Simulation apparatus, simulation system, simulation method, and simulation program

Abstract

A simulation apparatus (10) comprises a computation device (11), and a storage device (13) for storing a program executed by the computation device (11). The computation device (11) defines a lattice-form space representing a powder material, generates state data indicating the phase state of cells constituting the space, and outputs the state data to an Ising machine (20), thereby optimizing the state data using a QUBO model (210) of the Ising machine (20) and acquiring a simulation result indicating the binding state between a plurality of particles after a change.

Description

Simulation device, simulation system, simulation method, and simulation program

[0001] The present disclosure relates to a simulation device, a simulation system, a simulation method, and a simulation program for simulating changes in the bonding state between multiple particles contained in a powder material.

[0002] As the demand for calculating huge amounts of data in a short time using AI (Artificial Intelligence) increases, the power consumption of the computers that perform the calculations also increases significantly. AI is realized by von Neumann computers, also known as classical computers, which use processors such as GPUs (Graphics Processing Units) or TPUs (Tensor Processing Units). However, in recent years, non-von Neumann computers, typified by quantum computers, which consume less power than von Neumann computers, have been attracting attention.

[0003] While von Neumann computers can perform tasks that require a huge amount of calculations, quantum computers and related technologies among non-von Neumann computers can obtain optimal solutions in a very short time using unique algorithms. For example, quantum Ising machines (also known as "quantum annealing machines") perform calculations for optimization problems by utilizing the tunneling effect, which allows superconducting spin energy to rapidly reach the ground state. Digital annealers, which mimic the operation of quantum Ising machines using electronic circuits, can also obtain optimal solutions quickly by specializing in calculations for optimization problems. Ising machines (quantum Ising machines, digital annealers) can only solve QUBO (Quadratic Unconstrained Binary Optimization) problems and optimization problems of quadratic expressions with two-valued variables, known as the Ising model, which is a model equivalent to QUBO. However, they can reduce power consumption compared to von Neumann computers.

[0004] The above-mentioned Ising machine can also be applied to materials chemistry. For example, Non-Patent Document 1 discloses the use of an Ising machine to perform a simulation of phase separation in solid-phase materials.

[0005] "A phase-field model by an Ising machine and its application to the phase-separation structure of a diblock polymer," [Retrieved August 15, 2023], Internet<URL:https: / / www.nature.com / articles / s41598-022-14735-4>

[0006] The simulation disclosed in Non-Patent Document 1 can obtain simulation results for phase separation of solid-phase materials, but cannot be applied to simulations in other materials chemistry fields. For example, in the field of materials chemistry, sintered bodies are obtained by bonding multiple particles contained in powder materials through sintering or other processes. To form a good sintered body, it is necessary to find optimal sintering conditions by exploring various conditions, such as the initial state of the particles, the heat treatment time, the heat treatment temperature, and the type of additive. However, if heat treatment is performed under each sintering condition each time, it would take an enormous amount of time to find the optimal sintering conditions. Therefore, there is a need for a technology that can use an Ising machine to simulate changes in the bonding state between multiple particles contained in a powder material.

[0007] The present disclosure has been made to solve such problems, and its purpose is to provide a technology for using an Ising machine to perform a simulation of changes in the bonding state between multiple particles contained in a powder material.

[0008] According to an aspect of the present disclosure, a simulation device includes a calculation device and a storage device that stores a program executed by the calculation device. The calculation device defines a lattice-like space representing a powder material, generates state data indicating the phase state of each cell that constitutes the space, and outputs the state data to an Ising machine, thereby optimizing the state data using a QUBO model of the Ising machine and obtaining a simulation result indicating the bonding state between multiple particles after the change.

[0009] A simulation system according to another aspect of the present disclosure includes a simulation device and an Ising machine having a QUBO model. The simulation device defines a lattice-like space representing a powder material, generates state data indicating the phase state of each cell constituting the space, and outputs the state data to the Ising machine, thereby optimizing the state data using the QUBO model and obtaining a simulation result indicating the bonding state between a plurality of particles after the change.

[0010] A simulation method according to another aspect of the present disclosure includes, as processing executed by a computer, a step of defining a lattice-like space representing a powder material, a step of generating state data indicating the phase state of each cell constituting the space, and a step of outputting the state data to an Ising machine, thereby optimizing the state data using a QUBO model of the Ising machine, and obtaining a simulation result indicating the bonding state between a plurality of particles after the change.

[0011] A simulation program according to another aspect of the present disclosure causes a computer to execute the steps of defining a lattice-like space representing a powder material, generating state data indicating the phase state of each cell that constitutes the space, and outputting the state data to an Ising machine to optimize the state data using the QUBO model of the Ising machine and obtain simulation results indicating the bonding state between multiple particles after the change.

[0012] According to the present disclosure, by outputting state data indicating the phase state of each cell that constitutes the lattice-like space representing the powder material to an Ising machine, the state data can be optimized using the QUBO model of the Ising machine, and simulation results can be obtained that indicate the bonding state between multiple particles after the change.

[0013] FIG. 1 is a diagram showing the configuration of a simulation system according to embodiment 1. FIG. 2 is a diagram showing the bonding state between a plurality of particles before and after sintering. FIG. 3 is a diagram showing an example of simulation processing by a simulation device according to embodiment 1. FIG. 4 is a diagram showing an example of simulation processing by a simulation device according to embodiment 1. FIG. 5 is a diagram showing an example of simulation results obtained by the simulation device according to embodiment 1. FIG. 6 is a diagram showing an example of comparison of simulation results according to the location where state data is generated in a simulation system according to embodiment 2. FIG. 7 is a diagram showing an example of simulation processing by a simulation device according to embodiment 3.

[0014] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are designated by the same reference numerals, and description thereof will not be repeated.

[0015] First Embodiment A simulation system 1 according to a first embodiment will be described with reference to FIGS.

[0016] Fig. 1 is a diagram showing the configuration of a simulation system 1 according to embodiment 1. As shown in Fig. 1, the simulation system 1 includes a simulation device 10 and an Ising machine 20. The simulation device 10 uses the Ising machine 20 to execute a process (hereinafter also referred to as a "simulation process") for simulating changes in the bonding state between a plurality of particles contained in a powder material.

[0017] The simulation device 10 is configured as a von Neumann-type computer, such as a desktop, laptop, or tablet PC (Personal Computer), or a mobile terminal such as a smartphone. The simulation device 10 includes a calculation unit 11, a memory 12, a storage unit 13, a display 14, an input unit 15, a data reading unit 16, and a communication unit 17.

[0018] The arithmetic device 11 is a computing entity (computer) that executes predetermined processing. The arithmetic device 11 is configured with a processor such as a CPU (Central Processing Unit), MPU (Micro-Processing Unit), TPU (Tensor Processing Unit), or GPU (Graphics Processing Unit). A processor, which is an example of the arithmetic device 11, has the function of executing predetermined processing by executing a predetermined program. However, some or all of these functions may be implemented using dedicated hardware circuits such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field-Programmable Gate Array). The term "processor" is not limited to a processor in the narrow sense that executes processing using a stored program, such as a CPU, MPU, TPU, or GPU, but may also include hardwired circuits such as an ASIC or FPGA. The arithmetic device 11 described above can also be interpreted as a processing circuitry that executes predetermined processing. The arithmetic device 11 may be configured on a single chip or multiple chips. Furthermore, the processor and associated processing circuitry may be comprised of multiple computers interconnected by wire or wirelessly, such as via a local area network or a wireless network. The processor and associated processing circuitry may also be comprised of a cloud computer that performs remote calculations based on input data and outputs the results of the calculations to other devices at remote locations.

[0019] The memory 12 includes a volatile storage area (e.g., a working area) that temporarily stores program code, work memory, etc. when the arithmetic unit 11 executes various programs. Examples of the memory 12 include volatile memories such as DRAM (Dynamic Random Access Memory) and SRAM (Static Random Access Memory), and non-volatile memories such as ROM (Read Only Memory) and flash memory.

[0020] The storage device 13 stores various programs and various data executed by the arithmetic device 11. For example, the storage device 13 stores a simulation program 130 executed by the arithmetic device 11. The storage device 13 may be one or more non-transitory computer readable media, or may be one or more computer readable storage media. Examples of the storage device 13 include a hard disk drive (HDD) and a solid state drive (SSD).

[0021] The simulation program 130 includes a program that defines a processing procedure for the arithmetic device 11 to execute a simulation process. The arithmetic device 11 executes the simulation process in accordance with the simulation program 130, thereby obtaining a simulation result of a change in the bonding state between a plurality of particles contained in a powder material. The simulation program 130 may be designed by a user using the input device 15, may be read from the storage medium 30 by the data reading device 16, or may be obtained from another device such as a server via a network by the communication device 17.

[0022] The display 14 displays a predetermined image, such as a simulation image showing the simulation result obtained by the arithmetic unit 11 .

[0023] The input device 15 is an interface for allowing a user to input various data to the simulation device 10, and includes, for example, a keyboard or a mouse.

[0024] The data reader 16 is a device for reading data stored in the storage medium 30. The storage medium 30 may be any medium capable of storing various types of data, such as a CD (Compact Disc), a DVD (Digital Versatile Disc), or a USB (Universal Serial Bus) memory.

[0025] The communication device 17 is an interface that enables the arithmetic device 11 to communicate with other devices via a wired connection using an optical fiber line or the like or a wireless connection such as Wi-Fi (registered trademark). For example, the communication device 17 can communicate with the Ising machine 20 based on the control of the arithmetic device 11 and transmit and receive data to and from the Ising machine 20.

[0026] The Ising machine 20 is, for example, a quantum computer (cloud computer) provided by cloud computing. The Ising machine 20 uses the QUBO model 210 based on the data acquired from the simulation device 10 to execute a simulation of changes in the bonding state between multiple particles contained in the powder material, and outputs the simulation results to the simulation device 10. The simulation device 10 displays a simulation image indicating the simulation results acquired from the Ising machine 20 on the display 14.

[0027] Using the simulation system 1 configured as described above, a user can simulate the process of bonding a plurality of particles contained in a powder material by sintering or the like to obtain a sintered body.

[0028] Figure 2 is a diagram showing the bonding state between multiple particles before and after sintering. As shown in Figure 2, multiple particles are mixed in the powder material before sintering. When the powder material is sintered, multiple adjacent particles bond together to form a dense object called a sintered body. Sintering is a phenomenon in which multiple particles contained in a powder material are heated at a temperature lower than the melting point, causing multiple adjacent particles to bond together to form a sintered body.

[0029] To form a good sintered body, it is necessary to find optimal sintering conditions by exploring various conditions, such as the initial state of the particles (e.g., particle shape or size), the heat treatment time, the heat treatment temperature, or the type of additive. However, whether or not a good sintered body can be obtained requires actually subjecting the powder material to heat treatment, and if heat treatment is performed each time under each sintering condition, it takes an enormous amount of time to find the optimal sintering conditions. In this regard, by using the simulation system 1 according to the embodiment, a user can efficiently obtain simulation results of changes in the bonding state between multiple particles contained in the powder material without actually subjecting the powder material to heat treatment.

[0030] The simulation process performed by the simulation device 10 will be described with reference to Figures 3 and 4. Figures 3 and 4 are diagrams showing an example of the simulation process performed by the simulation device 10 according to the first embodiment. The simulation process can be realized by the arithmetic unit 11 of the simulation device 10 executing a simulation program 130.

[0031] First, the simulation device 10 acquires an enlarged image of the powder material. For example, the simulation device 10 acquires data of the image of the powder material obtained by a user using an electron microscope or the like. As shown in Fig. 3 , the image of the powder material includes a solid phase portion composed of multiple particles (in this example, particles A, B, and C) and a liquid phase portion present between the multiple particles.

[0032] The simulation device 10 performs image processing on the captured image of the powder material to define a grid-like space representing the powder material in the captured image. The simulation device 10 may define a grid-like space representing the powder material not only for the captured image of the powder material, but also for a picture (simulation model) that models the powder material shown in the captured image. Furthermore, the "space" is not limited to a three-dimensional space, but may also be a two-dimensional space on a plane. In the example of FIG. 3, a grid extending two-dimensionally is defined for the two-dimensional captured image.

[0033] For example, the simulation device 10 allocates and arranges a plurality of cells of a predetermined size on the captured image by defining a lattice-like space for the solid phase portions corresponding to each of the plurality of particles A to C and the liquid phase portions existing between the plurality of particles. The simulation device 10 also allocates coordinates to each cell. In the example of Figure 3, the i-axis is allocated to the vertical direction, and the j-axis is allocated to the horizontal direction.

[0034] The simulation device 10 generates data indicating the phase state of each cell to which coordinates are assigned (hereinafter also referred to as "state data"). Specifically, the simulation device 10 assigns data indicating whether the cell is in a liquid phase or a solid phase to each cell to which coordinates are assigned, as well as data for distinguishing each particle. In other words, the state data generated by the simulation device 10 includes data indicating whether the cell is in a liquid phase or a solid phase, and data for distinguishing each particle contained in the powder material.

[0035] Note that the "phase state" in the embodiments is a concept that includes differences in liquid or solid phases and differences in particles. In other words, when two cells have the same "phase state," the two cells have exactly the same state, without differences in liquid or solid phases or particles. On the other hand, when two cells have different "phase states," the two cells differ in either liquid or solid phase, or are composed of different particles.

[0036] The simulation device 10 generates state data that represents the phase state of each cell using vector components, as shown in the following equation (1).

[0037] In the formula (1), "i" and "j" indicate the position coordinates of each cell. ｉｊ０ " is assigned "1" when the target cell is particle A, and "0" when the target cell is a particle other than particle A or a liquid phase portion. ｉｊ１ " is assigned "1" when the target cell is particle B, and "0" when the target cell is a particle other than particle B or a liquid phase portion. ｉｊ２ " is assigned "1" when the target cell is particle C, and "0" when the target cell is a particle other than particle C or a liquid phase portion. ｉｊ３ " is assigned a "1" if the target cell is a liquid phase portion, and a "0" if the target cell is a solid phase portion.

[0038] Furthermore, the state of each cell before sintering is expressed as follows: ｉｊ " is added as a subscript to ".

[0039] In the example of Figure 3, if the coordinates of the pre-sintered cell located at the top left corner are "i" = 0 and "j" = 0, the state data of the pre-sintered cell is expressed by the following equation (3).

[0040] Furthermore, when the coordinates of the pre-sintered cell located at the bottom right end are "i" = 7 and "j" = 7, the state data of the pre-sintered cell is expressed by the following formula (4).

[0041] On the other hand, the equation for the energy (Hamiltonian) of the QUBO model 210 of the Ising machine 20 is expressed by at least one cost function. For example, as shown in FIG. 4 , the energy (H) of the QUBO model 210 is expressed by the first cost function (J ａｄｊ H ａｄｊ ) and the second cost function (J ｉｎｉｔ Hｉｎｉｔ ) and the third cost function (J ｓｕｍ H ｓｕｍ ) and

[0042] The first cost function (J ａｄｊ H ａｄｊ ) among them, "J ａｄｊ " is "H ａｄｊ " is a parameter for determining the weight of "H ａｄｊ " is expressed by the following equation (6).

[0043] In formula (6), "q ｉｊ " represents the state data of any cell including a solid phase portion and a liquid phase portion, as shown in the above formula (1). ｉｊ±1 " is "q ｉｊ represents the state data of cells located around (for example, adjacent to) the cell corresponding to "q ｉｊ " is "q ３３ "In the case of "q ｉｊ±1 " is "q ２２ "," "q ２３ "," "q ２４ "," "q ３２ "," "q ３４ "," "q ４２ "," "q ４３ " and "q ４４ " represents the state data of each cell in "H ａｄｊ " is expressed as the square of the L2 norm of the difference between the state data (vector components) of one cell and the state data (vector components) of each of the other cells located around the one cell.

[0044] The first cost function (J ａｄｊ H ａｄｊ ) has a small value when the phase state of a cell is the same as that of other cells located around the cell. For example, "q ｉｊ " is "q ３３ "In the case of "q ３３ " and "q ２２ "," "q ２３ "," "q ２４ "," "q ３２ "," "q３４ "," "q ４２ "," "q ４３ " and "q ４４ When each phase state of " is the same, the first cost function (J ａｄｊ H ａｄｊ ) becomes the minimum "0", and the energy (H) of the QUBO model 210 becomes stable.

[0045] The second cost function (J ｉｎｉｔ H ｉｎｉｔ ) among them, "J ｉｎｉｔ " is "H ｉｎｉｔ " is a parameter for determining the weight of "H ｉｎｉｔ " is expressed by the following equation (7).

[0046] In formula (7), "q ０ ｉｊ " represents the state data of any cell before sintering, as shown in the above-mentioned formula (2). ｉｊ " represents the state data of any cell after sintering, as shown in the above formula (1). That is, "H ｉｎｉｔ " is expressed as the square of the L2 norm of the difference between the state data (vector components) of a cell before sintering (before the state change) and the state data (vector components) of the cell after sintering (after the state change).

[0047] The second cost function (J ｉｎｉｔ H ｉｎｉｔ ) has a small value when the phase state of a cell before sintering is the same as that of the cell after sintering. For example, "q ｉｊ " is "q ３３ In the case of "q" before sintering ３３ " and the phase state of "q ３３ When the phase states of " and " are the same, the second cost function (J ｉｎｉｔ H ｉｎｉｔ ) becomes the minimum "0", and the energy (H) of the QUBO model 210 becomes stable.

[0048] The third cost function (J ｓｕｍ H ｓｕｍ ) among them, "J ｓｕｍ " is "H ｓｕｍ" is a parameter for determining the weight of "H ｓｕｍ " is expressed by the following equation (8).

[0049] In formula (8), "q ｉｊ " represents the state data of any cell, as shown in the above formula (1). That is, "H ｓｕｍ " is expressed as the L1 norm of the state data (vector components) of one cell.

[0050] The third cost function (J ｓｕｍ H ｓｕｍ ) has a small value when one cell is in one phase state. For example, "q ｉｊ " is "q ３３ "In the case of "q ３３ is (1,0,0,0), (0,1,0,0), (0,0,1,0), or (0,0,0,1). ｓｕｍ H ｓｕｍ ) becomes the minimum value of "1", and the energy (H) of the QUBO model 210 becomes stable.

[0051] As described above, the energy (H) of the QUBO model 210 expressed by the formula (5) is calculated by the first cost function (J ａｄｊ H ａｄｊ ), the second cost function (J ｉｎｉｔ H ｉｎｉｔ ), and the third cost function (J ｓｕｍ H ｓｕｍ ) are all minimized.

[0052] The user can select the parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) is determined, and each determined parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) into the simulation device 10 using the input device 15. For example, the user may input sintering conditions such as the initial state of the particles, the heat treatment time, the heat treatment temperature, and the type of additive, as well as each parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ) and each parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) can be input to the simulation device 10.

[0053] The user also defines a grid-like space in the captured image of the powder material using the procedure shown in FIG. 3. The user then assigns data indicating whether each cell is in a liquid phase or a solid phase, and assigns data for distinguishing each particle, thereby creating state data (q ０ ｉｊ The simulation device 10 generates a parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and state data (q ０ ｉｊ ) is output to the Ising machine 20.

[0054] The Ising machine 20 optimizes the state data based on at least one cost function that represents the energy (H) of the QUBO model 210. Specifically, the Ising machine 20 optimizes the state data based on the parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and the state data of each cell before sintering (q ０ ｉｊ ) into the energy (H) of the QUBO model 210, and calculate the state data (q ｉｊ The Ising machine 20 calculates the calculated state data (q ｉｊ ) is output to the simulation device 10 as a simulation result.

[0055] The simulation device 10 calculates the state data (q ｉｊ ) and displays a simulation image on the display 14 showing the bonding state between the plurality of particles after sintering.

[0056] In this way, the user can set the predetermined parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) is input to the simulation device 10, and the state data (q ０ ｉｊ ) and output it to the Ising machine 20, the state data (q ０ ｉｊ ) and optimize the state data (q ｉｊ ), i.e., simulation results showing the bonding state between multiple particles after sintering can be obtained. This allows users to simulate changes in the bonding state between multiple particles before and after sintering while suppressing increases in power consumption.

[0057] Furthermore, the user can select the state data (q ｉｊ ) is the state data (q ０ ｉｊ ) and again use the parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) into the simulation device 10 and output to the Ising machine 20, the state data (q ０ ｉｊ ) is optimized again to obtain the state data (q ｉｊ ), that is, a simulation result showing the bonding state between a plurality of particles after new sintering can be obtained. Note that the parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) uses the same value as in the first simulation.

[0058] For example, Fig. 5 is a diagram showing an example of a simulation result obtained by the simulation device 10 according to the first embodiment. Fig. 5 shows an example in which a powder compact formed from ceramic powder or the like is sintered in stages from timing (t = 0) to timing (t = 60) to finally form a sintered body. In the example of Fig. 5, the parameter (J ａｄｊ ) is set to “1.5”, and the parameter (J ｉｎｉｔ ) is set to “1.0”, and the parameter (J ｓｕｍ ) is set to "2.0".

[0059] As shown in FIG. 5, at a timing (t=0), the user uses the simulation device 10 to define a lattice space representing a powder compact and calculate the state data (q ０ ｉｊ ) and generate the parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and data indicating the timing (t=5) at which the simulation result is desired to be obtained, to the Ising machine 20. Then, the state data (q ｉｊ ), i.e., simulation results showing the bonding state between multiple particles at the initial stage of sintering are obtained.

[0060] Next, the user uses the simulation device 10 to calculate the state data (q ０ ｉｊ ) and generate the parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and data indicating the timing (t=30) at which the simulation result is desired to be obtained, to the Ising machine 20. Then, the state data (q ｉｊ ), i.e., simulation results showing the bonding state between multiple particles during the middle stage of sintering are obtained.

[0061] Next, the user uses the simulation device 10 to calculate the state data (q ０ ｉｊ ) and generate the parameter (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and data indicating the timing (t=60) at which the simulation result is desired to be obtained, to the Ising machine 20. Then, the state data (q ｉｊ ), i.e., a simulation result showing the bonding state between multiple particles at the end of sintering is obtained.

[0062] In this way, the user can set the predetermined parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ ) and the state data of each cell before sintering (q ０ ｉｊ ) are repeatedly input into the simulation device 10 in a time series, it is possible to obtain simulation results that show the change in the bonding state between a plurality of particles before and after sintering in a time series.

[0063] [Embodiment 2] A simulation system 1 according to embodiment 2 will be described with reference to Fig. 6. Only the differences between the simulation system 1 according to embodiment 2 and the simulation system 1 according to embodiment 1 will be described below. Fig. 6 is a diagram showing an example of a comparison of simulation results according to the location where state data is generated in the simulation system 1 according to embodiment 2.

[0064] In the simulation system 1 according to the first embodiment described above, the simulation device 10 is configured to generate state data for each of the plurality of cells constituting the space to which coordinates are assigned. However, as shown in FIG. 5 , during the process of bonding of the plurality of particles by sintering or the like, each particle gradually expands. Therefore, while the phase state of the contour portion (surface portion) of each particle may change, the phase state of the portion other than the contour portion (surface portion) of each particle (e.g., the interior of each particle) does not change. In other words, only the state data of the portion where the contour portion of each particle is adjacent to the liquid phase contributes to the simulation results. Therefore, in the simulation system 1 according to the second embodiment, the simulation device 10 is configured to generate state data for only the portion of the plurality of cells constituting the space to which coordinates are assigned, where the contour portion of each of the plurality of particles is adjacent to the liquid phase.

[0065] 6 , when the simulation device 10 generates state data for only cells in which the contour portions of each of a plurality of particles are adjacent to the liquid phase and outputs the state data to the Ising machine 20, the amount of calculations performed by the Ising machine 20 is smaller than when the simulation device 10 generates state data for all cells and outputs the state data to the Ising machine 20. This makes it less likely that the capacity of the memory 12 will be depleted, and also makes it less likely that the upper limit of the amount of data that can be handled by the Ising machine 20 will be exceeded, making it possible to increase the resolution of the simulation results, and thus enabling the user to obtain simulation results for a greater number of particles over a wider range.

[0066] [Third Embodiment] A simulation system 1 according to a third embodiment will be described with reference to Fig. 7. Only the differences between the simulation system 1 according to the third embodiment and the simulation systems 1 according to the first and second embodiments will be described below. Fig. 7 is a diagram showing an example of a simulation process performed by a simulation device 10 according to the third embodiment.

[0067] In the simulation system 1 according to the third embodiment, the energy (H) of the QUBO model 210 is calculated by the first cost function (J ａｄｊ H ａｄｊ ) and the second cost function (J ｉｎｉｔ H ｉｎｉｔ ) and the third cost function (J ｓｕｍ H ｓｕｍ ) and the fourth cost function (J ｌｉｑｕｉｄ H ｌｉｑｕｉｄ ) may be formed as a sum of

[0068] The fourth cost function (J ｌｉｑｕｉｄ H ｌｉｑｕｉｄ ) among them, "J ｌｉｑｕｉｄ " is "H ｌｉｑｕｉｄ " is a parameter for determining the weight of "H ｌｉｑｕｉｄ " is expressed by the following equation (10).

[0069] In formula (10), "q ｉｊ,ｌｉｕｉｄ " represents the state data of only the liquid phase cells. ｌｉｑｕｉｄ " indicates the state of the liquid phase (for example, the degree of stability of the liquid phase).

[0070] The user can set the parameters of the fourth cost function (J ｌｉｑｕｉｄ ) can be varied to adjust the bonding state of multiple particles by sintering. Note that the user can adjust the sintering conditions, such as the initial state of the particles, the heat treatment time, the heat treatment temperature, or the type of additive, and the parameter (J ｌｉｑｕｉｄ ) and the parameter (J ｌｉｑｕｉｄ For example, in the example of FIG. 7, the parameter (J ａｄｊ ) is set to “1.0”, and the parameter (J ｉｎｉｔ ) is set to “0.4”, and the parameter (J ｓｕｍ ) is set to "3.0". In this setting state, the parameter (J ｌｉｑｕｉｄ) is changed stepwise to "0.3", "0.5", "0.7", and "0.9", the simulation result of the bonding state of the plurality of particles at the timing (t=200) changes. In the example of FIG. 7, the parameter (J ｌｉｑｕｉｄ ) is larger, the smaller particles disappear and other particles grow to fill in the gaps, and the sintered body is formed by the larger particles.

[0071] In this way, the user can set the predetermined parameters (J ａｄｊ , J ｉｎｉｔ , J ｓｕｍ , J ｌｉｑｕｉｄ ) is input to the simulation device 10, and the state data (q ０ ｉｊ ) and output it to the Ising machine 20, the state data (q ０ ｉｊ ) and optimize the state data (q ｉｊ ), i.e., simulation results showing the bonding state between multiple particles after sintering can be obtained.

[0072] [Modifications] The simulation system 1 is not limited to the above embodiment, and various modifications and applications are possible.

[0073] The energy (H) of the QUBO model 210 is not limited to the example shown in equation (5), but can be expressed as the first cost function (J ａｄｊ H ａｄｊ ) and the second cost function (J ｉｎｉｔ H ｉｎｉｔ ) and the third cost function (J ｓｕｍ H ｓｕｍ ) and the fourth cost function (J ｌｉｑｕｉｄ H ｌｉｑｕｉｄ ) and the energy (H) of the QUBO model 210 may be calculated by the first cost function (J ａｄｊ H ａｄｊ ) and the second cost function (J ｉｎｉｔ H ｉｎｉｔ ) and the third cost function (J ｓｕｍ Hｓｕｍ ) and the fourth cost function (J ｌｉｑｕｉｄ H ｌｉｑｕｉｄ ) may be composed of a sum of at least two or more of these.

[0074] In the simulation system 1 according to the above-described embodiment, the Ising machine 20 is configured separately from the simulation device 10, but it may be a part of the configuration of the simulation device 10. For example, if the QUBO model 210 according to the embodiment is realized by pseudo-quantum annealing using the Monte Carlo method, the simulation device 10 may have the functionality of the Ising machine 20 having the QUBO model 210. In this way, a user can perform a simulation of changes in the bonding state between multiple particles contained in a powder material using only one simulation device 10.

[0075] <Aspects> (Item 1) A simulation device (10) according to one aspect includes a calculation device (11) and a storage device (13) that stores a program executed by the calculation device (11). The calculation device (11) defines a lattice-like space representing a powder material, generates state data indicating the phase state of each cell constituting the space, and outputs the state data to an Ising machine (20), thereby optimizing the state data using a QUBO model (210) of the Ising machine (20) to obtain a simulation result indicating the bonding state between a plurality of particles after the change.

[0076] (Item 2) In the simulation device (10) described in item 1, the state data includes data indicating whether each cell is in a liquid phase or a solid phase.

[0077] (Item 3) In the simulation device (10) described in item 1 or 2, the state data includes data for distinguishing each particle contained in the powder material.

[0078] (4) In the simulation device (10) according to any one of paragraphs 1 to 3, the Ising machine (20) optimizes the state data based on at least one cost function that represents the energy of the QUBO model (210). The calculation device (11) obtains a simulation result by outputting the state data and at least one parameter associated with each of the at least one cost function to the Ising machine (20).

[0079] (5) In the simulation device (10) described in 4, at least one cost function includes a first cost function whose value becomes small when the phase state of a cell is the same as that of other cells located around the cell.

[0080] (6) In the simulation device (10) described in paragraph 4 or 5, at least one cost function includes a second cost function whose value becomes smaller when the phase states of a cell before the change and a cell after the change are the same.

[0081] (7) In the simulation device (10) described in any one of paragraphs 4 to 6, at least one cost function includes a third cost function whose value becomes smaller when one cell is in one phase state.

[0082] (Item 8) In the simulation device (10) according to any one of Items 4 to 7, the at least one cost function includes a fourth cost function indicating the degree of stability of the liquid phase.

[0083] (Item 9) In the simulation device (10) described in Item 4, at least one cost function is composed of the sum of a first cost function whose value becomes small when the phase state of a cell is the same as that of other cells located around the cell, a second cost function whose value becomes small when the phase state of a cell before the change is the same as that of a cell after the change, and a third cost function whose value becomes small when the cell is in one phase state.

[0084] (Item 10) In the simulation device (10) described in Item 4, at least one cost function is composed of the sum of a first cost function whose value decreases when the phase state of a cell is the same as that of other cells located around the cell, a second cost function whose value decreases when the phase state of a cell before the change is the same as that of a cell after the change, a third cost function whose value decreases when the cell is in one phase state, and a fourth cost function that indicates the degree of stability of the liquid phase.

[0085] (Item 11) In the simulation device (10) according to any one of items 1 to 10, the calculation device (11) acquires a simulation result of a change in the bonding state between a plurality of particles due to sintering.

[0086] (Item 12) In the simulation device (10) described in any one of Items 1 to 11, the calculation device (11) generates state data for only cells of a plurality of cells constituting the space where the contours of each of a plurality of particles are adjacent to the liquid phase.

[0087] (Item 13) A simulation system (1) according to one aspect includes a simulation device (10) and an Ising machine (20) having a QUBO model (210). The simulation device (10) defines a lattice-like space representing a powder material, generates state data indicating the phase state of each cell constituting the space, and outputs the state data to the Ising machine (20), thereby optimizing the state data using the QUBO model (210) and obtaining a simulation result indicating the bonding state between multiple particles after the change.

[0088] (Item 14) A simulation method according to one aspect includes, as processing executed by a computer (11), a step of defining a lattice-like space representing a powder material, a step of generating state data indicating the phase state of each cell constituting the space, and a step of outputting the state data to an Ising machine (20) to optimize the state data using a QUBO model (210) of the Ising machine (20) and obtain a simulation result indicating the bonding state between a plurality of particles after the change.

[0089] (Item 15) A simulation program (130) according to one embodiment causes a computer (11) to execute the steps of defining a lattice-like space representing a powder material, generating state data indicating the phase state of each cell constituting the space, and outputting the state data to an Ising machine (20) to optimize the state data using a QUBO model (210) of the Ising machine (20) and obtain a simulation result indicating the bonding state between multiple particles after the change.

[0090] Although a number of embodiments have been described above, the features of each of these embodiments can be combined as appropriate within the scope of not causing any contradiction.

[0091] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present disclosure is defined by the claims, not by the description of the above embodiments, and is intended to include all modifications within the meaning and scope of the claims.

[0092] 1 Simulation system, 10 Simulation device, 11 Arithmetic device, 12 Memory, 13 Storage device, 14 Display, 15 Input device, 16 Data reading device, 17 Communication device, 20 Ising machine, 30 Storage medium, 130 Simulation program, 210 QUBO model.

Claims

1. A simulation device that executes a simulation of a change in the bonding state between multiple particles contained in a powder material, comprising: a calculation device; and a storage device that stores a program executed by the calculation device, wherein the calculation device defines a lattice-shaped space representing the powder material, generates state data indicating the phase state of each cell that constitutes the space, and outputs the state data to an Ising machine, thereby optimizing the state data using a QUBO model of the Ising machine to obtain a simulation result that indicates the bonding state between the multiple particles after the change.

2. The simulation device according to claim 1, wherein said state data includes data indicating whether each of said cells is in a liquid phase or a solid phase.

3. A simulation device according to claim 1 or 2, wherein the state data includes data for distinguishing each particle contained in the powder material.

4. The simulation device according to any one of claims 1 to 3, wherein the Ising machine optimizes the state data based on at least one cost function that represents the energy of the QUBO model, and the arithmetic device obtains the simulation result by outputting the state data and at least one parameter associated with each of the at least one cost function to the Ising machine.

5. The simulation device according to claim 4, wherein the at least one cost function includes a first cost function whose value is small when the phase state of a cell is the same as that of other cells located around the cell.

6. A simulation device as described in claim 4 or claim 5, wherein the at least one cost function includes a second cost function whose value is smaller when the phase state of a cell before the change and the phase state of the cell after the change are the same.

7. A simulation device according to any one of claims 4 to 6, wherein the at least one cost function includes a third cost function whose value becomes smaller when a cell is in a certain phase state.

8. A simulation device according to any one of claims 4 to 7, wherein the at least one cost function includes a fourth cost function indicating a degree of stability of the liquid phase.

9. The simulation device described in claim 4, wherein the at least one cost function is composed of a sum of a first cost function whose value is small when the phase state of a cell is the same as that of other cells surrounding the cell, a second cost function whose value is small when the phase state of the cell before the change is the same as that of the cell after the change, and a third cost function whose value is small when the cell is in a certain phase state.

10. The simulation device described in claim 4, wherein the at least one cost function is composed of a sum of a first cost function whose value becomes small when the phase state of a cell is the same as that of other cells surrounding the cell, a second cost function whose value becomes small when the phase state of the cell before the change is the same as that of the cell after the change, a third cost function whose value becomes small when the cell is in a phase state, and a fourth cost function indicating the degree of stability of a liquid phase.

11. The simulation device according to any one of claims 1 to 10, wherein the arithmetic device acquires the simulation result of a change in the bonding state between the plurality of particles due to sintering.

12. A simulation device according to any one of claims 1 to 11, wherein the calculation device generates the state data for only those cells among the plurality of cells constituting the space in which the contours of each of the plurality of particles are adjacent to the liquid phase.

13. A simulation system that performs a simulation of a change in a bonding state between multiple particles contained in a powder material, comprising: a simulation device; and an Ising machine having a QUBO model, wherein the simulation device defines a lattice-like space representing the powder material, generates state data indicating the phase state of each cell that constitutes the space, and outputs the state data to the Ising machine, thereby optimizing the state data using the QUBO model to obtain a simulation result that indicates the bonding state between the multiple particles after the change.

14. A simulation method for simulating a change in the bonding state between a plurality of particles contained in a powder material, the simulation method including, as processing executed by a computer, a step of defining a lattice-like space representing the powder material, a step of generating state data indicating the phase state of each cell constituting the space, and a step of outputting the state data to an Ising machine, thereby optimizing the state data using a QUBO model of the Ising machine, and obtaining a simulation result indicating the bonding state between the plurality of particles after the change.

15. A simulation program that executes a simulation of a change in the bonding state between multiple particles contained in a powder material, the simulation program causing a computer to execute the steps of: defining a lattice-like space representing the powder material; generating state data indicating the phase state of each cell that constitutes the space; and outputting the state data to an Ising machine, thereby optimizing the state data using a QUBO model of the Ising machine, and obtaining a simulation result indicating the bonding state between the multiple particles after the change.

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