Information processing device, information processing method, and program

Abstract

[Problem] To provide a highly accurate method for analyzing an atomic structure. [Solution] This information processing device comprises at least one memory and at least one processor. The at least one processor acquires a first result by analyzing an atomic structure in a first mode, acquires a second result by analyzing the atomic structure in a second mode, and acquires a third result on the basis of the first result, the second result, and a prescribed index.

Description

Information processing device, information processing method, and program

[0001] This disclosure relates to an information processing device, an information processing method, and a program.

[0002] Density functional theory (DFT) calculations used to generate training data for machine learning potentials (NNPs) face the challenge of improving the accuracy of reproducing transition metal oxides such as iron(II) oxide (FeO). The Hubbard-U correction is often used to address this challenge. However, the Hubbard-U correction requires defining scalar parameters for each element. These parameters are not uniquely determined even for the same element; appropriate values ​​may differ depending on the composition and structure, and different parameters may be used for the same element in different publications. Furthermore, it is known that applying the Hubbard-U correction to metals can lead to erroneous results.

[0003] The Hubbard-U correction is performed, for example, by constructing a computational database and using this database. The construction of this computational database is performed as follows, for example, when generating training data for NNP using DFT calculations: For some transition metal elements, the following steps are performed: (1) determine scalar values ​​for each element, (2) determine the necessity of correction using compositional information in a rule-based manner, and (3) if it is determined in (2) that correction is necessary, apply the Hubbard-U correction using the value determined in (1); if it is determined in (2) that correction is unnecessary, do not apply the Hubbard-U correction. By training NNP using the training data generated by this procedure, users can analyze the target atomic structure with NNP without explicitly specifying whether or not to apply the correction.

[0004] However, the conventional techniques described above have the problem that the output of NNP reflects whether or not corrections were applied during the generation of training data, and the application of corrections may switch between analysis targets, potentially leading to inconsistencies in analysis results. For example, Fe ∞ O1, Fe 1000 With compositions like O1, no correction is needed, whereas Fe 10While some adjustments are needed, such as requiring a weaker correction for O1 and a correction for FeO, or requiring no correction for Fe itself but a correction for FeO, and a weaker correction near the interface, it is difficult to properly implement these adjustments, and there is a high probability that some inconsistency will occur.

[0005] U.S. Patent Application Publication No. 2024 / 0105288, U.S. Patent Application Publication No. 2024 / 0395366

[0006] One of the non-limiting problems that embodiments of this disclosure aim to solve is to provide a highly accurate method for analyzing atomic structures.

[0007] According to one embodiment, the information processing device comprises at least one memory and at least one processor. The at least one processor obtains a first result by analyzing the atomic structure in a first mode, obtains a second result by analyzing the atomic structure in a second mode, and obtains a third result based on the first result, the second result and a predetermined index.

[0008] A flowchart showing an example of processing in an information processing device according to one embodiment. A flowchart showing an example of processing in an information processing device according to one embodiment. A block diagram showing an example of implementation of an information processing device according to one embodiment.

[0009] The contents of U.S. Patent Application Publication No. 2024 / 0105288 and U.S. Patent Application Publication No. 2024 / 0395366 are incorporated herein by reference.

[0010] The problems that the embodiments of this disclosure aim to solve are not limited to those described above, but may also include, as examples of several other problems, the problems corresponding to the effects described in the embodiments. That is, any problem corresponding to at least one of the effects described in the description of the embodiments of this disclosure may be the problem that the embodiments of this disclosure aim to solve. One of the non-limiting problems that the embodiments of this disclosure aim to solve is to switch between correction on and off without inconsistency and without user specification. Another non-limiting problem that the embodiments of this disclosure aim to solve is to apply appropriate corrections on an atom-by-atom / structure-by-structure basis, rather than having a binary choice of correction on or off.

[0011] The following drawings and descriptions of embodiments are for illustrative purposes only and do not limit the present invention. While this disclosure describes processing by an information processing device, this description can be implemented using one or more processors in one information processing device, or one or more processors in multiple information processing devices. When simply referred to as an information processing device, it means that a processor appropriate for the described operation is used, depending on the context.

[0012] (First Embodiment)

[0013] In this embodiment, the information processing device learns target NNPs using two types of databases: one with Hubbard-U correction and one without. The information processing device may be configured to operate in two modes: with correction and without correction. This operating mode can be realized, for example, using the technology described in U.S. Patent Application Publication No. 2024 / 0105288. As a modification, the information processing device can also learn two different NNPs: one learned in the database with correction and another in the database without correction.

[0014] FIG. 1 is a flowchart showing an example of the processing of an information processing apparatus according to an embodiment. First, the information processing apparatus acquires an atomic structure to be processed (S100). This atomic structure is data indicating an object for which features, such as energy, are to be inferred. The information processing apparatus can acquire atomic structure data, for example, in a format that is input to the NNP as a structure for which features are to be acquired. As will be described later, this atomic structure may be in a format that is input to a statistical model that acquires a scalar value β(r), or may include data in a format that is input to the statistical model as part of the atomic structure data.

[0015] The information processing apparatus acquires a first result for the structure from the acquired atomic structure (S102). The first result is data acquired from the atomic structure in the first mode. As a non-limiting example, the first result may be an energy value acquired under conditions with Hubbard-U correction.

[0016] The information processing apparatus acquires a second result for the structure from the acquired atomic structure (S104). The second result is data acquired from the atomic structure in the second mode. As a non-limiting example, the second result may be an energy value acquired under conditions without Hubbard-U correction.

[0017] The information processing apparatus acquires a predetermined index for the structure from the acquired atomic structure (S106). The predetermined index is, for example, a scalar value and is a value corresponding to β(r) described later.

[0018] The information processing apparatus acquires a third result based on the first result, the second result, and the predetermined index acquired in S102, S104, and S106 (S108). The third result is a feature amount in which the first mode and the second mode for the atomic structure are mixed at an appropriate ratio. As a non-limiting example, the third result indicates a feature amount with Hubbard-U correction applied to an appropriate degree.

[0019] Note that the execution order of S102, S104, and S106 is not limited to that shown in FIG. 1. The order of these processes may be changed, or at least two processes may be executed in parallel. For example, the information processing apparatus may be configured to execute the processes of S102 and S104 in parallel (multi-threaded or multi-headed), and may further execute the process of S106 in parallel.

[0020] Hereinafter, the details of the above processes will be described.

[0021] The information processing apparatus obtains, as a scalar value β(r), the necessity of correction for the atomic structure r to be analyzed by using a statistical model. r is, for example, a vector indicating the atomic structure to be analyzed. The atomic structure may include, as non-limiting examples, information regarding the type of atom (element, atomic number, etc.) and / or information regarding the position of the atom (three-dimensional coordinates, etc.). The atomic structure may also optionally include periodic boundary conditions, for example. β(r) is defined as a function that returns a scalar value within an arbitrary range, rather than a binary value of 0 and 1.

[0022] Typically, β(r) ∈ [0, 1] for all r, but it is not limited to this range. β(r) may return a scalar value according to the strength of the correction, for example, and in this case, it may be defined that a strong correction is made by returning a value greater than 1.

[0023] As a statistical model that outputs β(r), the information processing apparatus can use, as non-limiting examples, a model that uses a part of the layers of NNP (for example, from the input layer to the intermediate layer), a neural network model or a prediction model other than a neural network constructed to predict β(r).

[0024] When using an NNP intermediate layer, which is not an exhaustive example, as the statistical model that outputs β(r), the information processing device can use the technology described in U.S. Patent Application No. 2024 / 0395366. The information processing device may prepare, for example, either or both, a corrected NNP model trained on a dataset with Hubbard-U correction and an uncorrected NNP model trained on a dataset without Hubbard-U correction. These statistical models may also be pre-trained statistical models.

[0025] As an unrestricted example of a model that outputs β(r), a statistical model can be used that is trained to fit quantities such as generation energy and lattice constants obtained experimentally or through computationally expensive but highly accurate computational methods, where the NNP synthesized using β(r) is adapted. For example, in the case of highly accurate computation, a statistical model relating to β(r) can be trained to fit the force and / or total energy.

[0026] As an unrestricted example of a model that outputs β(r), if limited to Hubbard-U correction, a statistical model trained with U parameters defined by a computational method for determining U parameters for a given structure r (for example, a method using linear response theory) can be used. For example, if the U parameters defined by this method are Uref(r), and the U parameters used to construct the training dataset for the corrected NNP model are Uorig, then β(r) can be set by training such that β(r) = Uref(r) / Uorig. The above is the simplest example, and it is also possible to use a more complex function for Uref(r) rather than a simple linear function.

[0027] Furthermore, just as with results obtained from experiments or highly accurate computational methods, β(r) can be trained to fit the results of DFT calculations obtained using computationally determined U parameters.

[0028] Regardless of the method used, additional constraints can be added to ensure that β(r) is continuous with respect to r and that β(r) does not change abruptly in response to small variations in r. By imposing such constraints, it is possible to suppress discontinuities or abrupt changes in the results synthesized using β(r) in response to small variations in r, i.e., atomic positions, thereby increasing the likelihood of achieving more stable simulations.

[0029] The information processing device may obtain β(r) using either the corrected NNP model's intermediate layer or the uncorrected NNP model's intermediate layer. Alternatively, the information processing device may obtain β(r) using both the corrected NNP model's intermediate layer and the uncorrected NNP model's intermediate layer.

[0030] If a neural network model, a non-exclusive example, is used as the statistical model that outputs β(r), the information processing device can use a statistical model trained to obtain β(r) using a dataset containing atomic coordinates, elements, atomic structure, or some other feature as training data.

[0031] In a non-limiting example of an embodiment of the present disclosure, the input and output of a statistical model can be summarized as follows: In its basic form, the input of the statistical model is an atomic structure (which may be the same as the input of NNP), and the output is β(r) as an index of the entire atomic structure or an index of each atom contained in the atomic structure.

[0032] As another, though not limited, example, the input to a statistical model may be a combination of atomic structure and features. The features may be the output of the hidden layer when atomic structure is input to an NNP, or they may be features extracted based on other atomic structures, or they may be a combination of these.

[0033] As another, though not limited, example, the input to a statistical model may be features. These features may be the outputs of the hidden layers when input to an NNP of atomic structure, as described above, or features extracted based on other atomic structures, or a combination of these.

[0034] This neural network model may be, for example, a graph neural network, a network similar to an NNP, or another architecture, or a combination of any of these. This neural network model can be constructed as a statistical model that outputs β(r) when input data such as the coordinates of atoms, elements, or other features, or a combination of these.

[0035] When using a statistical model that outputs β(r), and not limited to neural network models (an example of an unspecified model), the information processing device can use statistical models such as support vector regression (SVR), Gaussian process regression, and linear regression models. Similar to the case using the neural network model described above, the information processing device can use statistical models that take atomic coordinates, elements, atomic structure, or any other feature quantities or combinations thereof as input.

[0036] The statistical models listed above, as examples without limitation, are trained and optimized to reproduce the following data, or combinations thereof: The statistical models may be trained to reproduce, for example, forces obtained using DFT calculations, energies such as atomization energy / formation energy, other physical properties (e.g., density, interatomic distance), or combinations thereof. The DFT calculations used in these statistical models may be more costly and / or produce more accurate data than the DFT calculations used to generate the data used to train the target NNP.

[0037] Furthermore, the training and optimization of this statistical model may also be performed using experimentally measured material properties. For example, the training of the statistical model can be performed using experimentally measured formation energy, three-dimensional structure of molecules and crystals, mechanical properties such as elastic constants, melting point and boiling point, other material properties, or a combination of these.

[0038] When β(r) is a rule-based statistical model, β(r) may be determined by a statistic such as the average number of oxygens present around a transition metal atom.

[0039] The statistical model that outputs β(r) desirably satisfies properties required for NNP such as translational symmetry, rotational symmetry, continuity, and differentiability with respect to the atomic structure r. More desirably, β(r) is represented by a smooth function.

[0040] For example, β(r) may be defined for each structure based on the distance and / or the number between specific elements present in the surroundings. The information processing apparatus may calculate β(r) of the atomic structure based on at least either the number of predetermined elements (e.g., oxygen) included in the atomic structure or the distance of predetermined element senses included in the atomic structure.

[0041] By using β(r) for the atomic structure r, the information processing apparatus can mix and output output values with and without the Hubbard-U correction. For example, when outputting an energy value, the output value may be calculated as follows. Here, E cor represents the energy value with the Hubbard-U correction, and E ncor represents the energy value without the Hubbard-U correction. When the mode for obtaining the energy with the Hubbard-U correction is the first mode and the mode for obtaining the energy without the Hubbard-U correction is the second mode, E cor is an example of the analysis result obtained in the first mode, and E ncor is an example of the analysis result obtained in the second mode. In the present embodiment, E cor and E ncor may be the output of the NNP.

[0042] In the case of energy, as shown in equation (1), it is a sum of scalar values, but of course, it is also possible to express vectors using a similar vector addition equation as in equation (1). This vector quantity may be, for example, a dipole moment. Furthermore, the method of this disclosure makes it possible to infer quantities represented by tensors of a higher order than vectors.

[0043] <Regarding reference values>

[0044] Energy E with and without correction cor , E ncor This can be calculated using a model with adjusted energy standards. For example, if the energy standard for the corrected output result is sufficiently smaller than the energy standard for the uncorrected output result, the calculation may result in a driving force being generated based on the standards of the two output values, and a force acting on the atoms from the uncorrected state to the corrected state.

[0045] To mitigate the effects of this driving force, the energy reference in the model used by the information processing device can be pre-adjusted.

[0046] The information processing device can, for example, use a model trained to output corrected and uncorrected energies, where the energy of a single atom in a vacuum is set to 0.

[0047] In another example, the information processing device can use a model that outputs a reference energy value determined by referencing corrections used when comparing the energy of the entire system using multiple calculation methods that have already been proposed. For example, in this embodiment, a model can be used that has a common reference value for the energy of the entire system, both with and without correction.

[0048] Furthermore, it is possible to use a model in which the formation energy of oxides is corrected for each element so that it matches the experimental value. Specifically, (formation energy) = E cor (FeO) - E ncor (Fe) - (1 / 2) E ncor (O2) + Δ(E FeΔ(E) was defined so that it is consistent with the experimental value. Fe By using this method, the reference values ​​for the output can be made the same for both the corrected and uncorrected cases.

[0049] Of course, information processing devices can also set and apply such reference values ​​to physical properties other than energy.

[0050] As described above, according to this embodiment, the information processing device can automatically perform processes such as applying Hubbard-U correction, not applying Hubbard-U correction, and / or partially applying Hubbard-U correction by obtaining the scalar value β(r) obtained from the statistical model as the degree of correction.

[0051] Applying Hubbard-U correction partially means, for example, applying a weaker or stronger Hubbard-U correction. As a result, instead of a binary choice of applying or not applying Hubbard-U correction, it becomes possible to obtain more accurate physical properties for atomic structures in intermediate states (for example, atomic structures in regions close to interfaces).

[0052] (Second Embodiment)

[0053] In the embodiments described above, calculations were performed for each atomic structure, but the embodiments of this disclosure are not limited thereto. The information processing device can, for example, acquire physical properties by mixing corrections and no corrections for each atom.

[0054] Figure 2 is a flowchart showing an example of processing in an information processing device according to one embodiment. First, the information processing device acquires the atomic structure to be processed (S200). This process is almost the same as S100 in the first embodiment described above, so the details are omitted.

[0055] The information processing device obtains a first result from the acquired atomic structure, for each atom constituting the atomic structure (S202). The first result is data obtained from the atomic structure in the first mode. In a non-limiting example, the first result in this embodiment may be the energy value for each atom constituting the atomic structure obtained under conditions with Hubbard-U correction.

[0056] The information processing device obtains a second result from the acquired atomic structure, for each atom constituting the atomic structure (S204). The second result is data obtained from the atomic structure in the second mode. In a non-limiting example, the second result in this embodiment may be the energy value for each atom constituting the atomic structure obtained under conditions without Hubbard-U correction.

[0057] The information processing device obtains a predetermined index for each atom constituting the atomic structure from the acquired atomic structure (S206). The predetermined index is, for example, a scalar value, and is β as described later. i This is the value corresponding to (r). In this embodiment, the predetermined index is a scalar value for each atom constituting the atomic structure.

[0058] The information processing device obtains atom-specific feature quantities in the atomic structure based on the first results for each atom obtained in S202, S204, and S206, the second results for each atom, and predetermined indicators for each atom, and obtains a third result based on these obtained values ​​(S208). The third result is a feature quantity obtained by mixing the first mode and the second mode for the atomic structure in an appropriate proportion. As an example, though not limited to this, the third result shows a feature quantity that has been corrected to an appropriate degree by Hubbard-U.

[0059] For example, the information processing device obtains a first result obtained for each atom, a second result obtained for each atom, and a predetermined index, and then obtains a third result, which is the characteristic value of the entire atomic structure, by calculating the sum of the obtained characteristic values.

[0060] As with the first embodiment, the execution order of S202, S204, and S206 is not limited to Figure 2. In addition to the calculation method described in the first embodiment, in this embodiment, for example, it is also possible to perform the acquisition of feature quantities and / or predetermined indices for each of multiple atoms in parallel.

[0061] The following provides a detailed explanation of the process described above.

[0062] The information processing device can use a trained and optimized NNP model (which may include a definition of a reference value) and a statistical model that obtains a value corresponding to β(r), similar to the first embodiment.

[0063] β is defined for each atom corresponding to β(r). i (r) may be determined more specifically based on the distance to one or more elemental species (e.g., oxygen) within a certain cutoff radius. In this case as well, β(r) may be defined so as not discontinuous within the cutoff radius, and furthermore, β may be defined just inside the cutoff radius. i (r) may be defined such that it can take the value exactly 0.

[0064] The information processing device determines the β of an atom based on at least one of the following: the number of predetermined elements within a predetermined distance from a certain atom, or the distance between a predetermined element within a predetermined distance from a certain atom and that atom. i You may also calculate (r).

[0065] Furthermore, the information processing device uses β(r) as defined in the first embodiment, and calculates β for each atom. i β(r) for an atomic structure may be calculated using a statistic on (r) (e.g., the mean value).

[0066] The information processing device obtains, for example, the energy value and scalar value for all atoms. Here, the energy value for the i-th atom is e i And the scalar value β iLet (r) be the value. For example, in the case of energy, the classical potential can be obtained as an additive value for each atom, so the information processing device synthesizes the energy value and scalar value for all atoms using the following formula. In this way, the information processing device, for example, uses the value that corresponds to β(r) defined for each structure in the first embodiment, as β defined for each atom. i You can perform operations using (r).

[0067] For example, in the first embodiment, β(r) is trained to minimize the energy error for each atomic structure, but in this embodiment, β i (r) is the number of β atoms i (r) By training each output, the energy of the entire structure, expressed as the sum of these outputs, is made to fit.

[0068] As described above, physical properties can be obtained by combining the output values ​​with and without Hubbard-U correction while each atom is separated. According to this embodiment, by combining the physical properties for each atom, it becomes possible to appropriately correct the physical properties for each finer region, thereby improving the accuracy of acquiring physical properties.

[0069] Although the above example concerns energy values, it is not limited to this. The information processing device can obtain physical properties that can be superimposed on individual atoms using an equation similar to equation (2).

[0070] Furthermore, β defined for each atom according to this embodiment i Using (r), it is also possible to calculate β(r) defined for each structure according to the first embodiment. For example, β for each atom included in the structure i Another approach is to calculate (r) for each atom forming the structure and obtain a statistical measure, such as the average of the scalar values ​​for each atom, as the β(r) of the structure.

[0071] (Variation 1)

[0072] In the embodiments described above, several forms of Hubbard-U correction and methods for mixing correction with and without correction have been explained, but the forms of this disclosure are not limited to these. The information processing device can be extended to calculations such as mixing various corrections with and without correction, calculation conditions, models used, and different modes, as are other examples that are not limited to these. In other words, as explained in equation (1), the presence or absence of Hubbard-U correction described above can each be considered as a form of the mode described below.

[0073] When mixing calculations in different modes (for example, with / without correction, differences in calculation conditions, and differences in models), the following formula can be used to obtain physical properties. Here, E MODE1 / MODE2 These are the energy calculated in mode 1 and mode 2, respectively, e i, MODE1 / MODE2 indicates the energy related to atom i calculated in mode 1 and mode 2, respectively.

[0074] Furthermore, in each embodiment, E MODE1 / MODE2 The analysis results, etc., may be calculated by setting Mode 1 and Mode 2 respectively within the same model, or they may be calculated from multiple models that produce outputs corresponding to each mode. i, The same applies to MODE1 / MODE2.

[0075] Equation (3) corresponds to equation (1) and can be applied to obtain material properties that can or cannot be superimposed on individual atoms. Equation (4) corresponds to equation (2) and can be applied to obtain material properties that can be superimposed on individual atoms, and can achieve more accurate calculations than equation (3) for material properties that can be superimposed.

[0076] Also, another way to express the above is as follows: E MODE2 (e i, MODE2 The scalar value corresponding to ) is β(r) (βi It is also possible to define a statistical model as (r). This is also true for the first embodiment, for example, in the first embodiment, the scalar value without Hubbard-U correction can be β(r), and a statistical model for obtaining this β(r) may be defined.

[0077] Equations (3) to (6) show that β is obtained from a single statistical model, but this is not the only way. For example, as shown in the following equation, it is also possible to obtain a scalar value using multiple statistical models defined for each mode. βMODE1 / MODE2 are scalar values ​​defined for each structure corresponding to the mode, and β i, MODE1 / MODE2 are scalar values ​​defined for each atom corresponding to a mode. The respective β values ​​in equations (3) to (8) are output from appropriate statistical models.

[0078] The information processing device can, for example, combine the results of calculation conditions suitable for molecular structures with the results of calculation conditions suitable for crystal structures. Examples of calculation conditions suitable for molecular structures include the respective modes learned for ωB97XD / 6-31G, and examples of calculation conditions suitable for crystal structures include the respective modes learned for PBE / PAW, but these are not limited to each other.

[0079] The information processing device can also utilize the above calculations to simulate reactions on solid catalyst surfaces, for example. These simulations involve the simultaneous appearance of computational targets such as crystals, surfaces, and molecules. Therefore, the information processing device can define β such that, for crystals and / or surfaces, the results of calculation conditions suitable for the crystal structure are strongly reflected, and for molecules, the results of calculation conditions suitable for the molecular structure are strongly reflected.

[0080] β may be defined using a framework that theoretically determines correction values ​​and mixing ratios for various modes.

[0081] As described above, the above embodiment may also be applied to models that predict physical properties other than energy. The information processing device can be applied, for example, to a model that predicts the band gap.

[0082] Other examples include applying this to models that predict the charge (scalar value) of each atom and the magnetic moment (vector or scalar value) of each atom. Furthermore, as mentioned above, it can also be applied to models that predict the formation energy.

[0083] As a model used by the information processing device, a new NNP may be created that has learned the values ​​(including at least one of energy, force, or stress) output by the first or second embodiment. That is, a new model may be trained using the inputs to the model at the stage of determining physical properties (for example, a model based on the calculations of equations (1) to (4)) and the physical properties for said input as a dataset. The new model may be a model of an NNP.

[0084] Furthermore, the information processing device may use interatomic potentials other than NNP as the model it employs. For example, in the first embodiment, the information processing device may use electronic state calculations or classical potentials. For example, in the second embodiment, the information processing device may use the energy of each atom (e i A potential that can output ) may also be used.

[0085] (Modification 2)

[0086] In the embodiments and modifications described above, output values ​​from two types of models are mixed, but the forms in this disclosure are not limited thereto. The information processing device can mix outputs from three or more types of NNPs or outputs from three or more types of modes. Equations (3) and (4) can be rewritten as follows when three types of outputs (including MODE3) are mixed. Here, β1 (β 1,i ), β2 (β 2,i), are scalar values ​​corresponding to Mode 1 and Mode 2, respectively, E MODE3 (E i, MODE3 ) indicates the output value for Mode 3.

[0087] Of course, even when defined by equations (5) to (8), it is possible to support three or more modes, as described above. For example, β or β corresponding to mode 1, mode 2, and mode 3, respectively. i A statistical model can be defined to output the following:

[0088] (Variation 3)

[0089] In the embodiments and modifications described above, for example, outputs in multiple modes, including corrected and uncorrected modes, were obtained from different prediction models (e.g., NNP), but the embodiments of this disclosure are not limited thereto.

[0090] The information processing device may, for example, use a single predictive model capable of simultaneously outputting features for multiple modes, thereby simultaneously outputting feature quantities for multiple modes. The information processing device can obtain the physical properties of the entire system by mixing the outputs of the multiple modes output from this predictive model. It should be noted that in this disclosure, "simultaneous" is not limited to strictly the same moment, but also includes being within a timing range with a predetermined temporal width, or outputting multiple results in the same process (for example, a process using the same model).

[0091] According to this modified version, the final result can be obtained from the output of a single model. Therefore, the information processing device can, for example, improve speed and reduce inference costs by obtaining output values ​​from different modes of the same model using multithreading.

[0092] Furthermore, this modified approach allows for the simultaneous acquisition of values ​​in different modes by using a multi-head model that enables multiple inferences for a single input r. This eliminates the need to perform NNP inference for each mode, thus reducing computational costs.

[0093] Furthermore, when calculating the force (the derivative of energy), a neural network model that outputs different modes, a statistical model that calculates β, and a single neural network model that combines these outputs to represent the energy of the entire system can be defined and operated. By backpropagating this neural network model that obtains the energy of the entire system, the force can be calculated.

[0094] When obtaining the force through backpropagation of a neural network model, the β corresponding to each atom i is used. i We also need to find the coordinate derivative of β. For example, if we consider the case of finding the position derivative of equation (4), we can see that we need the derivative of β using the product rule for differentiation. Defining this differential operation as a computation graph of a single neural network simplifies its application and makes it easier to optimize the computation graph.

[0095] In other words, when inferring force by backpropagating the energy inference model, it becomes possible to infer force by calculating dE(r) / dr including dβ(r) / dr.

[0096] For example, when the energy inference is given by equation (1), the force F(r) can be expressed as follows:

[0097] Furthermore, without being limited to this, it is also possible to implement force inference without using dβ(r) / dr. For example, in models that can output energy and force simultaneously, the scalar value β related to force can be used. f(r) may be defined separately. This implementation can reduce the inference cost by being used, as an example without limitation, when inferring force in a way that does not involve backpropagating the energy inference model.

[0098] The aspects of this disclosure can also be summarized as follows, without limitation:

[0099] (1) An information processing device comprising at least one memory and at least one processor, wherein the at least one processor obtains a first result by analyzing the atomic structure in a first mode, obtains a second result by analyzing the atomic structure in a second mode, and obtains a third result based on at least the first result, the second result and a predetermined index.

[0100] The specified index corresponds to the aforementioned β. For example, in equation (3), the first result is E MODE1 Therefore, the second result is E MODE2 And the third result is E. For example, in equation (4), the first result is Σ E i, MODE1 The second result is Σ E i, MODE2 Therefore, the third result is E.

[0101] As mentioned above, a mode can be a concept that includes various conditions for analyzing the object to be processed. Furthermore, the model used for analysis may be stored in a different storage device than the information processing device, or in a different information processing device than the information processing device. The same applies to the model used for calculating predetermined indicators, which may be stored in a different storage device than the information processing device, or in a different information processing device than the information processing device.

[0102] (2) The information processing apparatus according to (1), wherein the first result, the second result, and the third result are, respectively, energies related to the atomic structure.

[0103] (3) The information processing apparatus according to (2), wherein the first result is the energy of the atomic structure analyzed in the first mode, the second result is the energy of the atomic structure analyzed in the second mode, and the third result is the energy of the atomic structure based on at least the first mode and the second mode.

[0104] (4) The information processing apparatus according to any one of (1) to (3), wherein at least one processor obtains the third result by weighting and adding the first result and the second result based on the predetermined index.

[0105] (5) Let r be the vector representing the atomic structure, and E be the first result. cor E ncor The information processing apparatus according to any one of (1) to (4), wherein the third result is represented by the formula (3) described above, with E being the third result and β being the predetermined index which is a scalar value.

[0106] (6) The information processing apparatus according to (1) or (2), wherein the predetermined index includes an index for each atom included in the atomic structure.

[0107] (7) The information processing apparatus according to (6), wherein the first result is the energy of each atom in the atomic structure analyzed in the first mode, the second result is the energy of each atom in the atomic structure analyzed in the second mode, and the third result is the energy of the atomic structure based on at least both the first mode and the second mode.

[0108] (8) The information processing apparatus according to (1), (6), or (7), wherein at least one processor obtains the third result by weighting and adding the first result and the second result based on the predetermined index.

[0109] (9) Let r be the vector representing the atomic structure, and e be the first result corresponding to the i-th atom included in the atomic structure. i,MODE1 , the second result corresponding to the i-th atom included in the atomic structure is ei,MODE2 The information processing apparatus according to (8), wherein the third result is represented by the formula (4) described above, with E being the third result and β being the predetermined index which is a scalar value corresponding to the i-th atom included in the atomic structure.

[0110] (10) The information processing apparatus according to any one of (1) to (7), wherein at least one processor obtains the first result by operating the first model in the first mode and obtains the second result by operating the first model in the second mode.

[0111] (11) The information processing apparatus according to any one of (8), wherein the third result is the energy of the atomic structure, and the at least one processor calculates the force acting on each atom in the atomic structure by performing a backpropagation process of the first model.

[0112] (12) The information processing apparatus according to any one of (1) to (9), wherein at least one processor obtains the first result by analyzing the atomic structure using a first model and obtains the second result by analyzing the atomic structure using a second model different from the first model.

[0113] (13) The information processing apparatus according to (12), wherein the third result is the energy of the atomic structure, and the at least one processor calculates the force acting on each atom in the atomic structure by performing backpropagation processing of the first model and the second model.

[0114] (14) The information processing apparatus according to any one of (1) to (13), wherein at least one processor calculates the predetermined index using the third model.

[0115] This third model may be a model generated based on the first model of (8), or the first and / or second model of (10), or it may be a model that includes some components of these models.

[0116] This third model corresponds to the statistical model mentioned earlier.

[0117] (15) The information processing apparatus according to any one of (1) to (5), wherein the at least one processor calculates the predetermined index based on at least the distance between predetermined elements contained in the atomic structure or the number of predetermined elements.

[0118] (16) The information processing apparatus according to any one of (1) or (6) to (9), wherein the at least one processor calculates the predetermined index based on at least the number of predetermined elements contained within a predetermined distance from each atom in the atomic structure, or the distance between each atom and a predetermined element contained within a predetermined distance from each atom.

[0119] (17) The information processing apparatus described in any of (10) to (13), wherein the first model is an NNP.

[0120] (18) The information processing apparatus according to any one of (1) to (17), wherein the first mode is a mode that uses Hubbard-U correction, and the second mode is a mode that does not use Hubbard-U correction.

[0121] (19) The information processing apparatus according to any one of (1) to (17), wherein the first mode is a mode capable of performing analysis with higher accuracy than the second mode in crystal structure, and the second mode is a mode capable of performing analysis with higher accuracy than the first mode in molecular structure.

[0122] For example, inference using the first mode may be performed by a model trained with crystal structure training data for use in the analysis. In a non-limiting example, the amount of crystal structure data in the training data for the first mode may be greater than the amount of crystal structure data in the training data for the second mode.

[0123] For example, inference using the second mode may be performed by a model trained using molecular structure training data for the model used in the analysis. In a non-limiting example, the amount of molecular structure data in the training data for the second mode may be greater than the amount of molecular structure data in the training data for the first mode.

[0124] This configuration allows for more accurate feature inference even when the atomic structure includes crystalline and molecular structures, or when it includes regions that closely resemble crystalline structures and regions that closely resemble molecular structures.

[0125] The information processing apparatus according to any one of (1) to (19), wherein the at least one processor obtains one or more other results by analyzing the atomic structure in one or more other modes, and obtains the third result based on at least the first result, the second result, the one or more other results, and the predetermined index.

[0126] (21) An information processing method comprising: obtaining a first result by analyzing an atomic structure in a first mode using at least one processor; obtaining a second result by analyzing the atomic structure in a second mode; and obtaining a third result based on at least the first result, the second result and a predetermined index.

[0127] This information processing method can have the characteristics of the processing methods in the information processing devices described in (2) to (20).

[0128] (22) A program that causes at least one processor to perform the following: obtain a first result by analyzing the atomic structure in a first mode; obtain a second result by analyzing the atomic structure in a second mode; and obtain a third result based on at least the first result, the second result and a predetermined index.

[0129] (23) An information processing method comprising: obtaining a first result by analyzing an atomic structure in a first mode using an information processing device described in any of (1) to (20); obtaining a second result by analyzing the atomic structure in a second mode; and obtaining a third result based on at least the first result, the second result, and a predetermined index.

[0130] (24) A program that causes at least one processor to execute the information processing method described in (23).

[0131] This program allows at least one processor to perform the processing in the information processing devices (2) through (20).

[0132] (Example of device configuration)

[0133] The information processing apparatus that performs the embodiments or modifications described above may consist of hardware, or it may consist of information processing by software (programs) executed by a CPU (Central Processing Unit) or GPU (Graphics Processing Unit), etc. If it consists of information processing by software, the software that realizes at least some of the functions of each device in the embodiments described above may be stored on a non-temporary storage medium (non-temporary computer-readable medium) such as a CD-ROM (Compact Disc-Read Only Memory) or USB (Universal Serial Bus) memory, and the software information processing may be executed by loading it into a computer. Alternatively, the software may be downloaded via a communication network. Furthermore, all or part of the software processing may be implemented in a circuit such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array), so that the information processing by the software is executed by hardware.

[0134] The storage medium for the software may be a removable medium such as an optical disc, or a fixed storage medium such as a hard disk or memory. Furthermore, the storage medium may be located inside the computer (main memory or auxiliary storage, etc.) or outside the computer.

[0135] Figure 3 is a block diagram showing an example of the hardware configuration of an information processing device that implements the embodiments or modifications described above. Each device may be implemented as a computer 7, for example, comprising a processor 71, a main memory 72 (memory), an auxiliary memory 73 (memory), a network interface 74, and a device interface 75, all connected via a bus 76.

[0136] The computer 7 in Figure 3 has one of each component, but it may have multiple identical components. Also, although Figure 3 shows one computer 7, the software may be installed on multiple computers, and each of these computers may execute the same or different parts of the software's processing. In this case, it may be a distributed computing configuration in which each computer communicates via a network interface 74 or the like to execute processing. In other words, the information processing device that performs the above-described embodiment or modification may be configured as a system that realizes its function by having one or more computers execute instructions stored in one or more storage devices. Alternatively, it may be configured so that information transmitted from a terminal is processed by one or more computers located on the cloud, and the processing results are transmitted to the terminal.

[0137] The various calculations performed by the information processing device that executes the embodiments or modifications described above may be performed in parallel using one or more processors, or using multiple computers via a network. Alternatively, the various calculations may be distributed to multiple processing cores within a processor and executed in parallel. Furthermore, some or all of the processing and means of this disclosure may be implemented by at least one of a processor and a storage device located on a cloud that can communicate with computer 7 via a network. Thus, each device in the embodiments described above may be in the form of parallel computing using one or more computers.

[0138] The processor 71 may be an electronic circuit (processing circuit, processing circuitry, CPU, GPU, FPGA, ASIC, etc.) that performs at least one of the following: control of a computer or calculations. The processor 71 may also be a general-purpose processor, a dedicated processing circuit designed to perform specific calculations, or a semiconductor device including both a general-purpose processor and a dedicated processing circuit. Furthermore, the processor 71 may include optical circuits or quantum computing-based calculation functions.

[0139] The processor 71 may perform calculations based on data and software input from various devices within the computer 7, and may output calculation results and control signals to these devices. The processor 71 may also control the various components of the computer 7 by executing the computer 7's OS (Operating System) or applications.

[0140] An information processing device that performs the embodiments or modifications described above may be implemented by one or more processors 71. Here, processor 71 may refer to one or more electronic circuits arranged on one chip, or one or more electronic circuits arranged on two or more chips or two or more devices. When multiple electronic circuits are used, each electronic circuit may communicate by wire or wireless.

[0141] The main memory 72 may store instructions executed by the processor 71 and various data, and the information stored in the main memory 72 may be read by the processor 71. The auxiliary storage device 73 is a storage device other than the main memory 72. These storage devices mean any electronic component capable of storing electronic information, and may be semiconductor memory. The semiconductor memory may be either volatile memory or non-volatile memory. In the information processing apparatus that performs the above-described embodiment or modification, the storage device for storing various data may be implemented by the main memory 72 or the auxiliary storage device 73, or by the built-in memory of the processor 71. For example, the storage unit in the above-described embodiment may be implemented by the main memory 72 or the auxiliary storage device 73.

[0142] If an information processing device performing the above-described embodiment or modification comprises at least one storage device (memory) and at least one processor connected to (coupled with) this at least one storage device, then at least one processor may be connected to one storage device. Alternatively, at least one storage device may be connected to one processor. Furthermore, the configuration may include at least one processor among a plurality of processors being connected to at least one storage device among a plurality of storage devices. This configuration may also be realized by storage devices and processors included in a plurality of computers. Moreover, the configuration may include a storage device integrated with a processor (for example, a cache memory including an L1 cache and an L2 cache).

[0143] The network interface 74 is an interface for connecting to the communication network 8 wirelessly or via a wired connection. The network interface 74 can be any appropriate interface, such as one conforming to existing communication standards. Information may be exchanged between the computer 7 and an external device 9A connected via the communication network 8 through the network interface 74. The communication network 8 may be a WAN (Wide Area Network), LAN (Local Area Network), PAN (Personal Area Network), or a combination thereof, as long as information is exchanged between the computer 7 and the external device 9A. An example of a WAN is the Internet; an example of a LAN is IEEE 802.11 or Ethernet (registered trademark); and an example of a PAN is Bluetooth (registered trademark) or NFC (Near Field Communication).

[0144] Device interface 75 is an interface such as USB that connects directly to the external device 9B.

[0145] External device 9A is a device connected to computer 7 via a network. External device 9B is a device directly connected to computer 7.

[0146] External device 9A or external device 9B may, for example, be an input device. The input device may be, for example, a camera, microphone, motion capture device, various sensors, keyboard, mouse, or touch panel, and will provide the acquired information to computer 7. Alternatively, it may be a device equipped with an input unit, memory, and processor, such as a personal computer, tablet terminal, or smartphone.

[0147] Furthermore, external device 9A or external device 9B may, for example, be an output device. The output device may be a display device such as an LCD (Liquid Crystal Display) or an organic EL (Electro Luminescence) panel, or a speaker that outputs sound, etc. It may also be a device equipped with an output unit, memory, and a processor, such as a personal computer, tablet terminal, or smartphone.

[0148] Furthermore, external device 9A or external device 9B may be a storage device (memory). For example, external device 9A may be network storage, and external device 9B may be storage such as an HDD.

[0149] Furthermore, the external device 9A or external device 9B may be a device having some of the functions of the components of an information processing device that performs the embodiments or modifications described above. In other words, the computer 7 may transmit some or all of the processing results to the external device 9A or external device 9B, or receive some or all of the processing results from the external device 9A or external device 9B.

[0150] Where the expression "at least one of a, b, and c" or "at least one of a, b, or c" (including similar expressions) is used herein (including the claims), it includes any of a, b, c, a-b, a-c, b-c, or a-b-c. It also includes multiple instances of any element, such as a-a, a-b-b, a-a-b-b-c-c, etc. Furthermore, it includes adding other elements other than the enumerated elements (a, b, and c), such as a-b-c-d which has d.

[0151] In this specification (including the claims), when expressions such as "using data as input / based on data / according to / in accordance with data" (including similar expressions) are used, unless otherwise specified, this includes using the data itself or using data that has been processed in some way (e.g., data with added noise, normalized data, features extracted from the data, an intermediate representation of the data, etc.). Furthermore, when it is stated that some result is obtained "using data as input / based on data / according to / in accordance with data" (including similar expressions), unless otherwise specified, this includes cases where the result is obtained based solely on the data in question or where the result is influenced by other data, factors, conditions, and / or states other than the data in question. Furthermore, when it is stated that "data is output" (including similar expressions), unless otherwise specified, this includes cases where the data itself is used as output or where data that has been processed in some way (e.g., data with added noise, normalized data, features extracted from the data, an intermediate representation of the data, etc.) is used as output.

[0152] Where the terms “connected” and “coupled” are used herein (including in the claims), they are intended to be non-restrictive terms that include any direct connection / coupling, indirect connection / coupling, electrical connection / coupling, communicative connection / coupling, operational connection / coupling, or physical connection / coupling. The terms should be interpreted as appropriate in the context in which they are used, but any form of connection / coupling that is not intentionally or naturally excluded should be interpreted non-restrictively as being included in the terms.

[0153] In this specification (including the claims), when the expression "A configured to B" is used, it may include that the physical structure of element A has a configuration capable of performing operation B, and that the permanent or temporary setting / configuration of element A is configured to actually perform operation B. For example, if element A is a general-purpose processor, it is sufficient that the processor has a hardware configuration capable of performing operation B, and that it is configured to actually perform operation B by the setting of a permanent or temporary program (instruction). Furthermore, if element A is a dedicated processor or dedicated arithmetic circuit, it is sufficient that the circuit structure of the processor is implemented to actually perform operation B, regardless of whether control instructions and data are actually attached.

[0154] Wherever terms meaning "comprising" or "having" are used in this specification (including the claims), they are intended to be open-ended terms, including cases where the subject matter of such terms is not the object of the term. Where the object of such terms meaning "comprising" or "having" is an expression that does not specify a quantity or suggests a singular number (an expression with the article a or an), such expression should be interpreted as not being limited to a specific number.

[0155] In this specification (including the claims), even if expressions such as "one or more" or "at least one" are used in one place, and expressions that do not specify a quantity or suggest singularity (expressions using the articles a or an) are used in another place, the latter expressions are not intended to mean "one." In general, expressions that do not specify a quantity or suggest singularity (expressions using the articles a or an) should be interpreted as not necessarily limited to a specific number.

[0156] In this specification, if a particular configuration of an embodiment is described as yielding a specific advantage or result, it should be understood, unless otherwise stated, that the same advantage or result can also be obtained from one or more other embodiments having that configuration. However, it should be understood that the presence or absence of such advantage or result generally depends on various factors, conditions, and / or states, and that the configuration does not necessarily guarantee that the advantage or result can be obtained. The advantage or result can only be obtained from the configuration described in the embodiment when various factors, conditions, and / or states are met, and the advantage or result cannot necessarily be obtained in the invention claimed to define that configuration or a similar configuration.

[0157] In this specification (including the claims), when terms such as "maximize" are used, they include finding the global maximum value, finding an approximation of the global maximum value, finding the local maximum value, and finding an approximation of the local maximum value, and should be interpreted appropriately depending on the context in which the terms are used. They also include finding approximations of these maximum values ​​probabilistically or heuristically. Similarly, when terms such as "minimize" are used, they include finding the global minimum value, finding an approximation of the global minimum value, finding the local minimum value, and finding an approximation of the local minimum value, and should be interpreted appropriately depending on the context in which the terms are used. They also include finding approximations of these minimum values ​​probabilistically or heuristically. Similarly, when terms such as "optimize" are used, they include finding the global optimal value, finding an approximation of the global optimal value, finding the local optimal value, and finding an approximation of the local optimal value, and should be interpreted appropriately depending on the context in which the terms are used. This also includes finding approximate values ​​of these optimal values ​​probabilistically or heuristically.

[0158] In this specification (including the claims), when multiple hardware components perform a predetermined process, each component may cooperate to perform the predetermined process, or some components may perform all of the predetermined process. Alternatively, some components may perform part of the predetermined process, while other components perform the remainder. In this specification (including the claims), when expressions such as "one or more hardware components perform a first process, and the one or more hardware components perform a second process" (including similar expressions) are used, the hardware component performing the first process and the hardware component performing the second process may be the same or different. In other words, it is sufficient that the hardware component performing the first process and the hardware component performing the second process are included in the one or more hardware components. Hardware may include electronic circuits or devices containing electronic circuits.

[0159] In this specification (including the claims), when multiple storage devices (memories) store data, each of the multiple storage devices may store only a portion of the data or the entire data. Furthermore, a configuration in which some of the multiple storage devices store data is also included.

[0160] While embodiments of this disclosure have been described in detail above, this disclosure is not limited to the individual embodiments described above. Various additions, modifications, substitutions, and partial deletions are possible, provided that they do not deviate from the conceptual idea and spirit of this disclosure derived from the claims and their equivalents. For example, where numerical values ​​or mathematical formulas are used in the description of the embodiments described above, these are provided for illustrative purposes only and do not limit the scope of this disclosure. Similarly, the sequence of operations shown in the embodiments is also illustrative and does not limit the scope of this disclosure.

Claims

1. An information processing device comprising at least one memory and at least one processor, wherein the at least one processor obtains a first result by analyzing the atomic structure in a first mode, obtains a second result by analyzing the atomic structure in a second mode, and obtains a third result based on at least the first result, the second result and a predetermined index.

2. The information processing apparatus according to claim 1, wherein the first result, the second result, and the third result are each the energy related to the atomic structure.

3. The information processing apparatus according to claim 2, wherein the first result is the energy of the atomic structure analyzed in the first mode, the second result is the energy of the atomic structure analyzed in the second mode, and the third result is the energy of the atomic structure based on at least the first mode and the second mode.

4. The information processing apparatus according to any one of claims 1 to 3, wherein the at least one processor obtains the third result by weighting and adding the first result and the second result based on the predetermined index.

5. Let r be the vector representing the atomic structure, and E be the first result. MODE1 , the second result E MODE2 Let E be the third result and β be the predetermined index which is a scalar value. Then the third result is: An information processing apparatus according to any one of claims 1 to 4, represented by [the formula shown].

6. The information processing apparatus according to claim 1 or claim 2, wherein the predetermined index includes an index for each atom included in the atomic structure.

7. The information processing apparatus according to claim 6, wherein the first result is the energy of each atom included in the atomic structure analyzed in the first mode, the second result is the energy of each atom included in the atomic structure analyzed in the second mode, and the third result is the energy of the atomic structure based on at least the first mode and the second mode.

8. The information processing apparatus according to claim 1, claim 6, or claim 7, wherein the at least one processor obtains the third result by weighting and adding the first result and the second result based on the predetermined index.

9. Let r be the vector representing the atomic structure, and e be the first result corresponding to the i-th atom included in the atomic structure. i,MODE1 , the second result corresponding to the i-th atom included in the atomic structure is e i,MODE2 Let E be the third result and β be the predetermined index which is a scalar value corresponding to the i-th atom included in the atomic structure. Then the third result is: The information processing apparatus according to claim 8, as represented by [the specified method].

10. The information processing apparatus according to any one of claims 1 to 9, wherein the at least one processor obtains the first result by operating the first model in the first mode and obtains the second result by operating the first model in the second mode.

11. The information processing apparatus according to claim 10, wherein the third result is the energy of the atomic structure, and the at least one processor calculates the force acting on each atom in the atomic structure by performing a backpropagation process of the first model.

12. The information processing apparatus according to any one of claims 1 to 9, wherein at least one processor obtains the first result by analyzing the atomic structure using a first model, and obtains the second result by analyzing the atomic structure using a second model different from the first model.

13. The information processing apparatus according to claim 12, wherein the third result is the energy of the atomic structure, and the at least one processor calculates the force acting on each atom in the atomic structure by performing backpropagation processing of the first model and the second model.

14. The information processing apparatus according to any one of claims 1 to 13, wherein at least one processor calculates the predetermined index using a third model.

15. The information processing apparatus according to any one of claims 1 to 5, wherein the at least one processor calculates the predetermined index based on at least the distance between predetermined elements contained in the atomic structure or the number of predetermined elements.

16. The information processing apparatus according to claim 1 or any of claims 6 to 9, wherein the at least one processor calculates the predetermined index based on at least the number of predetermined elements contained within a predetermined distance from each atom in the atomic structure, or the distance between each atom and a predetermined element contained within a predetermined distance from each atom.

17. The information processing apparatus according to any one of claims 10 to 13, wherein the first model is an NNP.

18. The information processing apparatus according to any one of claims 1 to 17, wherein the first mode is a mode that uses Hubbard-U correction, and the second mode is a mode that does not use Hubbard-U correction.

19. The information processing apparatus according to any one of claims 1 to 17, wherein the first mode is a mode capable of performing analysis with higher accuracy than the second mode in terms of crystal structure, and the second mode is a mode capable of performing analysis with higher accuracy than the first mode in terms of molecular structure.

20. The information processing apparatus according to any one of claims 1 to 19, wherein the at least one processor obtains one or more other results by analyzing the atomic structure in one or more other modes, and obtains the third result based on at least the first result, the second result, the one or more other results, and the predetermined index.

21. An information processing method comprising: obtaining a first result by analyzing an atomic structure in a first mode using at least one processor; obtaining a second result by analyzing the atomic structure in a second mode; and obtaining a third result based on at least the first result, the second result, and a predetermined index.

22. A program that causes at least one processor to perform the following actions: obtain a first result by analyzing the atomic structure in a first mode; obtain a second result by analyzing the atomic structure in a second mode; and obtain a third result based on at least the first result, the second result, and a predetermined index.

23. An information processing method comprising: obtaining a first result by analyzing an atomic structure in a first mode using an information processing device according to any one of claims 1 to 20; obtaining a second result by analyzing the atomic structure in a second mode; and obtaining a third result based on at least the first result, the second result, and a predetermined index.

24. A program that causes at least one processor to execute the information processing method described in claim 23.

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