Learning device, estimation device, learning method, estimation method, and program

Abstract

To improve the accuracy of total energy estimation using Neural Network Potential (NNP).SOLUTION: A learning device is provided with a control unit that performs the training of an estimation model, the estimation model being a mathematical model that estimates the energy of an atom to be evaluated based on evaluation target features representing the sum from the first sum to the U-th sum, the U-th sum being the sum of a three-dimensional wave function representing the u-th atomic orbital, counted from the highest occupied level, of the atomic orbital of the evaluation target atom positioned in a system containing one or more atoms, and three-dimensional wave functions of the u-th atomic orbitals, counted from the highest occupied level, of atoms in the system different from the evaluation target atom that are within a predetermined distance from the evaluation target atom. In learning, the estimation model is updated to minimize the difference between the total sum of the result of executing the estimation model for each atom in the system and the energy of the system estimated by density functional theory with respect to the system.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a learning device, an estimation device, a learning method, an estimation method, and a program. [Background technology]

[0002] Density functional theory is being used to explore materials for purposes such as drug discovery and improving the performance of semiconductor devices. However, density functional theory calculations are computationally expensive, and the cell size (the size of the unit cell of the periodically repeating crystal) that can be used for composition exploration is limited to about 200 atoms, making it difficult to explore materials for larger systems. For example, to reproduce the composition of a solid electrolyte with trace amounts of dopant, a cell size of 500 atoms or more is required, making it difficult to explore materials sufficiently.

[0003] Therefore, active research is being conducted into reducing computational costs by modeling interatomic potentials with neural networks (Patent Document 1 and Non-Patent Documents 1-3). Here, training data is generated from density functional theory calculations of relatively small systems, and a mathematical model commonly referred to as Neural Network Potential (NNP) is created to accurately reproduce the results. By using NNP, the computational costs of interatomic forces and total energy are significantly reduced compared to density functional theory calculations. For this reason, it is applied to molecular dynamics calculations of large-scale systems. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] US Patent Application Publication No. 2022 / 0207393 [Non-patent literature]

[0005] [Non-Patent Document 1] J. Behler and M. Parrinello, “Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces”, Phys. Rev. Lett. Vol.98, pp.146401 (2007) [Non-patent document 2] APBartok et al. “Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons”, Phys. Rev. Lett. Vol.104, pp.136403 (2010) [Non-patent document 3] APThompson, et al. "Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials." Journal of Computational Physics 285 (2015): 316-330. Summary of the Invention [Problem to be solved by the invention]

[0006] However, the accuracy of the total energy predictions of the NNPs proposed so far has been low, making it difficult to analyze physical properties that require calculation of the total energy, such as the formation energy and elastic properties of materials.

[0007] In view of the above circumstances, an object of the present invention is to provide a technique for improving the accuracy of total energy estimation using Neural Network Potential (NNP). [Means for solving the problem]

[0008] One aspect of the present invention is a learning device that includes a control unit that performs training of an estimation model, which is a mathematical model that estimates the energy of an atom to be evaluated based on evaluation object features that represent a u-th sum, which is a sum, from a 1st sum to a U-th sum, of: a three-dimensional wave function that represents the u-th atomic orbital (where u is an integer greater than or equal to 1 and less than or equal to U, and U is an integer greater than or equal to 1), counting from the highest energy of the occupied level of an atom to be evaluated that is located in a system including one or more atoms; and a three-dimensional wave function of each atomic orbital, from a 1st sum to a U-th atomic orbital, counting from the highest energy of the occupied level of each atom in the system that is different from the evaluation object and that is within a predetermined distance from the evaluation object. During the training, the estimation model is updated so as to reduce the difference between the sum of results obtained by executing the estimation model for each atom in the system and the energy of the system estimated by density functional theory for the system.

[0009] One aspect of the present invention is an estimation device comprising: a control unit that performs training of an estimation model, which is a mathematical model that estimates the energy of an atom to be evaluated based on an evaluation target feature that represents a u-th sum, which is a sum, from a 1st sum to a U-th sum, of: a three-dimensional wave function that represents the u-th atomic orbital (u is an integer greater than or equal to 1 and less than or equal to U, and U is an integer greater than or equal to 1), counting from the highest energy of the occupied level of an atom to be evaluated that is located in a system including one or more atoms; and a three-dimensional wave function of each atomic orbital, from a 1st sum to a U-th atomic orbital, counting from the highest energy of the occupied level of each atom in the system that is different from the atom to be evaluated and that is within a predetermined distance from the atom to be evaluated; wherein the estimation model is updated during the training so as to reduce the difference between the sum of results obtained by executing the estimation model for each atom in the system and the energy of the system estimated by density functional theory for the system; and an estimation unit that performs estimation using the trained estimation model obtained by a learning device.

[0010] One aspect of the present invention is a learning method performed by a learning device, the learning method including: a control unit that performs training of an estimation model, which is a mathematical model that estimates the energy of an atom to be evaluated based on evaluation object features representing a u-th sum, which is a sum, from 1 to U-th sum, of: a three-dimensional wave function that represents the u-th atomic orbital (where u is an integer greater than or equal to 1 and less than or equal to U, and U is an integer greater than or equal to 1), of an atomic orbital of an atom to be evaluated that is located in a system including one or more atoms, and a three-dimensional wave function of each atomic orbital of an atom to be evaluated that is the u-th atomic orbital, counting from the highest energy of the occupied level, of each atom in the system that is different from the evaluation object and that is within a predetermined distance from the evaluation object, the atomic orbital being counting from the highest energy of the occupied level; and

[0011] One aspect of the present invention is an estimation method executed by an estimation device comprising an estimation unit that performs training of an estimation model, which is a mathematical model that estimates the energy of an atom to be evaluated based on an evaluation target feature quantity that represents, from a 1st sum to a Uth sum, a uth sum, which is a sum of: a three-dimensional wave function that represents the uth atomic orbital (u is an integer greater than or equal to 1 and less than or equal to U, and U is an integer greater than or equal to 1) of an atomic orbital of an atom to be evaluated that is located in a system including one or more atoms, and a three-dimensional wave function of each atomic orbital of an atom to be evaluated that is the uth atomic orbital of an atom to be evaluated that is located in a system including one or more atoms, and a 3D wave function of each atomic orbital of an atom to be evaluated that is the uth atomic orbital of an occupied level counted from the highest energy level; and a control unit that performs training of an estimation model, which is a mathematical model that estimates the energy of the atom to be evaluated based on an evaluation target feature quantity that represents, from a 1st sum to a Uth sum, a uth sum that is a sum of: a three-dimensional wave function that represents the uth atomic orbital of an atom to be evaluated that is located in a system including one or more atoms, and a three-dimensional wave function of each atomic orbital of an atom to be evaluated that is the uth atomic orbital of an atom to be evaluated that is located in a system

[0012] One aspect of the present invention is a program for causing a computer to function as the learning device described above.

[0013] One aspect of the present invention is a program for causing a computer to function as the above-described estimation device. [Effects of the Invention]

[0014] According to the present invention, it is possible to improve the accuracy of total energy estimation using Neural Network Potential (NNP). [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is an explanatory diagram illustrating an estimation system according to an embodiment. [Figure 2] FIG. 2 is a diagram illustrating an example of a hardware configuration of a learning device according to an embodiment. [Figure 3] 10 is a flowchart showing an example of a flow of processing executed by a learning device according to an embodiment. [Figure 4] FIG. 2 is a diagram illustrating an example of a hardware configuration of an estimation apparatus according to an embodiment. [Figure 5] 1 is a flowchart showing an example of a flow of processing executed by an estimation device according to an embodiment. [Figure 6] FIG. 1 is a first diagram showing an example of experimental results in the embodiment. [Figure 7] FIG. 2 is a second diagram showing an example of experimental results in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] FIG. 1 is an explanatory diagram illustrating an estimation system 100 according to an embodiment. The estimation system 100 includes a learning device 1 and an estimation device 2. The estimation device 2 performs estimation using a trained mathematical model obtained by the learning device 1. Specifically, the trained mathematical model obtained by the learning device 1 is a trained estimation model (hereinafter referred to as a "trained estimation model") described below. The trained estimation model is a type of so-called Neural Network Potential (NNP).

[0017] The learning device 1 includes a control unit 11 including a processor 91, such as a central processing unit (CPU), a graphics processing unit (GPU), or a neural network processing unit (NPU), and a memory 92, connected via a bus. The control unit 11 executes, for example, a learning process. The learning process is a process for obtaining a trained estimation model by learning an estimation model, which is a mathematical model to be learned, until a predetermined condition for terminating learning (hereinafter referred to as a "learning termination condition") is satisfied.

[0018] The estimation model is a mathematical model that estimates the energy of the atom to be evaluated based on the feature quantity to be evaluated. The feature quantity to be evaluated is a quantity that represents the u-th sum (u is an integer between 1 and U, and U is an integer greater than or equal to 1) from the 1st sum to the U-th sum. The u-th sum is the sum of a three-dimensional wave function representing the u-th central atomic orbital and a three-dimensional wave function representing the u-th peripheral atomic orbital.

[0019] The u-th central atomic orbital is the u-th atomic orbital counting from the highest energy occupied level of the atom to be evaluated that is located in the system to be analyzed (hereinafter referred to as the "system to be analyzed") that includes one or more atoms.

[0020] The u-th peripheral atomic orbital is the atomic orbital of each atom within a predetermined distance from the object of evaluation among the peripheral atoms, and is the u-th atomic orbital from the highest energy level of the occupied level. Peripheral atoms are atoms in the system under analysis that are different from the object of evaluation.

[0021] For example, if the system to be analyzed is Li6PS5Cl and the atom to be evaluated is S, the peripheral atoms are, for example, Li, P, and Cl. In this case, when u=1, the u central atomic orbital is a 3p orbital, the u central atomic orbital of one of the peripheral atoms, Li, is a 2s orbital, and the u central atomic orbitals of the other peripheral atoms, P and Cl, are 3p orbitals.

[0022] <Examples of features to be evaluated> The feature to be evaluated is, for example, a vector expressed by the following formula (1). Note that in the example of formula (1), the number of elements of the vector is 2 because u=2 is used as an example, but this does not mean that the number of elements must be 2 regardless of the value of u. The dimension of the vector representing the feature to be evaluated is u. u=1 may also be the case, in which case the feature to be evaluated is a scalar.

[0023]

number

[0024]

number

[0025] where (n,l) i represents the principal quantum number n and azimuthal quantum number l of the i-th atom. N represents the number of atoms located within a sphere of a given radius centered on the i-th atom. The given radius is, for example, 7 Å. ρ i represents the wave function of the i-th atom. j represents the wave function of the jth atom, which is different from the ith atom. R represents the position in three-dimensional space. r i represents the position of the i-th atom in three-dimensional space. j represents the position of the jth atom in three-dimensional space. j represents the position of the jth atom in three-dimensional space.

[0026] For example, the evaluation target feature quantity of a sulfur atom when u=2 is expressed by the following formula (3).

[0027]

number

[0028] In the learning process, for each atom in the system under analysis, the energy of the atom under evaluation is estimated based on the feature values ​​of the evaluation target when each atom is the evaluation target. The estimation model performs the process of estimating the energy of the atom under evaluation based on the feature values ​​of the atom under evaluation.

[0029] During the learning process, the estimation model is updated to reduce the difference between the sum (i.e., total energy) of the estimated energies (i.e., the results of running the estimation model) and the energy of the system being analyzed estimated by the density functional theory for the system being analyzed.

[0030] Therefore, in the training of the estimation model, a set of information indicating the evaluation target feature for each atom in the analyzed system (hereinafter referred to as "training input data") and information indicating the energy of the analyzed system estimated by the density functional theory (hereinafter referred to as "training label") is used for training. The training label is a label indicating the correct answer. Therefore, the above set is so-called labeled training data.

[0031] The density functional theory for the system to be analyzed may be executed by the control unit 11 during the learning process, or may have been executed by the control unit 11 or a device other than the learning device 1 before the learning process is executed, or may be executed by a device other than the learning device 1 in synchronization with the execution of the learning process by the control unit 11.

[0032] The three-dimensional wave function may be, for example, a three-dimensional radial wave derivative.

[0033] The system to be analyzed may be, for example, a part of a semiconductor crystal. 24 P4S 20It is Cl4.

[0034] The learning termination condition may be any condition related to the termination of learning, such as that the estimation model, which is the mathematical model to be learned, has been updated a predetermined number of times, that the change in the estimation model due to the update is smaller than a predetermined change, or that all of the previously prepared labeled or unlabeled learning data has been used.

[0035] <Effects of learning processing> As mentioned above, a three-dimensional wave function is used in learning. On the other hand, the NNP technology described in Patent Document 1 uses a charge density (the sum of the squares of the magnitudes of one-dimensional radial wave functions for the u-th occupied level (u is an integer between 1 and U, U is an integer greater than or equal to 1) counting from the highest energy level) converted into one-dimensional information by solid angle integration, rather than a three-dimensional wave function.

[0036] Incidentally, when the position of an atom changes in three-dimensional space, the distribution of the wave function in the three-dimensional space changes. Therefore, when learning is performed by the learning device 1 that uses values ​​containing information about the three-dimensional wave function for learning, a trained mathematical model is generated that also takes into account information about the position of the atom. On the other hand, when charge density converted into one-dimensional information is used instead of the three-dimensional wave function, the change in the distribution of the wave function in the three-dimensional space that accompanies the change in the position of the atom cannot be adequately expressed because it is not three-dimensional.

[0037] Therefore, the learning device 1 can obtain a mathematical model with higher estimation accuracy than the technology described in Patent Document 1. Because the accuracy of estimating the energy of individual atoms is high, the accuracy of estimating the energy of the system to be analyzed using the learned mathematical model obtained by the learning device 1 is also high.

[0038] <Example of hardware configuration of learning device 1> 2 is a diagram showing an example of the hardware configuration of a learning device 1 according to an embodiment. The learning device 1 includes a control unit 11 having a processor 91 and a memory 92 connected by a bus, and executes a program. By executing the program, the learning device 1 functions as a device including the control unit 11, an interface unit 12, and a storage unit 13.

[0039] More specifically, the processor 91 reads out a program stored in the storage unit 13 and stores the read out program in the memory 92. When the processor 91 executes the program stored in the memory 92, the learning device 1 functions as a device including the control unit 11, the interface unit 12, and the storage unit 13.

[0040] The control unit 11 controls the operation of each functional unit included in the learning device 1. The control unit 11 acquires a pair of learning input data and learning correct answer data, for example, via the interface unit 12. The control unit 11 executes, for example, a learning process. Therefore, the control unit 11 executes, for example, an estimation model. The control unit 11 acquires, for example, information stored in the memory unit 13. Specifically, the process of acquiring information stored in the memory unit 13 is reading.

[0041] The interface unit 12 includes a communication interface for connecting the learning device 1 to an external device. The interface unit 12 communicates with the external device via wired or wireless communication. The external device is, for example, a device that transmits pairs of training input data and training labels. In such a case, the interface unit 12 acquires pairs of training input data and training labels by communicating with the device that transmits the pairs of training input data and training labels.

[0042] Interface unit 12 may be configured to include input devices such as a mouse, keyboard, or touch panel. Interface unit 12 may be configured as an interface that connects these input devices to learning device 1. In this way, interface unit 12 accepts input of various information to learning device 1 via an input device, either wired or wireless. Note that the various data acquired by the communication interface provided in interface unit 12 described above does not necessarily have to be input to the communication interface provided in interface unit 12, but may also be input to an input device provided in interface unit 12.

[0043] The interface unit 12 outputs, for example, various types of information. The interface unit 12 includes a display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, or an organic EL (Electro-Luminescence) display. The interface unit 12 may be configured as an interface that connects these display devices to the learning device 1. The display device included in the interface unit 12 outputs, for example, information input to a communication interface or input device of the interface unit 12.

[0044] The storage unit 13 is configured using a computer-readable storage medium device (non-transitory computer-readable recording medium) such as a magnetic hard disk drive or a semiconductor storage device. The storage unit 13 stores various information related to the learning device 1. The storage unit 13 stores various information generated by the operation of the control unit 11, for example. The storage unit 13 stores information acquired by the interface unit 12, for example.

[0045] 3 is a diagram showing an example of the flow of processing executed by the learning device 1 in the embodiment. The control unit 11 acquires a pair of learning input data and a learning label (step S101). Next, the control unit 11 executes a learning process (step S102). By executing the learning process, a trained estimation model is obtained.

[0046] <Example of hardware configuration of estimation device 2> 4 is a diagram illustrating an example of a hardware configuration of the estimation device 2 according to an embodiment. The estimation device 2 includes a control unit 21 (an example of an estimation unit) including a processor 93 and a memory 94 connected by a bus, and executes a program. By executing the program, the estimation device 2 functions as a device including the control unit 21, an interface unit 22, and a storage unit 23.

[0047] More specifically, the processor 93 reads out a program stored in the storage unit 23 and stores the read program in the memory 94. The processor 93 executes the program stored in the memory 94, causing the estimation device 2 to function as a device including the control unit 21, the interface unit 22, and the storage unit 23.

[0048] The control unit 21 controls the operation of each functional unit included in the estimation device 2. The control unit 21 executes, for example, a trained estimation model. The control unit 21 acquires, for example, information to be input to the trained estimation model (hereinafter referred to as "estimated input data").

[0049] The control unit 21 acquires, for example, information stored in the storage unit 23. The process of acquiring information stored in the storage unit 23 is specifically a read process.

[0050] The interface unit 22 includes a communication interface for connecting the estimation device 2 to an external device. The interface unit 22 communicates with the external device via wired or wireless communication. The external device is, for example, a device that has transmitted estimated input data. In such a case, the interface unit 22 acquires estimated input data by communicating with the device that has transmitted the estimated input data. The external device is, for example, the learning device 1. In such a case, the interface unit 22 acquires a trained estimation model by communicating with the learning device 1.

[0051] The interface unit 22 may be configured to include input devices such as a mouse, a keyboard, or a touch panel. The interface unit 22 may be configured as an interface that connects these input devices to the estimation device 2. In this way, the interface unit 22 accepts input of various information to the estimation device 2 via the input device, either wired or wireless. Note that the various data acquired by the communication interface included in the interface unit 22 described above does not necessarily need to be input to the communication interface included in the interface unit 22, and may be input to an input device included in the interface unit 22.

[0052] The interface unit 22 outputs, for example, various types of information. The interface unit 22 includes a display device such as a CRT display, a liquid crystal display, or an organic EL display. The interface unit 22 may be configured as an interface that connects these display devices to the estimation device 2. The display device included in the interface unit 22 outputs, for example, information input to a communication interface or an input device of the interface unit 22.

[0053] The storage unit 23 is configured using a computer-readable storage medium device (non-transitory computer-readable recording medium) such as a magnetic hard disk device or a semiconductor storage device. The storage unit 23 stores various information related to the estimation device 2. The storage unit 23 stores various information generated by the operation of the control unit 21, for example. The storage unit 23 stores information acquired by the interface unit 22, for example.

[0054] 5 is a flowchart showing an example of the flow of processing executed by the estimation device 2 in the embodiment. The control unit 21 acquires estimated input data (step S201). Next, the control unit 21 executes the trained estimation model on the acquired estimated input data (step S202). By the processing of step S202, a result according to the estimated input data is estimated. In this way, in step S202, the control unit 21 performs estimation using the trained estimation model.

[0055] <Experimental Results> Below are examples of experimental results verifying the accuracy of estimations made by the trained estimation model. The number of wave functions used for each element was set to two (u=2). In the experiment, the estimation accuracy of each technique was verified: NNP (hereinafter referred to as "Technology 1"), which estimates the energy of the analyzed system based on Behler-Parrinello-type descriptors; NNP (hereinafter referred to as "Technology 2"), which estimates the energy of the analyzed system based on electron density; and the trained estimation model. When using charge density, there is only one function, so u=1. Note that Technology 2 estimates energy based on electron density; more specifically, it treats electron density three-dimensionally and estimates energy based on this three-dimensional electron density.

[0056] FIG. 6 is a first diagram showing an example of experimental results in the embodiment. FIG. 7 is a second diagram showing an example of experimental results in the embodiment. More specifically, FIG. 6 is a diagram showing the root mean square errors of the estimation results by the first technology, the second technology, and the trained estimation model. FIG. 7 is a diagram showing the coefficient of determination R 2 Shows.

[0057] In Figures 6 and 7, "Behler-Parrinello" indicates the first technique, "Density" indicates the second technique, and "Present method" indicates the trained estimation model. In Figures 6 and 7, the "Composition" column indicates the system to be analyzed. Therefore, for example, "Li 24 P4S 20 The Cl4" row indicates that the analysis target system is a semiconductor crystal. 24 P4S 20 Indicates that it was CL4.

[0058] The results in Figure 6 show that the estimation accuracy of the trained estimation model is higher than that of the first and second techniques, regardless of the system being analyzed. 2Since a larger value indicates higher accuracy, the results in Figure 7 show that the estimation accuracy of the trained estimation model is higher than that of the first and second techniques.

[0059] The learning device 1 configured in this way executes a learning process to obtain a trained estimation model. The learning process produces the effects described above in <Effects of the Learning Process>. Therefore, the learning device 1 can improve the accuracy of total energy estimation by NNP.

[0060] Furthermore, the estimation device 2 configured in this manner performs estimation using the learned estimation model obtained by the learning device 1. This makes it possible to improve the accuracy of total energy estimation by NNP.

[0061] Furthermore, the estimation system 100 configured in this manner includes the learning device 1. Therefore, it is possible to improve the accuracy of the total energy estimation by NNP.

[0062] (Variation) As described above, the feature to be evaluated represents the sum of three-dimensional wave functions. That is, the feature to be evaluated represents the sum of wave functions at each position in three-dimensional space. Coordinates are required to represent each position in space. The coordinates used by the feature to be evaluated to represent the sum of three-dimensional wave functions may be localized coordinates.

[0063] Localized coordinates are coordinates determined for each atom in a system under analysis, with each atom as the origin. The axes of the localized coordinates may be, for example, three axes: an axis connecting the origin and the atom nearest to the atom at the origin (hereinafter referred to as the "first axis"), an axis connecting the origin and the second nearest atom of the atom at the origin (hereinafter referred to as the "second axis"), and an axis perpendicular to the first and second axes (hereinafter referred to as the "third axis"). The axes of the localized coordinates may be, for example, a total of three axes: a pair of two orthogonal axes in a plane spanned by the first and second axes, different from the pair of the first and second axes, and the third axis.

[0064] The learning device 1 and the estimation device 2 may each be implemented using a plurality of information processing devices communicably connected via a network. In this case, each of the processes executed by the control unit 11 and the control unit 21 may be executed in a distributed manner by a plurality of information processing devices.

[0065] Note that all or part of the functions of the learning device 1 and the estimation device 2 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array). The program may be recorded on a computer-readable recording medium. Examples of computer-readable recording media include portable media such as flexible disks, magneto-optical disks, ROMs, and CD-ROMs, and storage devices such as hard disks built into computer systems. The program may be transmitted via a telecommunications line.

[0066] Although an embodiment of the present invention has been described above in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and includes designs within the scope of the gist of the present invention. [Explanation of symbols]

[0067] 100...estimation system, 1...learning device, 2...estimation device, 11...control unit, 12...interface unit, 13...storage unit, 21...control unit, 22...interface unit, 23...storage unit, 91...processor, 92...memory, 93...processor, 94...memory

Claims

1. a control unit that performs learning of an estimation model, which is a mathematical model that estimates the energy of the atom of the evaluation object based on an evaluation object feature quantity that represents a u-th sum, which is a sum from a 1st sum to a U-th sum, which is a sum of: a three-dimensional wave function that represents the u-th (u is an integer of 1 to U, inclusive, and U is an integer of 1 or more) atomic orbital of an atom of the evaluation object located in a system including one or more atoms, counting from the highest energy of the occupied level; and a three-dimensional wave function of each atomic orbital of each atom of the system different from the evaluation object, which is the u-th atomic orbital counting from the highest energy of the occupied level, and which is within a predetermined range of distance from the evaluation object. Equipped with In the learning, the estimation model is updated so as to reduce the difference between the sum of results obtained by executing the estimation model for each atom in the system and the energy of the system estimated by a density functional theory for the system. Learning device.

2. The three-dimensional wave function is a three-dimensional radial wave derivative. The learning device according to claim 1 .

3. The system is part of a semiconductor crystal. The learning device according to claim 1 .

4. a control unit that performs learning of an estimation model, which is a mathematical model that estimates the energy of the atom to be evaluated based on an evaluation object feature quantity that represents a u-th sum, which is a sum, from a 1st sum to a U-th sum, of: a three-dimensional wave function that represents the u-th atomic orbital (u is an integer of 1 to U, U is an integer of 1 or more) counting from the highest energy of an occupied level of an atom to be evaluated that is located in a system including one or more atoms; and a three-dimensional wave function of each atomic orbital that is the u-th atomic orbital counting from the highest energy of an occupied level of each atom in the system that is different from the evaluation object and is located within a predetermined range at a distance from the evaluation object; and An estimation device comprising:

5. a control unit that performs learning of an estimation model, which is a mathematical model that estimates energy of an atom of an evaluation object, based on an evaluation object feature quantity that represents a u-th sum, which is a sum, from a 1st sum to a U-th sum, of: a three-dimensional wave function that represents an atomic orbital that is a u-th atomic orbital (u is an integer of 1 to U, U is an integer of 1 or more) counting from the highest energy of an occupied level of an atom of an evaluation object located in a system including one or more atoms; and a three-dimensional wave function of each atomic orbital that is a u-th atomic orbital counting from the highest energy of an occupied level of each atom in the system that is different from the evaluation object and is within a predetermined range of distance from the evaluation object; and a control step in which the control unit learns the estimation model; A learning method that has

6. an estimation method performed by an estimation device comprising an estimation unit that performs estimation using the trained estimation model obtained by a learning device, the estimation method comprising: a control unit that performs learning of an estimation model that is a mathematical model that estimates energy of an atom of an evaluation object, based on an evaluation object feature quantity that represents a 1st sum to a Uth sum, the 1st sum being a sum of: a three-dimensional wave function that represents a u-th atomic orbital (u is an integer of 1 to U, inclusive, U is an integer of 1 or more) counting from the highest energy of an occupied level of an atom of the evaluation object located in a system including one or more atoms; and a three-dimensional wave function of each atomic orbital that is the u-th atomic orbital counting from the highest energy of an occupied level of each atom in the system that is different from the evaluation object and is within a predetermined range of distance from the evaluation object; an estimation step in which the estimation unit performs estimation using the trained estimation model; An estimation method having:

7. A program for causing a computer to function as the learning device according to any one of claims 1 to 3.

8. A program for causing a computer to function as the estimation device according to claim 4.

Images