Training apparatus, estimation apparatus, training method, estimation method, and program

Abstract

The objective is to improve the estimation accuracy of total energy by using neural network potential (NNP). One aspect of the present invention is a training apparatus comprising a control unit for training an estimation model, which is a mathematical model for estimating, on the basis of a feature quantity to be evaluated representing from a first sum to a u-th sum, the energy of an atom to be evaluated, wherein the u-th sum is the sum of: a three-dimensional wave function representing a u-th atomic orbit from the one having the largest occupied energy level as an atomic orbit of the atom to be evaluated located in a system including one or multiple atoms; and a three-dimensional wave function of each u-th atomic orbit from the one having the largest occupied energy level as an atomic orbit of each atom within a predetermined range of distance from the object to be evaluated from among atoms in a system different from that of the object to be evaluated, and, in training, the estimation model is updated such that 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 is reduced.

Description

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

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

[0002] This application claims priority to Japanese Application No. 2024-056799, filed March 29, 2024, the entire disclosure of which is incorporated herein by reference.

[0003] Density functional methods are being used to explore materials for purposes such as new drug development and improving the performance of semiconductor devices. However, density functional method calculations are computationally expensive, and the cell size (the size of the periodic unit cell of a crystal) that allows composition exploration is limited to about 200 atoms, making large-scale material exploration beyond that difficult. For example, reproducing the composition of trace dopants in solid electrolytes requires a cell size of 500 atoms or more, making sufficient material exploration impossible.

[0004] Therefore, active research is being conducted to reduce computational costs by modeling interatomic potentials using neural networks (Patent Document 1 and Non-Patent Documents 1 to 3). In this approach, training data is generated from density functional method calculations of relatively small-scale systems, and a mathematical model, commonly called a neural network potential (NNP), is developed to accurately reproduce the results. Using NNP, the computational costs of interatomic forces and total energy are significantly reduced compared to density functional method calculations. Therefore, it is being applied to molecular dynamics calculations of large-scale systems.

[0005] <Prior Art Literature>

[0006] [Patent Document]

[0007] Patent Document 1: Specification of U.S. Patent Publication No. 2022 / 0207393

[0008] [Non-patent literature]

[0009] 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)

[0010] Non-patent Document 2: AP Bartok et al. “Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons”, Phys. Rev. Lett. Vol. 104, pp. 136403(2010)

[0011] Non-patent Document 3: AP Thompson, et al. “Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials.” Journal of Computational Physics 285 (2015): 316-330.

[0012] However, the NNPs proposed so far have had low prediction accuracy for total energy. Consequently, the interpretation of physical properties that require calculation of total energy, such as material formation energy and elastic properties, has been difficult.

[0013] In consideration of the above circumstances, the present invention aims to provide a technique for improving the accuracy of estimation of total energy by neural network potential (NNP).

[0014] One embodiment of the present invention comprises a control unit that learns an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated, based on an evaluation target feature quantity representing a first sum to the u-th sum, which is a three-dimensional wave function representing an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with the largest occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation target, the atomic orbital being the u-th from the side with the largest occupied level energy, and

[0015] In the above learning, the learning device is one in which the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small.

[0016] One embodiment of the present invention comprises a control unit that learns an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated, based on an evaluation target feature quantity representing a first sum to the u-th sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation target, the atomic orbital being the u-th atomic orbital from the side with a large occupied level energy, and

[0017] In the above learning, the learning device is provided with an estimation unit that performs estimation using the estimation model acquired by the learning device, in which the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small.

[0018] One embodiment of the present invention comprises a control unit that learns an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated, based on an evaluation target feature quantity representing a first sum to the u-th sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation target, the atomic orbital being the u-th atomic orbital from the side with a large occupied level energy, and

[0019] In the above learning, the learning method executed by the learning device is such that the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small.

[0020] The above control unit is a learning method having a control step for performing learning of the above estimation model.

[0021] One embodiment of the present invention comprises a control unit that learns an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated, based on an evaluation target feature quantity representing a first sum to the u-th sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation target, the atomic orbital being the u-th atomic orbital from the side with a large occupied level energy, and

[0022] In the above learning, the estimation method is performed by an estimation device having an estimation unit that performs estimation using the estimation model acquired by the learning device, in which the estimation model is updated so that the difference between the sum of the results of the estimation model being executed for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small,

[0023] The above estimation method has an estimation step that performs estimation using the above estimation model for which learning has been completed.

[0024] One aspect of the present invention is a program for causing a computer to function as the learning device.

[0025] One embodiment of the present invention is a program for causing a computer to function as the above estimation device.

[0026] According to the present invention, the accuracy of estimation of total energy by neural network potential (NNP) can be improved.

[0027] Figure 1 is an explanatory diagram illustrating an estimation system according to an embodiment.

[0028] Figure 2 is a drawing showing an example of a hardware configuration of a learning device according to an embodiment.

[0029] Figure 3 is a flowchart showing an example of the flow of processing executed by a learning device according to an embodiment.

[0030] Fig. 4 is a drawing showing an example of the hardware configuration of an estimation device according to an embodiment.

[0031] Figure 5 is a flowchart showing an example of the flow of processing executed by an estimation device according to an embodiment.

[0032] Figure 6 is a first drawing showing an example of an experimental result according to an embodiment.

[0033] Figure 7 is a second drawing showing an example of experimental results according to an embodiment.

[0034] Fig. 1 is a 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 learned mathematical model obtained by the learning device (1). Meanwhile, the learned mathematical model obtained by the learning device (1) is, specifically, a learned estimation model (hereinafter referred to as a “learned estimation model”) described below. The learned estimation model is a type of so-called neural network potential (NNP).

[0035] The learning device (1) has a control unit (11) having a processor (91) such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), or an NPU (Neural Network Processing Unit) connected by a bus, and a memory (92). The control unit (11) executes, for example, a learning process. The learning process is a process of acquiring a learned estimation model by performing learning of an estimation model, which is a mathematical model of a learning target, until a predetermined condition for the end of learning (hereinafter referred to as a “learning end condition”) is satisfied.

[0036] The estimation model is a mathematical model that estimates the energy of the target atom based on the target feature quantity. The target feature quantity is a quantity that represents the u-sum (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) from the first sum to the u-sum. The u-sum is the sum of the three-dimensional wave function representing the u-th central atomic orbital and the three-dimensional wave function representing the u-th peripheral atomic orbital.

[0037] The u-th central atomic orbital is the atomic orbital of the atom to be evaluated located within the system of the analysis target that includes one or more atoms (hereinafter referred to as the “analysis target system”), and is the u-th atomic orbital from the side with the highest occupied level energy.

[0038] The u-th peripheral atomic orbital is the atomic orbital of each atom whose distance from the evaluation target is within a predetermined range among the peripheral atoms, and is the u-th atomic orbital from the one with the highest occupied level energy. The peripheral atoms are atoms in the analysis target system that are different from the evaluation target.

[0039] For example, if the target system to be analyzed is Li6PS5Cl, and the atom to be evaluated is S, the surrounding atoms are, for example, Li, P, and Cl. In this case and when u=1, the u-th central atomic orbital is a 3p orbital, the u-th central atomic orbital of one surrounding atom Li is a 2s orbital, and the u-th central atomic orbitals of the other surrounding atoms P and Cl are 3p orbitals.

[0040] <Examples of feature quantities to be evaluated>

[0041] The feature to be evaluated is a vector, for example, represented by the following equation (1). In the example of equation (1), since the case of u = 2 is taken as an example, the number of elements in the vector is 2. However, 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. It can also be u = 1, and in this case, the feature to be evaluated is a scalar.

[0042]

[0043]

[0044] Here (n,l) i represents the principal quantum number n and the azimuthal quantum number l of the ith atom. N represents the number of atoms located within a sphere of a given radius centered on the ith atom. The given radius is, for example, 7 Å. ρ i represents the wave function of the ith atom. ρ j represents the wave function of the jth atom. The jth atom is different from the ith atom. R represents a position in three-dimensional space. r i represents the position of the ith atom in three-dimensional space. r j represents the position of the jth atom in three-dimensional space. r j represents the position of the jth atom in three-dimensional space.

[0045] For example, the evaluation target characteristic of the sulfur atom when u=2 is expressed by the following equation (3).

[0046]

[0047] In learning, for each atom within the target system, the energy of the evaluated atom is estimated based on the evaluation target feature quantity for each atom. The estimation model performs the process of estimating the energy of the evaluated atom based on the evaluation target feature quantity.

[0048] And, in learning, the estimation model is updated so that the difference between the sum of these estimated energies (i.e., the results of executing the estimation model) (i.e., the total energy) and the energy of the analysis target system estimated by the density functional method for the analysis target system becomes smaller.

[0049] Therefore, in learning an estimation model, a pair of information representing the evaluation target feature for each atom in the analysis target system (hereinafter referred to as "learning input data") and information representing the energy of the analysis target system estimated by the density functional method (hereinafter referred to as "learning label") are used for learning. The learning label is a label indicating the correct answer. Therefore, the above pair is so-called labeled learning data.

[0050] The density functional method for the target system of the interpretation may be executed by the control unit (11) during the learning process, or may be executed by a device other than the control unit (11) or 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).

[0051] Meanwhile, the three-dimensional wave function can be, for example, a three-dimensional radial wave function.

[0052] Meanwhile, the target system for interpretation can be, for example, a part of a semiconductor crystal. A semiconductor crystal is, for example, Li 24 P4S 20It's Cl4.

[0053] Meanwhile, the learning termination condition can be any condition related to the termination of learning, for example, a condition that the estimation model, which is a mathematical model of the learning target, has been updated a predetermined number of times, a condition that the change in the estimation model due to the update is smaller than a predetermined change, or a condition that all of the labeled or unlabeled learning data prepared in advance have been used.

[0054] About the effects of learning processing

[0055] As mentioned above, a three-dimensional wave function is used in learning. On the other hand, in the NNP technology described in Patent Document 1, rather than a three-dimensional wave function, a charge density (the sum of the squares of the magnitudes of the one-dimensional radial wave functions up to the uth (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)) converted into one-dimensional information by solid angle integration is used.

[0056] However, when the position of an atom changes in a three-dimensional space, the distribution of the wave function in the three-dimensional space changes. Therefore, in the case of learning by a learning device (1) that uses a value having information of a three-dimensional wave function for learning, a learning-filed mathematical model that also considers the position information of the atom is generated. On the other hand, when a charge density converted into one-dimensional information is used instead of a three-dimensional wave function, it is not three-dimensional, so the change in the distribution of the wave function in the three-dimensional space according to the change in the position of the atom cannot be sufficiently expressed.

[0057] Therefore, the learning device (1) can obtain a mathematical model with a higher estimation accuracy than the technique described in patent document 1. Since the estimation accuracy of the energy for each atom is high, the estimation accuracy of the energy of the analysis target system using the learned mathematical model acquired by the learning device (1) is also high.

[0058] <Example of hardware configuration of learning device (1)>

[0059] Fig. 2 is a diagram showing an example of the hardware configuration of a learning device (1) according to an embodiment. The learning device (1) is equipped with a control unit (11) having a processor (91) and a memory (92) connected by a bus, and executes a program. The learning device (1) functions as a device equipped with a control unit (11), an interface unit (12), and a memory unit (13) by executing a program.

[0060] More specifically, the processor (91) reads a program stored in the memory (13) and stores the read program in the memory (92). By the processor (91) executing the program stored in the memory (92), the learning device (1) functions as a device having a control unit (11), an interface unit (12), and a memory unit (13).

[0061] The control unit (11) controls the operation of each functional unit of the learning device (1). The control unit (11) acquires pairs of learning input data and learning correct data, for example, through the interface unit (12). The control unit (11) executes, for example, learning processing. Accordingly, 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 processing for acquiring the information stored in the memory unit (13) is reading.

[0062] The interface unit (12) is configured to include 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 means. The external device is, for example, a transmitter device for pairs of learning input data and learning labels. In this case, the interface unit (12) obtains pairs of learning input data and learning labels by communicating with the transmitter device for pairs of learning input data and learning labels.

[0063] The interface unit (12) may be configured to include an input device such as a mouse, a keyboard, or a touch panel. The interface unit (12) may be configured as an interface for connecting these input devices to the learning device (1). In this way, the interface unit (12) receives input of various types of information about the learning device (1) via an input device, either wired or wireless. Meanwhile, the various types of data acquired by the communication interface provided by the interface unit (12) described above do not necessarily need to be input into the communication interface provided by the interface unit (12), and may be input into the input device provided by the interface unit (12).

[0064] The interface unit (12) outputs, for example, various types of information. The interface unit (12) is configured to include, for example, 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 provided in the interface unit (12) outputs, for example, information input to a communication interface or input device of the interface unit (12).

[0065] The memory unit (13) is configured using a non-transitory computer-readable recording medium, such as a magnetic hard disk drive or a semiconductor memory device. The memory unit (13) stores various information regarding the learning device (1). The memory unit (13) stores, for example, various information generated by the operation of the control unit (11). The memory unit (13) stores, for example, information acquired by the interface unit (12).

[0066] Figure 3 is a diagram illustrating an example of the processing flow performed by a learning device (1) according to an embodiment. The control unit (11) acquires pairs of learning input data and learning labels (step S101). Next, the control unit (11) executes learning processing (step S102). By executing the learning processing, a learned estimation model is acquired.

[0067] <Example of hardware configuration of estimation device (2)>

[0068] Fig. 4 is a diagram showing an example of the hardware configuration of an estimation device (2) according to an embodiment. The estimation device (2) includes a control unit (21) (an example of an estimation unit) having a processor (93) and a memory (94) connected by a bus, and executes a program. The estimation device (2) functions as a device including a control unit (21), an interface unit (22), and a memory unit (23) by executing a program.

[0069] More specifically, the processor (93) reads a program stored in the memory (23) and stores the read program in the memory (94). By the processor (93) executing the program stored in the memory (94), the estimation device (2) functions as a device having a control unit (21), an interface unit (22), and a memory unit (23).

[0070] The control unit (21) controls the operation of each functional unit of the estimation device (2). The control unit (21) executes, for example, a learned estimation model. The control unit (21) acquires, for example, information input to the learned estimation model (hereinafter referred to as “estimation input data”).

[0071] The control unit (21) acquires, for example, information stored in the memory unit (23). The processing of acquiring information stored in the memory unit (23) is, specifically, reading.

[0072] The interface unit (22) is configured to include 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 means. The external device is, for example, a device that is a transmitter of estimation input data. In this case, the interface unit (22) obtains estimation input data by communicating with the device that is a transmitter of estimation input data. The external device is, for example, a learning device (1). In this case, the interface unit (22) obtains a learned estimation model by communicating with the learning device (1).

[0073] The interface unit (22) may be configured to include an input device 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) receives input of various types of information for the estimation device (2) via an input device, either wired or wireless. Meanwhile, the various types of data acquired by the communication interface provided by the interface unit (22) described above do not necessarily need to be input to the communication interface provided by the interface unit (22), and may be input to the input device provided by the interface unit (22).

[0074] The interface unit (22) outputs, for example, various types of information. The interface unit (22) is configured to include, for example, 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 provided in the interface unit (22) outputs, for example, information input to the communication interface or input device of the interface unit (22).

[0075] The memory unit (23) is configured using a non-transitory computer-readable recording medium, such as a magnetic hard disk drive or a semiconductor memory device. The memory unit (23) stores various information regarding the estimation device (2). The memory unit (23) stores, for example, various information generated by the operation of the control unit (21). The memory unit (23) stores, for example, information acquired by the interface unit (22).

[0076] Fig. 5 is a flowchart illustrating an example of a processing flow executed by an estimation device (2) according to an embodiment. The control unit (21) acquires estimation input data (step S201). Next, the control unit (21) executes a learned estimation model on the acquired estimation input data (step S202). Through the processing of step S202, a result according to the estimation input data is estimated. In this way, in step S202, the control unit (21) performs estimation using the learned estimation model.

[0077] Experimental Results

[0078] Here are examples of experimental results verifying the accuracy of estimation by a learned estimation model. The number of wave functions used in each element was 2 (u=2). In the experiment, the estimation accuracy of each technique of the NNP (hereinafter referred to as the "first technique") that estimates the energy of the analysis target system based on a Behler-Parrinello type descriptor, the NNP (hereinafter referred to as the "second technique") that estimates the energy of the analysis target system based on the electron density, and the learned estimation model were verified. When the charge density is used, there is only one function, so u=1. On the other hand, the second technique is a technique that estimates energy based on the electron density, but more specifically, it is a technique that treats the electron density three-dimensionally and estimates energy based on the three-dimensional electron density.

[0079] Fig. 6 is a first drawing showing an example of an experimental result according to an embodiment, and Fig. 7 is a second drawing showing an example of an experimental result according to an embodiment. More specifically, Fig. 6 is a drawing showing the root mean square error of each estimation result by the first technique, the second technique, and the learned estimation model. Fig. 7 is a drawing showing the coefficient of determination R of each of the first technique, the second technique, and the learned estimation model. 2 It represents.

[0080] In Figures 6 and 7, "Behler-Parrinello" represents the first technique, "Density" represents the second technique, and "Present method" represents the learned estimation model. In Figures 6 and 7, the column "Composition" represents the analysis target system. Therefore, for example, "Li 24 P4S 20 The row of Cl4" is the LI of the semiconductor crystal, which is the target of interpretation. 24 P4S 20 Indicates that it is CL4.

[0081] The results in Figure 6 show that, regardless of the target system for interpretation, the estimation accuracy of the learning-based estimation model is higher than that of the first and second techniques. R 2 Since a larger value indicates higher precision, the results in Fig. 7 indicate that the estimation precision of the learning-fill estimation model is higher than that of the first and second techniques.

[0082] The learning device (1) configured in this manner executes a learning process to acquire a learning-based estimation model. The learning process produces the effects described in the aforementioned "Effects of Learning Processing." Consequently, the learning device (1) can improve the accuracy of the overall energy estimation by NNP.

[0083] In addition, the estimation device (2) configured in this manner performs estimation using the learning-based estimation model acquired by the learning device (1). As a result, the estimation accuracy of the total energy by NNP can be improved.

[0084] In addition, the estimation system (100) configured in this manner is equipped with a learning device (1). This allows the estimation accuracy of the total energy by NNP to be improved.

[0085] (variant example)

[0086] Meanwhile, the feature quantity to be evaluated represents the sum of three-dimensional wave functions, as described above. In other words, the feature quantity to be evaluated represents the sum of wave functions at each location in three-dimensional space. Coordinates are required to represent each location within space. The coordinates used to represent the sum of three-dimensional wave functions for the feature quantity to be evaluated can be local coordinates.

[0087] Local coordinates are coordinates determined for each atom within the analysis target system, and are coordinates with each atom as the origin. The axes of the local coordinates may be three axes, for example, an axis connecting the nearest atom of the atom at the origin and the origin (hereinafter referred to as the “first axis”), an axis connecting the second nearest atom of the atom at the origin and the origin (hereinafter referred to as the “second axis”), and an axis orthogonal to the first and second axes (hereinafter referred to as the “third axis”). The axes of the local coordinates may be three axes, for example, a total of two axes within a plane extended by the first and second axes, including a pair of two axes orthogonal to the pair of the first and second axes and the third axis.

[0088] Meanwhile, the learning device (1) and the estimation device (2) may each be implemented using multiple information processing devices that are connected to each other in a manner that allows communication via a network. In this case, each process executed by the control unit (11) and each process executed by the control unit (21) may be executed in a distributed manner by multiple information processing devices.

[0089] Meanwhile, all or part of each function of the learning device (1) and the estimation device (2) may be realized using hardware such as an Application Specific Integrated Circuit (ASIC), a Programmable Logic Device (PLD), or a Field Programmable Gate Array (FPGA). The program may be recorded on a computer-readable recording medium. The computer-readable recording medium is, for example, a transportable / movable medium such as a flexible disk, a magneto-optical disk, a ROM, or a CD-ROM, or a storage device such as a hard disk built into a computer system. The program may be transmitted via a telecommunication line.

[0090] Above, the embodiments of the present invention have been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and designs that do not deviate from the scope of the present invention are also included.

Claims

1. A control unit is provided for learning an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated based on a feature quantity of the evaluation object representing a first sum to the u-th sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation object, the distance from the evaluation object being within a predetermined range, In the above learning, the learning device is such that the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small.

2. In paragraph 1, A learning device wherein the above three-dimensional wave function is a three-dimensional radial wave function.

3. In paragraph 1, The above system is a learning device that is part of a semiconductor crystal.

4. A control unit is provided for learning an estimation model, which is a mathematical model for estimating the energy of the atom to be evaluated, based on an evaluation target feature quantity representing a first sum to a u-sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation target, the distance from the evaluation target being within a predetermined range, In the above learning, an estimation device having an estimation unit that performs estimation using the estimation model acquired by the learning device, in which the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small.

5. A control unit is provided for learning an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated, based on a feature quantity of the evaluation object representing a first sum to the u-sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation object, the distance from the evaluation object being within a predetermined range, In the above learning, the learning method executed by the learning device is such that the estimation model is updated so that the difference between the sum of the results of executing the estimation model for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small. A learning method, wherein the control unit has a control step for performing learning of the estimation model.

6. A control unit is provided for learning an estimation model, which is a mathematical model for estimating the energy of an atom to be evaluated based on a feature quantity of the evaluation object representing a first sum to the u-sum, which is a sum of a three-dimensional wave function representing an atomic orbital of an atomic orbital of an atom to be evaluated located in a system including one or more atoms, which is the u-th atomic orbital from the side with a large occupied level energy (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), and a three-dimensional wave function of each atomic orbital of an atom in the system other than the evaluation object, the distance from the evaluation object being within a predetermined range, In the above learning, the estimation method is performed by an estimation device having an estimation unit that performs estimation using the estimation model acquired by the learning device, in which the estimation model is updated so that the difference between the sum of the results of the estimation model being executed for each atom in the system and the energy of the system estimated by the density functional method for the system becomes small, An estimation method having an estimation step for performing estimation using the estimation model for which the estimation part has completed learning.

7. A program for making a computer function as a learning device as described in any one of paragraphs 1 to 3.

8. A program for making a computer function as the estimation device described in Article 4.

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