Information processing system, information processing method, and program
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2026-01-26
- Publication Date
- 2026-08-13
Smart Images
Figure JP2026002370_13082026_PF_FP_ABST
Abstract
Description
Information processing systems, information processing methods, and programs
[0001] This invention relates to an information processing system, an information processing method, and a program.
[0002] Patent Document 1 discloses a technique for efficiently reproducing structural changes involving the rearrangement of covalent bonds in materials with complex compositions containing multiple elements, while faithfully reproducing structural energy changes dependent on the coordination state of each atom, in molecular dynamics simulations of large-scale systems dealing with thousands or more atoms.
[0003] Non-patent documents 1 and 2 are references.
[0004] Japanese Patent Publication No. 2008-052308
[0005] J. Behler and M. Parrinello, Phys. Rev. Lett. 98, 146401 (2007). Ko, T. W. , Finkler, J. A. , Goedecker, S. et al. "A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local "Nature Commun 12, 398 (2021).
[0006] Incidentally, when performing machine learning molecular dynamics (MLMD) calculations, the machine learning potential of the system, described by the contributions of interatomic interactions, is calculated, and the change in atomic position is sometimes described from the forces acting on each atom based on this machine learning potential. In this case, the structural similarity around the atoms constituting the material is calculated within the cutoff radius.
[0007] However, as the cutoff radius increases, the computational cost of structural similarity increases. Here, if the cutoff radius is shorter than the length scale that describes the spatial distribution of electrons (for example, the length scale of electron polarization, the scale of long-range electron transport phenomena such as electric current, the length scale that describes the positional relationship of the same elements with different valencies, etc.), it is difficult to describe such phenomena caused by the spatial distribution of electrons or their temporal evolution by simply performing machine learning molecular dynamics calculations from the position coordinates of atoms.
[0008] According to one aspect of the present invention, an information processing system is provided, comprising at least one processor, the processor being configured to execute a program such that the following steps are performed: a first acquisition step, which acquires first material information relating to a target substance to be analyzed, the first material information including information relating to the atomic species of atoms constituting the target substance and position coordinates representing the positions of the atoms constituting the target substance; a distribution calculation step, which calculates distribution information relating to the electron density distribution in the target substance based on the first material information; a force calculation step, which calculates the force acting on the atoms using a predetermined trained model based on the first material information and the distribution information, the trained model being pre-trained to estimate the machine learning potential in the target substance by inputting at least the position coordinates of the atoms constituting the target substance and to output a force based on the machine learning potential; and an update step, which generates second material information including the latest position coordinates of the atoms by updating the acquired position coordinates of the atoms based on the force.
[0009] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0010] It is a block diagram representing the information processing system 1. It is a block diagram showing the hardware configuration of the information processing apparatus 2. It is a block diagram showing the hardware configuration of the user terminal 3. It is a flowchart showing the flow of the first information processing executed in the information processing system 1. It is a diagram showing an example of a method for correcting a force based on a machine learning potential. It is a flowchart showing the flow of the second information processing. It is a diagram showing an example of a method for generating a descriptor for each atom based on atomic arrangement and distribution information.
[0011] Hereinafter, embodiments of the present invention will be described with reference to the drawings. Various characteristic matters shown in the following embodiments can be combined with each other.
[0012] By the way, a program for realizing software appearing in one embodiment may be provided as a non-temporary computer-readable recording medium (Non-Transitory Computer-Readable Medium) readable by a computer, may be provided so as to be downloadable from an external server, or may be provided so as to start the program on an external computer and realize its function on a client terminal (so-called cloud computing).
[0013] Also, in various information processes according to one embodiment, an input and an output corresponding to the input can be realized. Here, if an output is obtained as a result of the input, the mode of information (hereinafter referred to as reference information) referred to in such information processing is not limited. The reference information may be, for example, rule-based information such as a database, a lookup table, a predetermined function (including a determination formula such as a regression formula constructed by a statistical method), a learned model in which the correlation between the input and the output has been learned in advance, or a large language model capable of outputting a desired result by inputting a prompt (these models include parameters for constructing the correlation between the input and the output) or a generative AI such as a vision language model.
[0014] Furthermore, in one embodiment, "part" may include, for example, hardware resources implemented by a circuit in a broad sense, and the information processing of software that can be specifically realized by these hardware resources. Also, in one embodiment, various types of information are handled, and this information can be represented, for example, by the physical values of signal values representing voltage and current, the high or low values of signal values as a set of binary bits composed of 0s or 1s, or by quantum superposition (so-called qubits), and communication and calculations can be performed on a circuit in a broad sense.
[0015] Furthermore, a circuit in a broad sense is a circuit realized by combining at least an appropriate combination of circuits, circuits, processors, and memory. The processor may be a general-purpose processor or a dedicated circuit. In other words, this includes application-specific integrated circuits (ASICs), programmable logic devices (for example, simple programmable logic devices (SPLDs), complex programmable logic devices (CPLDs), and field programmable gate arrays (FPGAs)), etc.
[0016] 1. Hardware Configuration This section describes the hardware configuration of the information processing system 1 according to this embodiment. <Information Processing System 1> Figure 1 is a configuration diagram representing the information processing system 1. The information processing system 1 comprises an information processing device 2 and a user terminal 3. The information processing device 2 and the user terminal 3 are configured to communicate with each other via a telecommunications line. In one embodiment, the information processing system 1 consists of one or more devices or components. For example, if it consists only of the information processing device 2, the information processing system 1 can be the information processing device 2. These components will be described below.
[0017] <Information Processing Apparatus 2> FIG. 2 is a block diagram showing the hardware configuration of the information processing apparatus 2. The information processing apparatus 2 includes a communication unit 21, a storage unit 22, and at least one processor 23, and these components are electrically connected via a communication bus 20 inside the information processing apparatus 2. Each component will be further described below.
[0018] <Communication Unit 21> Although the communication unit 21 preferably uses wired communication means such as USB, IEEE1394, Thunderbolt (registered trademark), wired LAN network communication, etc., it may include wireless LAN network communication, mobile communication such as 3G / LTE / 5G, and BLUETOOTH (registered trademark) communication as required. That is, it is more preferably implemented as a collection of these multiple communication means. That is, the information processing apparatus 2 may communicate various information from the outside via the communication unit 21 and the network.
[0019] <Storage Unit 22> The storage unit 22 stores various information defined as described above. This can be implemented as a storage device such as a solid state drive (SSD) that stores various programs related to the information processing apparatus 2 executed by the processor 23, or as a memory such as a random access memory (RAM) that stores temporarily necessary information (arguments, arrays, etc.) related to the operation of the program. The storage unit 22 stores various programs, variables, etc. related to the information processing apparatus 2 executed by the processor 23.
[0020] <Processor 23> The processor 23 performs processing and control of the overall operation related to the information processing device 2. The processor 23 is, for example, a Central Processing Unit (CPU) not shown. The processor 23 realizes various functions related to the information processing device 2 by reading predetermined programs stored in the storage unit 22. That is, information processing by software stored in the storage unit 22 is concretely realized by the processor 23, which is an example of hardware, and can be executed as each functional unit included in the processor 23. Note that the processor 23 is not limited to being a single unit, and may be implemented with multiple processors 23 for each function. It may also be a combination of such processors.
[0021] The processor 23 is configured as an acquisition unit to acquire various information related to information processing, as described later, from the user terminal 3, which will be described later. The processor 23 is configured to acquire various information by reading various information stored in the storage area, which is at least a part of the memory unit 22, and writing the read information to the work area, which is at least a part of the memory unit 22. The storage area is, for example, the area of the memory unit 22 that is implemented as a storage device such as an SSD. The work area is, for example, the area that is implemented as memory such as RAM.
[0022] The processor 23 is configured as an output unit capable of outputting various types of information. This information can be presented to the user via the display unit 34 of the user terminal 3 (described later) or other devices. In such cases, for example, the processor 23 controls the display unit 34 of the user terminal 3 to display visual information such as screens, images including still images or videos, icons, and messages. The processor 23 may generate only rendering information for displaying the visual information on the user terminal 3. The processor 23 may also present the outputted information to the user without going through the user terminal 3 or other devices.
[0023] <User Terminal 3> Next, the hardware configuration of user terminal 3 will be described. Figure 3 is a block diagram showing the hardware configuration of user terminal 3. User terminal 3 comprises a communication unit 31, a storage unit 32, a processor 33, a display unit 34, and an input unit 35, and these components are electrically connected within user terminal 3 via a communication bus 30. The explanation of the communication unit 31, storage unit 32, and processor 33 is the same as the explanation of each part in the information processing device 2, so it will be omitted.
[0024] <Display Unit 34> The display unit 34 may be included in the casing of the user terminal 3 or it may be an external unit. The display unit 34 displays a graphical user interface (GUI) screen that can be operated by the user. This is preferably done by using different display devices such as a CRT display, liquid crystal display, organic EL display, and plasma display depending on the type of user terminal 3.
[0025] <Input Unit 35> The input unit 35 may be included in the casing of the user terminal 3 or it may be an external unit. For example, the input unit 35 may be implemented as a touch panel integrated with the display unit 34. If it is a touch panel, the user can input tap operations, swipe operations, etc. Of course, instead of a touch panel, a switch button, mouse, QWERTY keyboard, etc. may be used. In other words, the input unit 35 receives operation input made by the user. This input is transferred as a command signal to the processor 33 via the communication bus 30, and the processor 33 can execute predetermined controls and calculations as needed.
[0026] 3. Information Processing This chapter describes the information processing performed in the information processing system 1 mentioned above. 3.0. Overview The information processing method includes the following steps. In the first acquisition step, first material information concerning the target substance to be analyzed is acquired. The first material information includes information on the atomic species of the atoms constituting the target substance and position coordinates representing the positions of the atoms constituting the target substance. In the distribution calculation step, distribution information concerning the electron density distribution in the target substance is calculated based on the first material information. In the force calculation step, the force acting on the atoms is calculated using a predetermined trained model based on the first material information and distribution information. The trained model is pre-trained to estimate the machine learning potential in the target substance by inputting at least the position coordinates of the atoms constituting the target substance, and to output the force based on the machine learning potential. In the update step, second material information including the latest position coordinates of the atoms is generated by updating the acquired position coordinates of the atoms based on the force. With this configuration, it is possible to perform molecular dynamics calculations that take into account the dynamic state of electrons while utilizing the advantages of machine learning molecular dynamics.
[0027] 3.1. Flow of the First Information Processing First, we will explain the first information processing, which is an example of the above information processing. Figure 4 is a flowchart of the flow of the first information processing executed in the information processing system 1. Note that the first information processing may include arbitrary exception handling. Exception handling may include interruption of the first information processing or omission of each process. The selection or input performed in the first information processing may be based on user operation or may be performed automatically without user operation.
[0028] This first information processing method can be used, for example, to identify the optimal atomic arrangement in any given substance. While the following description uses natural units, other unit systems such as the SI system and the CGS system can also be arbitrarily adopted.
[0029] [Step S101] First, in step S101, the processor 23 acquires first material information relating to the target substance to be analyzed as a first acquisition step. The target substance may include any substance defined by the arrangement of atoms (including ionized atoms). For example, the target substance may be a crystal having a long-term periodic structure or an amorphous substance not having a long-term periodic structure. The crystal may be a single crystal, a polycrystalline substance or a quasicrystal. The target substance is any substance that is the subject of molecular dynamics calculations and may be inorganic or organic.
[0030] The first material information includes information about the atomic species of the atoms constituting the substance and positional coordinates representing the positions of the atoms constituting the substance. Information about the atomic species of an atom can be described, for example, from the chemical formula or empirical formula of the substance. Information about the atomic species may include basic information about the electronic state, such as the number of electrons belonging to the atom, the electron orbitals in the case of an isolated atom, and information about the valence. For example, if the substance is magnetite (Fe ３ O ４ In the case of ), the information regarding the atomic species is that the substance in question is one Fe ２＋ Ions, two Fe ３＋ Ions, four O ２－ The information may indicate that the material is composed of atomic species with ions as the unit. Alternatively, the information regarding atomic species may simply indicate that the material consists of three Fe atoms and four O atoms as the unit. Furthermore, the information regarding atomic species may include information regarding magnetism corresponding to the spin state of the outermost electrons. Position coordinates are described, for example, using three-dimensional position coordinates with respect to a certain origin. If the material has a long-term periodic structure, the position coordinates may be described using the shape of the unit cell (space group, lattice constant, angles between each fundamental translation vector, etc.) and fractional coordinates of each atom. Such first material information may be, for example, a CIF file pre-registered in a crystal structure database, or data obtained by crystal structure analysis of a sample.
[0031] [Step S102] Next, in step S102, the processor 23 determines the initial atomic arrangement of the target substance based on the acquired first substance information. The initial atomic arrangement is preferably an arrangement that is in line with experimental facts, such as the arrangement described in the CIF file mentioned above, but is not limited to this and may be an arrangement of a given number of atomic species arranged randomly.
[0032] [Step S103] Next, in step S103, the processor 23 inputs the latest atomic arrangement (initially the position coordinates of each atom described by the initial atomic arrangement calculated in step S102) into the trained model.
[0033] The trained model is pre-trained to estimate the machine learning potential in a target substance by inputting at least the position coordinates of the atoms constituting the target substance, and to output a force based on that machine learning potential. More specifically, the trained model can be trained to represent a machine learning potential with the position coordinates of atoms for each atomic species (i.e., information about the target substance described by the first substance information) as explanatory variables by optimizing a predetermined potential using a set of training data that includes pre-prepared training substance information and the results of first-principles calculations on the training substance information. For example, the training substance information may include information about the atomic species of atoms constituting the pre-prepared training substance and the position coordinates representing the positions of the atoms constituting the training substance. The training substance information is, for example, substance information registered in a trusted database (e.g., CIF files of the various substances mentioned above), and the results of first-principles calculations using the structures described in the CIF files (especially the results of potential energy calculations). In other words, the trained model here is a trained model used in machine learning molecular dynamics calculations (MLMD). The trained model may be stored in the memory unit 22 or in a dedicated server outside the information processing system 1.
[0034] In MLMD, for example, the interaction potential energy V of the entire system ｔｏｔ This is the atomic potential energy v associated with an atom, as shown below. ｉ It is divided into.
[0035] In the above formula, i = 1, 2, ..., N, where N is the number of atoms in the system, and r ｃ is the cutoff radius centered on the i-th atom. H_{r ｃ i} is a feature quantity invariant to translational and rotational transformations and is called a "descriptor". The descriptor H_{r ｃ i} plays a role in ensuring symmetry with respect to the interchange of atoms of the same kind. In MLMD, the neural network constituting the learned model represents the non-linear function expressed by the above formula and is obtained by learning the above-described set of teacher data (results of first-principles calculations). At this time, the neural network is configured in such a manner that v(H_{r ｃ i}) is separable as a partial network. As a result, even when the number of atoms increases, the input layer does not change in terms of the system size, and the system size can be scaled simply by increasing the partial network of the learned model. The algorithm for constructing the neural network is arbitrary. For example, density functional calculations are performed from the atomic arrangement, and the total energy of the entire system as the target variable is calculated first-principles. Thereafter, the atomic arrangement as the explanatory variable is reduced to a lower dimension by various methods such as Symmetry Function, Structural Fingerprint, Smooth overlap of atomic position (SOAP) descriptor, Coulomb Matrix, MBTR, etc. Thereafter, a regression model is created using the reduced explanatory variable and the target variable. The specific manner of creating the regression model is arbitrary, and examples include neural network polynomial expansion, Gaussian process regression, kernel ridge regression, etc. As a result, a learned model capable of outputting a machine learning potential is obtained.
[0036] [Step S104] Next, in step S104, the processor 23 acquires the machine learning potential output from the learned model.
[0037] [Step S105] Next, as a force calculation step, the processor 23 calculates the force acting on the atoms based on the first material information and distribution information using a predetermined trained model. In this embodiment, as a force calculation step, the processor 23 outputs a first force that does not depend on the distribution information, based on the machine learning potential output from the trained model.
[0038] In MLMD, the explanatory variables (input variables) of the trained model are limited to atomic configuration (atomic species and positional coordinates), and the electron density distribution is incorporated as a black box into the atomic potential under various conditions. Therefore, it was difficult to obtain a potential that reproduced situations where the system's symmetry deteriorated due to the influence of the electron density distribution, such as potential bias around a particular atom or long-range order. Furthermore, there were limitations to the types of submodels used for each atomic species, making it difficult to adequately reproduce potential changes in situations where the electron density distribution changes slightly due to factors such as electron or hole doping. Also, because the subnetwork is constructed for each atomic species, the atomic potential energy is calculated using the same subnetwork even when the valence states are different. Thus, conventional MLMD has the problem of not being able to incorporate the contribution of electron density distribution bias or the contribution of electrostatic interaction potential arising from dynamic physical phenomena of electrons such as charge transfer. Additionally, MLMD has a cutoff radius r. ｃ The cutoff radius r is set. ｃ Learning is performed using structural similarity within the model as the evaluation metric. Therefore, the cutoff radius r ｃ There was also the problem that the influence from larger charged regions could not be incorporated into the potential.
[0039] The inventors of this application have found, through various studies, that the calculation accuracy of MLMD may be lower than that of other calculation methods in systems such as the following: (1) Long-distance charge transfers with a cutoff radius r ｃ(2) Systems in which phenomena on longer distance scales are occurring; (3) Systems in which an external field that affects the electron density distribution, such as an electric field, is applied; (4) Systems containing elements that can take on different valencies (such as divalent / trivalent Fe, Ni, Co, etc.).
[0040] Therefore, the inventors of the present invention examined the relationship between such systems and MLMD, and for example, in relation to (1) above, they focused on the possibility that the calculation accuracy can be improved by fundamentally incorporating the influence from the charged portion outside the cutoff radius from the electron density distribution when performing calculations for materials in which the Charge Transfer is outside the cutoff radius using the MLMD described above. Furthermore, in relation to (2), the inventors of the present invention found that the influence of an applied electric field can be incorporated by correcting the force acting on each atom from the difference in the electron density distribution between cases where an electric field, an example of an external field, is applied and cases where it is not applied. Furthermore, in relation to (3), the inventors of the present invention found the possibility that when creating a machine learning potential for MLMD, it is possible to learn the potential in a situation in which elements with different valencies are distinguished by explanatory variables by explanatory variables by training a model that outputs a machine learning potential under conditions in which explanatory variables such as the charge state of each atom are added from OFDFT or tight binding. By using the learned potential and actually updating the position coordinates of atoms by MLMD, the charge state of each atom can be extracted periodically or irregularly from OFDFT or tight binding, and by running MLMD with the charge state of each atom included as a feature vector in addition to the position coordinates of the atoms, accuracy can be improved. Below, we will describe an information processing method that can solve at least one of the problems (1) to (3) exemplified. Note that these problems are merely examples, and the first information processing method may be directed towards any problem arising from the fact that conventional MLMD has not been trained to incorporate information related to electron density distribution.
[0041] The advantage of OFDFT is that it allows for the calculation of electron density with relatively low computational cost. The order of computational cost is O (number of electrons to the power of 1). In particular, the calculation speed is very fast when using a plane wave basis. Also, although the obtained electron density depends on the approximation accuracy, a generally good electron density distribution can be obtained. The tight binding method also allows for the calculation of electron density with relatively low computational cost. The order of computational cost is O (number of electrons to the power of 3).
[0042] [Step S106] Next, in step S106, the processor 23 determines whether or not the omission condition is met. The omission condition is a condition for determining whether or not to calculate the first force based on the electron density distribution. The omission condition may be defined based on the difference in distribution information before and after the update. For example, the omission condition may be met if the change between the latest atomic arrangement and the atomic arrangement immediately preceding it is less than or equal to a specified value (for example, the sum of the changes in atomic positions is less than or equal to a certain standard length). Alternatively, the omission condition may be defined to be met if, for example, the estimation accuracy of the force calculated based solely on the machine learning potential is greater than or equal to a specified value. Alternatively, the omission condition may be defined based on the number of iterations or frequency of the calculation of distribution information described later. The omission condition may be defined to satisfy at least one or more of these conditions. If the atomic arrangement has not been updated, the omission condition is automatically met.
[0043] [Step S107] If the omission conditions are not met, the processor 23 calculates distribution information regarding the electron density distribution in the target substance based on the first material information as a distribution calculation step. The distribution information may be the electron density distribution itself, or it may be a number distribution such as the number of electrons belonging to an atom, which can be obtained from the electron density distribution. The distribution information may also be an index that shows the bias in the spatial distribution of electrons. For example, as a distribution calculation step, the processor 23 may calculate distribution information regarding the electron density distribution in the target substance based on the first material information using an electronic state calculation based on the density functional theory or the tight binding method. With such a configuration, the reliability of the obtained distribution information can be increased. In one exemplary embodiment, as a distribution calculation step, the processor 23 may calculate distribution information regarding the electron density distribution in the target substance based on the first material information using an electronic state calculation based on the orbital density functional theory. With such a configuration, since the dynamic changes in material information can be simulated using a trained model based on distribution information obtained using the orbital density functional theory, which has relatively high accuracy in electronic state calculations in static systems, molecular dynamics calculations that are closer to actual materials can be performed at a lower computational cost. In one exemplary embodiment, the processor 23 may, as a distribution calculation step, calculate distribution information regarding the electron density distribution in a target substance based on first material information using an electronic state calculation based on the density functional tight binding method. With such a configuration, the reliability of the obtained distribution information can be increased. In this way, the processor 23 calculates distribution information regarding the electron density distribution using various existing calculation methods. The electron density distribution, which is an example of distribution information, may be first-principles or an optimized version of a specific model. Furthermore, the distribution information may also be information regarding the valence of each atom contained in the CIF file, schematically calculated from the nearest neighbor atoms.
[0044] In this embodiment, the distribution information consists of various physical quantities calculated from the first-principles electron density distribution, which is determined using first-principles calculations (e.g., density functional theory) for the latest atomic arrangements. These quantities include, for example, the electron density distribution under electric field application, electron-hole dope calculations, the charge state of atoms, the electron density and polarization around atoms, and the spin density distribution.
[0045] In this case, the processor 23 may further calculate distribution information based on external field information relating to the external field applied to the target material. The external field can be any quantity of field that affects the most stable energy state of electrons, such as an electric field or a magnetic field. For example, when a uniform electric field is applied to the target material, the force experienced by atoms due to the potential of the electric field changes according to the surrounding electron density. By performing electronic state calculations under the conditions in which such an external field potential exists and calculating distribution information, the processor 23 can incorporate the influence of the external field into MLMD using a trained model that does not consider the influence of such a potential. In such a case, the processor 23 can calculate various information correlated with the electron distribution as distribution information, such as electron density distribution when an external field is applied, electron-hole dope calculations, atomic charge state, electron density around atoms, polarization state, and spin density distribution.
[0046] Thus, the inventors of this application have found a method to correct forces calculated solely from MLMD by combining electron density information obtained from methods that calculate electron density distribution with relatively low computational cost, such as the OFDFT (Orbital Free DFT) method and the tight binding method, with the MLMD method. This method involves obtaining the electron density distribution for a given atomic position coordinate using various methods such as the OFDFT method and the tight binding method, and then adding the electrostatic interaction potential to the obtained electron density distribution information.
[0047] [Step S108] Next, in step S108, the processor 23 corrects the first force based on the distribution information as a force calculation step. In one exemplary embodiment, the processor 23 may calculate the force acting on the atom using a trained model based on at least one of the following as distribution information: the contribution of charge transfer obtained from the electron density distribution, the contribution due to charge bias, and the contribution due to the difference in valence between atoms representing the same element. With such a configuration, for example, the dynamic properties of a system such as electron transport phenomena such as electric current, the properties of a system with reduced spatial symmetry such as electric polarization, and the electrical or magnetic properties of a complex material containing the same element with different valences (e.g., magnetite) can be obtained with relatively low computational cost as machine learning molecular dynamics calculations.
[0048] For example, the processor 23 determines a threshold (e.g., cutoff radius r) from the position coordinates of an atom in relation to electron-electron interactions centered on that atom. ｃ The machine learning potential (or force based on the machine learning potential) is corrected based on components originating from positions farther away from the target. The correction of the machine learning potential may be performed, for example, by superimposing electron-electron interactions onto the machine learning potential, or by using a trained model that outputs an electron-derived potential by inputting an electron density distribution separately.
[0049] Alternatively, since machine learning potentials often do not take magnetic interactions into account, the processor 23 may first calculate an electron density distribution that takes spin degrees of freedom into account, calculate spin-involved interactions (e.g., exchange interaction, spin-spin interaction, hyperfine interaction, spin-orbit interaction, etc.) from this electron density distribution, and perform force correction by superimposing these interactions onto the machine learning potential.
[0050] Furthermore, interactions that are difficult to incorporate into the machine learning potential as described above may be due to the electron density distribution reducing the symmetry of the material. In this case, the positions of atoms may be shifted to an extent that cannot be discerned with the accuracy of the analysis obtained from the database mentioned above. Also, even if the positions of atoms do not change, a bias in the electron density distribution alone may result in, for example, electron polarization that cannot be explained by atomic arrangement alone. The processor 23 may perform force correction by reflecting the component of such electron density distribution-based interactions that changes the symmetry from the atomic arrangement (particularly reducing symmetry) into the machine learning potential as described above.
[0051] Furthermore, the processor 23 may calculate the valence of each atom based on the electron density distribution and correct the force by correcting the partial potential described by the partial network of each atom based on said valence. Alternatively, the processor 23 may use said valence to calculate the force that each ion receives from an external electric field.
[0052] [Step S109] Subsequently, in step S109, the processor 23 generates second material information including the latest atomic position coordinates by updating the acquired atomic position coordinates based on the calculated forces as an update step. With this configuration, it is possible to perform molecular dynamics calculations that take into account the dynamic state of electrons while taking advantage of the advantages of machine learning molecular dynamics. The processor 23 treats the second material information as the latest atomic arrangement. At this time, if the forces have been corrected in step S108, the processor 23 updates the atomic position coordinates based on the corrected forces.
[0053] [Step S110] Next, in step S110, the processor 23 determines whether the termination condition is met. The termination condition is met, for example, when the position coordinates have been updated a specified number of times or more. If it is determined that the termination condition is not met, the process returns to step S103, and the processor 23 inputs the latest atomic arrangement into the trained model again, obtains the machine learning potential, and recursively calculates the force and updates the position coordinates of the atoms. At this time, if the omission condition is met, the force correction based on the distribution information is omitted. The processor 23 may omit only the calculation of the distribution information and correct the force again using the latest distribution information used previously. In other words, the omission condition is not limited to the condition for omitting the force correction, but may also be a condition that only omits the updating of the distribution information.
[0054] For example, as shown above, the processor 23 may acquire second material information, which is the material information updated in the update step, as a second acquisition step. In this case, the processor 23 may recursively update the second material information by using the second material information as the first material information and executing the distribution calculation step, the force calculation step, and the update step as a recursive optimization step. With such a configuration, it is possible to perform molecular dynamics calculations that take into account the dynamic state of electrons while taking advantage of the advantages of machine learning molecular dynamics.
[0055] In one exemplary embodiment, the processor 23 may, as a recursive optimization step, skip the distribution calculation step if a predetermined first omission condition is met, and instead execute the force calculation step and the update step using the distribution information calculated in the previous distribution calculation step. The first omission condition may be defined based on the number of iterations or frequency of the distribution calculation step. With such a configuration, it is possible to perform molecular dynamics calculations that take into account the dynamic state of electrons while taking advantage of the advantages of machine learning molecular dynamics.
[0056] In one exemplary embodiment, the processor 23 may, as a recursive optimization step, skip the distribution calculation step and execute the force calculation step and the update step using the distribution information calculated in the previous distribution calculation step if a second omission condition, defined based on the difference between the distribution information before and after the update, is met. The second omission condition may be defined to be met according to the difference between the latest second material information and the second material information before the update. With such a configuration, for example, changes in electronic states that contribute greatly to the accuracy of the calculation, such as changes in the valence state of atoms during molecular dynamics calculations, can be incorporated during the optimization of atomic positions. Therefore, more accurate molecular dynamics calculations can be performed within a relatively realistic range of computational costs. In one exemplary embodiment, the omission condition may be defined to be met when the latest second material information changes by a specified value or less compared to the second material information before the update, or the distribution information calculated based on the second material information before the update. Alternatively, the omission condition may be defined to be met when the period during which the distribution calculation step is continuously omitted is less than or equal to a specified value.
[0057] [Step S111] On the other hand, if it is determined that the termination condition is met, in step S111, the processor 23 outputs the optimization result of the atomic positions (i.e., the latest second material information) or the trajectory of the atomic positions (i.e., the history of the second material information) as the result of the first information processing, and then terminates the first information processing. The output results may be presented to the user via the display unit 34, for example, or used in other material property simulations.
[0058] 3.2. An Example of Processing to Correct Forces Based on Machine Learning Potential in the First Information Processing Next, an example of processing to correct forces based on machine learning potential in steps S103 to S108 described above will be explained. Figure 5 shows an example of a method for correcting forces based on machine learning potential.
[0059] As shown in Figure 5, the processor 23 first determines the positions of the N atoms included in the immediately preceding system, using the position coordinates R of the i-th atom. ｉ and that atomic species s ｉAtomic arrangement using {R ｉ ,s ｉ The position coordinates R of each atom are obtained as {i = 1 to N}. Next, the processor 23 determines the position coordinates R of each atom based on the symmetry with respect to atomic substitution and translational movement. ｉ and atomic species s ｉ descriptor H ｉ This is converted and input into the trained model. This allows the machine learning potential E to be extracted from the trained model. ｓｈｏｒｔ The output is: Machine learning potential E ｓｈｏｒｔ Since it extracts only the contributions below the cutoff radius r_c, it is described as a relatively short-range force. Subsequently, the processor 23 calculates the position coordinates R of each atom. ｉ Machine learning potential E ｓｈｏｒｔ From the gradient, the force F based on the machine learning potential acting on each atom ｉ，ｓｈｏｒｔ Calculate.
[0060] On the other hand, the processor 23 has an atomic arrangement {R ｉ ,s ｉ An electronic state calculation is performed separately based on {i = 1 to N}. In Figure 5, the processor 23 performs the calculation using the OFDFT method or the tight binding method. As a result, the processor 23 can obtain information about the charge distribution as distribution information. Here, the distribution information is the charge Q attributed to the i-th atom. ｉ And the polarization vector μ in the atom in question. ｉ This includes the following. Subsequently, the processor 23 controls the electrostatic potential E ｅｌｅｃ The processor 23 then calculates the electrostatic potential E ｅｌｅｃ From the gradient, the force F based on the electrostatic potential acting on each atom ｉ，ｅｌｅｃ The electrostatic potential is calculated using the cutoff radius r. ｃ This may include Coulomb interactions between more distant atoms, interactions between electric fields and polarizations associated with an applied electric field, and interactions between dipole moments.
[0061] Subsequently, processor 23 F ｉ，ｓｈｏｒｔ and F ｉ，ｅｌｅｃ By adding them together, F ｉ，ｓｈｏｒｔ After correcting for this, the final force F acting on each atom ｉ，ｔｏｔａｌThe processor 23 calculates the two potentials E ｅｌｅｃ , E ｓｈｏｒｔ From the gradient after adding them together, the above force F ｉ，ｔｏｔａｌ You may calculate this.
[0062] Thus, while MLMD has recently attracted considerable attention as a computational method that yields excellent accuracy in molecular dynamics calculations of various materials such as metals, semiconductors, and organic materials, it lacks information on electron density and presents challenges when dealing with phenomena where the electron density distribution changes. On the other hand, OFDFT and tight binding methods have the advantage of obtaining electron density distributions with low computational cost, but they have significant challenges in force calculations. As an example, each of the above embodiments may enable more universal and accurate MD by combining the strengths of these two methods.
[0063] 3.3. Second Information Processing In the first information processing, the machine learning potential was output in a manner independent of the distribution information described above, but this is not limited to this. For example, the processor 23 may correct the information input to the trained model based on the distribution information. This section describes the second information processing, which is another example of the information processing outlined above. Each step included in the first and second information processing can be combined as appropriate to the extent that it is not technically contradictory.
[0064] Figure 6 is a flowchart showing the flow of the second information processing. Steps included in the second information processing that are common to or correspond to those in the first information processing may be omitted from explanation by assigning the same number.
[0065] [Step S201] As shown in Figure 6, first in step S201, the processor 23 acquires first material information, similar to step S101.
[0066] [Step S202] Next, in step S202, the processor 23 determines the initial atomic arrangement, similar to step S102.
[0067] [Step S203] Next, in step S203, the processor 23 determines whether the omitted condition is met, similar to step S106.
[0068] [Step S204] If it is determined that the omission condition is met, in step S204, the processor 23 generates an atom descriptor from the latest atom arrangement (initially the initial atom arrangement determined in step S202). In the first information processing, an atom descriptor is generated as H in the preprocessing before input to the trained model, and the same preprocessing is performed in the second information processing.
[0069] [Step S205] If it is determined that the omission conditions are not met, in step S205, the processor 23 calculates the distribution information based on the latest atomic arrangement, similar to step S107.
[0070] [Step S206] Next, in step S206, the processor 23 generates a descriptor for each atom based on the latest atomic arrangement and distribution information. An example of the method for generating the descriptors will be described later.
[0071] [Step S207] Subsequently, in step S207, the descriptor generated in step S204 or step S206 is input to the trained model. In this case, the trained model may be configured to represent a machine learning potential with the training material information and the training distribution information as explanatory variables by optimizing a predetermined potential using a set of training data that includes pre-prepared training material information, training distribution information relating to the electron density distribution in the material defined by the training material information, and the results of first-principles calculations on the training material information and the training distribution information. In this case, as an example, the training material information may include information on the atomic species of atoms constituting the pre-prepared training material and position coordinates representing the positions of the atoms constituting the training material. At this time, the processor 23 may calculate the force by inputting the first material information and distribution information to the trained model as a force calculation step. With such a configuration, it is possible to perform molecular dynamics calculations that take into account the dynamic state of electrons while making use of the advantages of machine learning molecular dynamics. For example, the trained model may be pre-trained to output the machine learning potential with various physical quantities included in the distribution information as additional explanatory variables. If data for which electron density distribution calculations have not been performed, as in step S204, is input to such a trained model, the processor 23 may assume that the atomic species are neutral, automatically allocate the number of electrons for each atom based on the atomic species information, and input this information into the trained model.
[0072] [Step S208] Then, in step S208, the processor 23 acquires the machine learning potential output from the trained model, similar to step S104.
[0073] [Step S209] Next, in step S209, the processor 23 calculates the force acting on the atom based on the machine learning potential, similar to step S105.
[0074] [Step S210] Next, in step S210, the processor 23 updates the position coordinates of each atom based on the calculated force, similar to step S109.
[0075] [Step S211] Next, in step S211, the processor 23 determines whether the termination condition is met, similar to step S110. If it is determined that the termination condition is not met, the process returns to step S203, and the series of processes from determining the omitted condition to updating the position coordinates of each atom are repeated. This optimizes the arrangement of atoms.
[0076] [Step S212] If it is determined that the termination condition has been met, in step S212 the processor 23 outputs the atomic position optimization result, similar to step S111, and terminates this information processing.
[0077] Thus, information processing may use distributional information as an input variable that influences the output of the machine learning potential, or as a factor that modifies the input variable.
[0078] 3.4. An Example of Method for Generating Atom-Specific Descriptors Based on Atom Arrangement and Distribution Information Here, an example of a method for generating atom-specific descriptors based on atomic arrangement and distribution information in step S206 will be described. Figure 7 shows an example of a method for generating atom-specific descriptors based on atomic arrangement and distribution information. As shown in Figure 7, the processor 23, as in the case shown in Figure 5, uses the latest atomic arrangement information to generate atom position coordinates R ｉ and that atomic species s ｉ combination {R ｉ ,s ｉ It possesses {i = 1 to N}. The processor 23, as shown in Figure 5, uses the latest information on atomic arrangement to perform electron density distribution calculations such as OFDFT and tight binding, and calculates, for example, the charge Q of each atom. ｉ The electrostatic potential E is calculated based on this. ｅｌｅｃ Calculate.
[0079] On the other hand, processor 23 is {R ｉ ,s ｉ The values :i = 1 to N are converted into descriptors for each atom. At this time, the processor 23 calculates the charge Q ｉ Based on this, descriptor H reflects the symmetry of different atomic arrangements. ｉ A charge Q is generated. ｉDescriptor H using ｉ Regarding the method of generating it, for example, as described in Non-Patent Document 2, a descriptor determined solely by the atomic arrangement, i.e., H in Figure 5, is used. ｉ In addition, a method can be applied in which scalar quantities representing the charge around each atom (ion) are directly input as descriptors into the machine learning model. Such charges around each atom can include, for example, Bader charge or Hirshfeld charge. These are not limited to scalar quantities representing the charge around each atom (ion); multidimensional quantities such as polarization vectors or electron density distribution functions in space are also acceptable. That is, by constructing the machine learning model NN2 such that the descriptor H takes charge Q as a variable, distribution information can be reflected in the machine learning potential. Subsequently, the descriptor H into which the machine learning model NN2 has been input... ｉ Based on the machine learning potential E ｓｈｏｒｔ Output E ｓｈｏｒｔ and E ｅｌｅｃ Adding these together gives the final potential E of the entire system. ｔｏｔａｌ Calculate E ｔｏｔａｌ The final force is calculated from the gradient.
[0080] [Other] The above embodiment can be implemented as appropriate, for example, as follows.
[0081] Regarding the MLMD portion, it is not limited to pre-trained MLMDs; generally, any MLMD is acceptable. For example, On-The-Fly MD and OFDFT can be combined. If the accuracy of force calculations using the machine learning force field is deemed poor, information on the electron density around each atom can be calculated and extracted using OFDFT calculations, added as explanatory variables, and then the machine learning potential can be learned and updated.
[0082] The information processing device 2 may be on-premise or in a cloud-based configuration. In the case of a cloud-based information processing device 2, for example, it may provide the above-mentioned functions and processing in the form of SaaS (Software as a Service) or cloud computing.
[0083] In the above embodiment, the information processing device 2 performed various storage and control functions, but instead of the information processing device 2, multiple external devices may be used. That is, various information and programs may be distributed and stored across multiple external devices using blockchain technology or the like.
[0084] The embodiments described above are not limited to the information processing system 1, but may also be an information processing method or an information processing program. The information processing method includes each step of the information processing system 1. The program causes at least one computer to execute each step of the information processing system 1.
[0085] The above embodiments may also be provided in the following embodiments.
[0086] (1) An information processing system comprising at least one processor, wherein the processor is configured to execute a program such that the following steps are performed: a first acquisition step, which acquires first material information relating to a target substance to be analyzed, wherein the first material information includes information relating to the atomic species of atoms constituting the target substance and position coordinates representing the positions of the atoms constituting the target substance; a distribution calculation step, which calculates distribution information relating to the electron density distribution in the target substance based on the first material information; a force calculation step, which calculates the force acting on the atoms using a predetermined trained model based on the first material information and the distribution information, wherein the trained model is pre-trained to estimate a machine learning potential in the target substance by inputting at least the position coordinates of atoms constituting the target substance and to output the force based on the machine learning potential; and an update step, which generates second material information including the latest position coordinates of the atoms by updating the acquired position coordinates of the atoms based on the force.
[0087] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0088] (2) In the information processing system described in (1) above, the trained model is trained to represent the machine learning potential with the position coordinates of the atoms for each atomic species as explanatory variables by optimizing a predetermined potential using a set of training data including pre-prepared training material information and the results of first-principles calculations on the training material information, the training material information includes information on the atomic species of atoms constituting the pre-prepared training material and position coordinates representing the positions of the atoms constituting the training material, and in the force calculation step, the machine learning potential is estimated by inputting the first material information to the trained model, a first force independent of the distribution information is output based on the machine learning potential, and the force is calculated by correcting the first force based on the distribution information.
[0089] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0090] (3) In the information processing system described in (1) above, the trained model is configured to represent the machine learning potential with the trained material information and the trained distribution information as explanatory variables by optimizing a predetermined potential using a set of training data which includes pre-prepared training material information, training distribution information relating to the electron density distribution in a substance defined by the training material information, and the results of first-principles calculations on the training material information and the trained distribution information, wherein the training material information includes information on the atomic species of atoms constituting the pre-prepared training material and position coordinates representing the positions of the atoms constituting the training material, and in the force calculation step, the force is calculated by inputting the first material information and the distribution information into the trained model.
[0091] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0092] (4) An information processing system according to any one of (1) to (3) above, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the density functional theory or the tight binding method.
[0093] This configuration can improve the reliability of the distribution information obtained.
[0094] (5) An information processing system according to any one of (1) to (4) above, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the orbital-free density functional method.
[0095] With this configuration, it is possible to simulate the dynamic changes in material information using a trained model based on distribution information obtained using the orbital-free density functional method, which has relatively high accuracy in calculating the electronic state in static systems. This allows for molecular dynamics calculations that are closer to those of actual materials to be performed at a lower computational cost.
[0096] (6) An information processing system according to any one of (1) to (5) above, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the density functional tight binding method.
[0097] This configuration can improve the reliability of the distribution information obtained.
[0098] (7) An information processing system according to any one of (1) to (6) above, wherein in the force calculation step, the system calculates the force acting on the atom using the learned model, based on at least one of the following as distribution information: the contribution of charge transfer obtained from the electron density distribution, the contribution due to charge bias, and the contribution due to the difference in valence between atoms representing the same element.
[0099] With this configuration, for example, the dynamic properties of a system, such as electron transport phenomena like electric current, the properties of a system with reduced spatial symmetry, such as electric polarization, and the electrical or magnetic properties of a complex material containing the same element with different valencies (e.g., magnetite) can be obtained with relatively low computational cost using machine learning molecular dynamics calculations.
[0100] (8) An information processing system according to any one of (1) to (7) above, wherein in the second acquisition step, the second material information updated in the update step is acquired, and in the recursive optimization step, the distribution calculation step, the force calculation step, and the update step are executed to recursively update the second material information by using the second material information as the first material information.
[0101] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0102] (9) In the information processing system described in (8) above, in the recursive optimization step, if a predetermined first omission condition is met, the distribution calculation step is omitted and the force calculation step and the update step are executed using the distribution information calculated in the previous distribution calculation step, and the first omission condition is defined based on the number of repetitions or frequency of repetitions of the distribution calculation step.
[0103] This configuration allows us to leverage the advantages of machine learning molecular dynamics while performing molecular dynamics calculations that take into account the dynamic states of electrons.
[0104] (10) In the information processing system described in (8) or (9) above, the recursive optimization step omits the distribution calculation step when the second omission condition is met, and the force calculation step and the update step are executed using the distribution information calculated in the previous distribution calculation step, and the second omission condition is defined to be met according to the difference between the latest second material information and the second material information before the update.
[0105] With this configuration, changes in electronic states that significantly contribute to the accuracy of calculations, such as changes in the valence state of atoms during molecular dynamics calculations, can be incorporated during the optimization of atomic positions. Therefore, more accurate molecular dynamics calculations can be performed within a relatively realistic range of computational costs.
[0106] (11) In the information processing system described in (10) above, the second omission condition is defined to be satisfied when the latest second material information changes to less than or equal to a specified value in the number of electrons corresponding to the atom in the distribution information calculated based on the second material information before the update or the second material information before the update.
[0107] (12) In the information processing system described in (10) above, the second omission condition is defined such that it is satisfied when the period during which the distribution calculation step is continuously omitted is less than or equal to a specified value.
[0108] (13) An information processing system according to any one of (1) to (12) above, comprising an information processing device including the processor and a terminal that can access the information processing device.
[0109] (14) An information processing method comprising each step of the information processing system described in any one of (1) to (12) above.
[0110] (15) A program that causes at least one computer to perform each step of the information processing system described in any one of (1) to (12) above. Of course, this is not limited to this.
[0111] Finally, various embodiments of the present invention have been described, but these are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be implemented in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims and their equivalents.
[0112] 1: Information processing system, 2: Information processing device, 20: Communication bus, 21: Communication unit, 22: Storage unit, 23: Processor, 3: User terminal, 30: Communication bus, 31: Communication unit, 32: Storage unit, 33: Processor, 34: Display unit, 35: Input unit
Claims
1. An information processing system comprising at least one processor, the processor configured to execute a program such that the following steps are performed: a first acquisition step, which acquires first material information relating to a target substance to be analyzed, the first material information including information relating to the atomic species of atoms constituting the target substance and position coordinates representing the positions of the atoms constituting the target substance; a distribution calculation step, which calculates distribution information relating to the electron density distribution in the target substance based on the first material information; a force calculation step, which calculates the force acting on the atoms using a predetermined trained model based on the first material information and the distribution information, the trained model being pre-trained to estimate a machine learning potential in the target substance by inputting at least the position coordinates of atoms constituting the target substance and to output the force based on the machine learning potential; and an update step, which generates second material information including the latest position coordinates of the atoms by updating the acquired position coordinates of the atoms based on the force.
2. The information processing system according to claim 1, wherein the trained model is trained to represent the machine learning potential with the position coordinates of the atoms for each atomic species as explanatory variables by optimizing a predetermined potential using a set of training data including pre-prepared training material information and the results of first-principles calculations on the training material information, the training material information includes information on the atomic species of atoms constituting the pre-prepared training material and position coordinates representing the positions of the atoms constituting the training material, and in the force calculation step, the machine learning potential is estimated by inputting the first material information to the trained model, a first force independent of the distribution information is output based on the machine learning potential, and the force is calculated by correcting the first force based on the distribution information.
3. The information processing system according to claim 1, wherein the trained model is configured to represent the machine learning potential with the trained material information and the trained distribution information as explanatory variables by optimizing a predetermined potential using a set of training data including pre-prepared training material information, training distribution information relating to the electron density distribution in a substance defined by the training material information, and the results of first-principles calculations on the training material information and the trained distribution information, wherein the training material information includes information on the atomic species of atoms constituting the pre-prepared training material and position coordinates representing the positions of the atoms constituting the training material, and in the force calculation step, the system calculates the force by inputting the first material information and the distribution information into the trained model.
4. An information processing system according to any one of claims 1 to 3, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the density functional theory or the tight binding method.
5. An information processing system according to any one of claims 1 to 4, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the orbital-free density functional method.
6. An information processing system according to any one of claims 1 to 5, wherein in the distribution calculation step, distribution information relating to the electron density distribution in the target substance is calculated based on the first substance information using an electronic state calculation based on the density functional tight binding method.
7. An information processing system according to any one of claims 1 to 6, wherein in the force calculation step, the system calculates the force acting on the atom using the learned model, based on at least one of the following as distribution information: the contribution of charge transfer obtained from the electron density distribution, the contribution due to charge bias, and the contribution due to the difference in valence between atoms representing the same element.
8. An information processing system according to any one of claims 1 to 7, wherein in a second acquisition step, the second material information updated in the update step is acquired, and in a recursive optimization step, the second material information is recursively updated by performing the distribution calculation step, the force calculation step, and the update step using the second material information as the first material information.
9. The information processing system according to claim 8, wherein in the recursive optimization step, if a predetermined first omission condition is met, the distribution calculation step is omitted, and the force calculation step and the update step are executed using the distribution information calculated in the previous distribution calculation step, the first omission condition is defined based on the number of repetitions or frequency of repetitions of the distribution calculation step.
10. An information processing system according to claim 8 or claim 9, wherein in the recursive optimization step, if the second omission condition is met, the distribution calculation step is omitted and the force calculation step and the update step are executed using the distribution information calculated in the previous distribution calculation step, and the second omission condition is defined to be met according to the difference between the latest second material information and the second material information before the update.
11. The information processing system according to claim 10, wherein the second omission condition is defined to be satisfied when the latest second material information changes to less than or equal to a specified value in the number of electrons corresponding to the atom in the distribution information calculated based on the second material information before the update or the second material information before the update.
12. The information processing system according to claim 10, wherein the second omission condition is defined to be satisfied when the period during which the distribution calculation step is continuously omitted is less than or equal to a specified value.
13. An information processing system according to any one of claims 1 to 12, comprising an information processing device including the processor and a terminal capable of accessing the information processing device.
14. An information processing method comprising each step of an information processing system described in any one of claims 1 to 12.
15. A program that causes at least one computer to perform each step of the information processing system described in any one of claims 1 to 12.