises an integration unit that generates an integrated formula using the first formula and the second formula, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. Information processing device.

13. A formula generation unit that generates a first formula showing the relationship between a first group of explanatory variables and a first dependent variable, and a second formula showing the relationship between a second group of explanatory variables including the first dependent variable and a second dependent variable, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The formula generation unit further generates a third formula that shows the relationship between the third group of explanatory variables, including the second objective variable, and the third objective variable. One or more variables included in the third group of explanatory variables are variables relating to physical properties, The third objective variable is a variable relating to a physical property on a larger scale than either the first or second objective variable. Information processing device.

14. The computer is used as a formula generation means to generate a first formula that shows the relationship between a first group of explanatory variables and a first dependent variable, and a second formula that shows the relationship between a second group of explanatory variables, which includes the first dependent variable, and a second dependent variable. The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The formula generation means generates the first formula and the second formula by symbolic regression. program.

15. A computer, A formula generation means for generating a first formula that shows the relationship between a first group of explanatory variables and a first dependent variable, and a second formula that shows the relationship between a second group of explanatory variables including the first dependent variable and a second dependent variable, and Integration means for generating an integrated formula using the first formula and the second formula. To make it function as, The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. program.

16. The computer functions as a formula generation means for generating a first formula that shows the relationship between a first group of explanatory variables and a first target variable, and a second formula that shows the relationship between a second group of explanatory variables, which includes the first target variable, and a second target variable. The one or more variables included in the first explanatory variable group and the one or more variables included in the second explanatory variable group are variables relating to physical properties, The second objective variable is a variable relating to a physical property on a larger scale than the first objective variable. The formula generation means further generates a third formula that shows the relationship between the third group of explanatory variables, including the second objective variable, and the third objective variable. One or more variables included in the third group of explanatory variables are variables relating to physical properties, The third objective variable is a variable relating to a physical property on a larger scale than either the first or second objective variable. program.

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