Information processing device, information processing method, and program

Abstract

To efficiently optimize an initial condition in a particle flow simulation.SOLUTION: An information processing device 10 includes: a data acquisition section 11 for acquiring an average speed of a particle flow to be an object of a simulation; a position estimation section 12 for assuming that an interval between respective particles constituting the particle flow is equal, so as to estimate positions of the respective particles with the use of the acquired average speed; a speed estimation section 13 for estimating a speed of each particle so as to allow a distribution of the speeds of the respective particles to be the minimum value; and an output section 14 for outputting the estimated positions and speeds of the respective particles.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to an information processing device and information processing method for setting initial conditions in a simulation of a flow of a particle group (hereinafter referred to as a "particle flow"), and further to a program for realizing these. [Background technology]

[0002] In recent years, various simulations have been performed for analysis, optimization, and future prediction. To perform a simulation, it is necessary to create a model that faithfully reproduces the actual situation. In creating a model, initial conditions are set based on data measured in the real world (hereinafter referred to as "observed data"). However, data that cannot be measured in the real world (hereinafter referred to as "unmeasured data") may be required. In such cases, it is necessary to estimate the unmeasured data and set optimal initial conditions.

[0003] Patent Document 1 discloses an apparatus for optimizing initial conditions when a simulation is performed. The apparatus disclosed in Patent Document 1 optimizes the initial conditions by repeatedly setting and updating non-measured data that serve as the initial conditions so as to reduce the error between observed data and simulation data. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2023 / 042612 Summary of the Invention [Problem to be solved by the invention]

[0005] However, the optimization of the initial conditions using the device disclosed in the above-mentioned Patent Document 1 requires a large number of repetitions of complex calculation processing, which is problematic in that it is inefficient and takes too much time.

[0006] An example of an objective of the present disclosure is to solve the above problems and efficiently optimize initial conditions in particle flow simulations. [Means for solving the problem]

[0007] In order to achieve the above object, an information processing device according to one aspect of the present disclosure includes: a data acquisition unit for acquiring an average velocity of the particle flow to be simulated; a position estimation unit that estimates a position of each of the particles by using the obtained average velocity, assuming that the intervals between the particles constituting the particle stream are uniform; a velocity estimation unit that estimates the velocity of each of the particles so that the variance of the velocity of each of the particles is minimized; an output unit that outputs the estimated position and velocity of each of the particles; The present invention is characterized in that it is provided with:

[0008] In order to achieve the above object, an information processing method according to one aspect of the present disclosure includes: a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; The present invention is characterized by having the following:

[0009] Furthermore, in order to achieve the above object, a program according to one aspect of the present disclosure includes: On the computer, a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; The method is characterized in that: [Effects of the Invention]

[0010] As described above, according to the present disclosure, the initial conditions in a particle flow simulation can be efficiently optimized. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating an example of the configuration of an information processing device. [Figure 2] FIG. 2 is a configuration diagram showing an example of the configuration of the information processing device in more detail. [Figure 3] FIG. 3 is a flow diagram illustrating an example of the operation of the information processing device. [Figure 4] FIG. 4 is a diagram conceptually illustrating an example of traffic flow. [Figure 5] FIG. 5 is a diagram illustrating an example of the relationship between the average speed of vehicles and the average density of vehicles. [Figure 6] FIG. 6 is a diagram showing an example of the output result. [Figure 7] FIG. 7 is a block diagram showing an example of a computer that realizes the information processing device according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] (Embodiment) An information processing device, an information processing method, and a program according to an embodiment will be described below with reference to FIGS.

[0013] [Device configuration] First, an example of a schematic configuration of an information processing device will be described with reference to Fig. 1. Fig. 1 is a configuration diagram showing an example of the configuration of an information processing device.

[0014] The information processing device 10 shown in Fig. 1 is a device for setting initial conditions in a simulation of a flow of a particle group (particle flow). The information processing device 10 also functions as an initial condition setting device. As shown in Fig. 1, the information processing device 10 includes a data acquisition unit 11, a position estimation unit 12, a velocity estimation unit 13, and an output unit 14.

[0015] The data acquisition unit 11 acquires the average velocity of the particle flow to be simulated. The position estimation unit 12 estimates the position of each particle, assuming that the intervals between the particles constituting the particle flow are uniform.

[0016] The velocity estimation unit 13 estimates the velocity of each particle so that the variance of the velocity of each particle is minimized. The output unit 14 outputs the estimated position and velocity of each particle.

[0017] In this way, the information processing device 10 can estimate the position and velocity of each particle, which are the initial conditions for the simulation, without repeating complex calculation processes many times. The information processing device 10 can efficiently optimize the initial conditions for the particle flow simulation.

[0018] Next, the configuration and functions of the information processing device 10 will be specifically described with reference to Fig. 2. Fig. 2 is a configuration diagram showing an example of the configuration of the information processing device in more detail.

[0019] As shown in FIG. 2, an information processing device 10 is connected to a terminal device 20 and a computer system 30 via a network or the like.

[0020] The computer system 30 generates a model of the particle flow using the initial conditions (positions and velocities of particles) output by the information processing device 10, and executes a simulation of the particle flow using the generated model.

[0021] A user inputs the average velocity of a particle flow, which is actual simulation data, via the terminal device 20. In this embodiment, the data acquisition unit 11 acquires the average velocity of the particle flow input from the terminal device.

[0022] In this embodiment, the position estimation unit 12 first calculates the average density of the particle flow using a relationship between the average velocity and average density of the particle flow that has been calculated in advance. Furthermore, the position estimation unit 12 calculates the total number of particles from the average density of the particles. Next, the position estimation unit 12 estimates the position of each particle using the calculated total number of particles so that the above-mentioned assumption that "the particles constituting the particle flow are spaced equally apart" holds true.

[0023] In this embodiment, the velocity estimation unit 13 first uses the acquired average velocity to estimate multiple types of velocities that are assumed to be particle velocities in accordance with a preset rule so that the variance of the velocities takes a minimum value. The rule is set in the applied simulation or model.

[0024] Next, the velocity estimation unit 13 determines which of the estimated velocities the velocity of each particle corresponds to so that the variance of the particle velocities in the particle flow is the minimum value. The result of this determination is the estimated result of the velocity of each particle.

[0025] The output unit 14 outputs the position of each particle estimated by the position estimation unit 12 and the velocity of each particle estimated by the velocity estimation unit 13 to the computer system 30. In this way, the computer system executes a simulation of the particle flow.

[0026] [Device operation] Next, an example of the operation of the information processing device 10 will be described with reference to Fig. 3. Fig. 3 is a flow diagram showing an example of the operation of the information processing device. In the following description, Figs. 1 and 2 will be referenced as appropriate. In addition, in the embodiment, an information processing method is implemented by operating the information processing device 10. Therefore, the description of the information processing method in the embodiment will be replaced with the description of the operation of the information processing device below.

[0027] As shown in FIG. 3, first, the data acquisition unit 11 acquires the average velocity of the particle flow to be simulated via the terminal device 20 (step A1).

[0028] Next, the position estimation unit 12 assumes that the particles constituting the particle flow are spaced apart at equal intervals, and estimates the position of each particle using the obtained average velocity (step A2).

[0029] Specifically, in step A2, the position estimation unit 12 first calculates the average density of the particle flow by applying the average velocity acquired in step A1 to the previously calculated relationship between the average velocity and average density of the particle flow. The position estimation unit 12 then calculates the total number of particles from the average density of the particle flow. The position estimation unit 12 then estimates the position of each particle using the calculated particle number so that the above-mentioned assumption holds true.

[0030] Next, the velocity estimation unit 13 estimates the velocity of each particle so that the variance of the velocity of each particle takes the minimum value (step A3).

[0031] Specifically, in step A3, the velocity estimation unit 13 first estimates multiple types of velocities that are expected as particle velocities in accordance with a preset rule using the average velocity acquired in step A1, and then determines which of the multiple estimated velocities the velocity of each particle corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value.

[0032] Thereafter, the output unit 14 outputs the positions of each particle estimated in step A2 and the velocities of each particle estimated in step A3 to the computer system 30 (step A4). After executing step A4, the computer system 30 generates a model of the particle flow using the positions and velocities of the particles output in step A4 as initial conditions, and executes a simulation of the particle flow using the generated model.

[0033] [Specific example] Next, a specific example of the operation of the information processing device 10 will be described along the steps shown in Fig. 3 with reference to Fig. 4, Fig. 5, and Fig. 6. In the following, an example will be described in which the particle flow to be simulated is the flow of moving bodies (vehicles) in a traffic flow.

[0034] Figure 4 is a conceptual diagram of an example of traffic flow. As shown in Figure 4, when observing each section of a road, it can be seen that the faster the average speed in a section, the lower the vehicle density, and the slower the average speed in a section, the higher the vehicle density. In traffic engineering, it is known as an empirical rule that there is a certain relationship between the average speed of vehicles and vehicle density. Note that vehicle density in this case can be calculated from the average number of vehicles in a specific road section and within a specific time range. Therefore, hereafter, this will be referred to as "average vehicle density."

[0035] FIG. 5 is a diagram showing an example of the relationship between the average vehicle speed and the average vehicle density. The plotted points in FIG. 5 are actual measurements taken on a road. By fitting the following equation (1) to these actual measurements, the relationship between the average vehicle speed and the average vehicle density in a traffic flow can be determined. In the following equation (1), v is the average vehicle speed, and k is the average vehicle density. a and b are parameters determined by fitting. The dashed line shown in FIG. 5 is a graph of equation (1) determined by fitting.

[0036] (Number 1) v=a exp(-k / b)

[0037] Step A1: In step A1, the data acquisition unit 11 acquires the average speed of vehicles in the traffic flow as the average speed of the particle flow to be simulated via the terminal device 20. Here, the acquired average vehicle speed is a value actually measured in a specific section of the road (specific road section). The specific section is the section to be simulated.

[0038] Step A2: In step A2, the position estimation unit 12 first calculates the average density of vehicles by substituting the average speed obtained in step A1 into the above equation 1. Furthermore, the position estimation unit 12 calculates the number of vehicles in the corresponding road section from the average density. Next, the position estimation unit 12 estimates the position of each vehicle using the calculated number of vehicles so that the assumption that "the intervals between each particle constituting the particle flow are uniform" is valid.

[0039] Specifically, the position estimation unit 12 determines the position of each vehicle based on the entropy maximization principle so that the distance between vehicles is equal. For example, if N vehicles exist in a specific section, the position estimation unit 12 determines the position x of the i (=1, 2, ... N)th vehicle. i is calculated using the following formula 2. In the following formula 2, x s indicates the position of the start point of the interval, and x e indicates the location of the end point of the section. If the target road has two or more lanes, it is possible to estimate the vehicle position by assuming the proportion of vehicles in each lane, calculating the number of vehicles in each lane, and then using the following equation 2 for each lane.

[0040] (Number 2) x i =x s +i(x e -x s ) / (N+1)

[0041] Step A3: In step A3, the speed estimation unit 13 estimates the speed of each vehicle so that the variance of the speed of each vehicle is minimized. When the variance of the speed is large, the possibility of a rear-end collision is high. However, since the possibility of a rear-end collision is low in reality, it is assumed that the variance of the speed is minimized as described above.

[0042] Specifically, the speed estimation unit 13 first uses the average speed obtained in step A1 to estimate multiple types of speeds that are expected to be the speed of the vehicle in accordance with pre-set simulation rules so that the variance of the speed of each vehicle takes on a minimum value.

[0043] For example, suppose that the speed resolution is set to a multiple of 20 km / h in the simulation model. In this case, this becomes the rule. Therefore, the speed estimation unit 13 sets the speed based on the average speed so that it is a multiple of 20 km / h and the speed variance is minimized.

[0044] That is, if the average speed in a certain section is 48.5 [Km / h], the speed estimation unit 13 sets the possible vehicle speed values ​​to 60 [km / h] and 40 [km / h], which are multiples of 20 [km / h]. In this case, if the vehicle speed is estimated as possible values ​​of 80 [km / h] and 20 [km / h], the variance will not be the minimum value, which violates the restriction.

[0045] Next, the speed estimation unit 13 calculates the number of vehicles corresponding to each set speed. For example, if the set speed is the low speed V l and the speed on the high speed side V h The total number of vehicles is N, and the speed is V l The number of vehicles is N l , velocity V h Number of vehicles: N h Let's say.

[0046] In this case, the speed estimation unit 13 calculates the speed V lNumber of vehicles N l and velocity V h N in the algebra of vehicles h In the following equation 3, dv indicates the speed resolution [km / h], and v s indicates the average speed [km / h] acquired by the data acquisition unit 11. "round" indicates that the value is rounded off. Also, the following equation 3 expresses the speed V l The number of vehicles is N l , velocity V h The number of vehicles is N h In this case, the harmonic mean of each vehicle speed is derived from the condition that it matches the obtained average speed (in traffic engineering, the average vehicle speed is defined as the harmonic mean rather than the arithmetic mean of each vehicle).

[0047] (Number 3) N l =round[NV l (V l +dv-v s )] / v s domestic violence

[0048] (Number 4) N h =NN l

[0049] In the case where the above-mentioned average speed is 48.5 [Km / h] and the vehicle speeds are set to 60 [km / h] and 40 [km / h], it is further assumed that the distance of the section is 1 km and the average vehicle density is 49 [vehicles / km]. In this case, the speed estimation unit 13 calculates, using the above-mentioned equations 3 and 4, that there are 23 vehicles traveling at a speed of 40 [km / h] and 26 vehicles traveling at a speed of 60 [km / h].

[0050] Then, the speed estimation unit 13 randomly assigns a set speed to each vehicle whose position has been calculated in step A2 so as to match the number of vehicles at each calculated speed.

[0051] Step A4: In step A4, the output unit 14 outputs the position of each vehicle calculated in step A2 and the speed of each vehicle calculated in step A3 to the computer system 30. Fig. 6 is a diagram showing an example of the output result. The result shown in Fig. 6 is output for each section (1 km) every minute.

[0052] After step A4 is executed, the computer system 30 generates a traffic flow model using the positions and speeds of each vehicle output in step A4 as initial conditions, and executes a traffic flow simulation using the generated model.

[0053] [Effects of the embodiment] As described above, in the embodiment, the position and speed of each vehicle in a traffic flow can be estimated without repeating complex calculation processes many times, and these can be used as initial conditions for a simulation. According to the embodiment, the initial conditions for a traffic flow simulation can be efficiently optimized.

[0054] Furthermore, although the above example describes a case where the particle flow is a traffic flow, the present disclosure is not limited to this example and can also be used to simulate various particles flowing inside a pipe, duct, etc.

[0055] [program] The program in the embodiment may be any program that causes a computer to execute steps A1 to A4 shown in Fig. 3. By installing and executing this program in a computer, the information processing device and information processing method in the embodiment can be realized. In this case, the processor of the computer functions as a data acquisition unit 11, a position estimation unit 12, a speed estimation unit 13, and an output unit 14, and performs processing. In addition to a general-purpose PC, examples of the computer include a smartphone and a tablet terminal device.

[0056] The program in the embodiment may be executed by a computer system constructed by a plurality of computers, in which case, for example, each computer may function as any one of the data acquisition unit 11, the position estimation unit 12, the speed estimation unit 13, and the output unit 14.

[0057] [Physical configuration] A computer that implements the information processing device 10 by executing the program in the embodiment will now be described with reference to Fig. 7. Fig. 7 is a block diagram showing an example of a computer that implements the information processing device in the embodiment.

[0058] 7, the computer 110 includes a CPU (Central Processing Unit) 111, a main memory 112, a storage device 113, an input interface 114, a display controller 115, a data reader / writer 116, and a communication interface 117. These components are connected to each other via a bus 121 so as to be able to communicate data with each other.

[0059] Furthermore, the computer 110 may include a GPU (Graphics Processing Unit) or an FPGA (Field-Programmable Gate Array) in addition to or instead of the CPU 111. In this aspect, the GPU or FPGA can execute the programs in the embodiments.

[0060] The CPU 111 loads a program in the embodiment, which is composed of a group of codes and stored in the storage device 113, into the main memory 112 and executes each code in a predetermined order to perform various calculations. The main memory 112 is typically a volatile storage device such as a DRAM (Dynamic Random Access Memory).

[0061] The program in the embodiment is provided in a state stored in a computer-readable recording medium 120. The program in the embodiment may be distributed over the Internet connected via the communication interface 117.

[0062] Specific examples of the storage device 113 include a hard disk drive and a semiconductor storage device such as a flash memory. The input interface 114 mediates data transmission between the CPU 111 and input devices 118 such as a keyboard and a mouse. The display controller 115 is connected to a display device 119 and controls the display on the display device 119.

[0063] The data reader / writer 116 mediates data transmission between the CPU 111 and the recording medium 120, reads programs from the recording medium 120, and writes processing results from the computer 110 to the recording medium 120. The communication interface 117 mediates data transmission between the CPU 111 and other computers.

[0064] Specific examples of the recording medium 120 include general-purpose semiconductor storage devices such as CF (Compact Flash (registered trademark)) and SD (Secure Digital), magnetic recording media such as flexible disks, or optical recording media such as CD-ROMs (Compact Disk Read Only Memory).

[0065] Note that the information processing device 10 in the embodiment can be realized not by a computer on which a program is installed, but by hardware corresponding to each unit, for example, an electronic circuit. Furthermore, the information processing device 10 may be partially realized by a program and the remaining unit by hardware. In the embodiment, the computer is not limited to the computer shown in FIG. 7.

[0066] Some or all of the above-described embodiments can be expressed by (Supplementary Note 1) to (Supplementary Note 12) described below, but are not limited to the following descriptions.

[0067] (Appendix 1) a data acquisition unit for acquiring an average velocity of the particle flow to be simulated; a position estimation unit that estimates a position of each of the particles by using the obtained average velocity, assuming that the intervals between the particles constituting the particle stream are uniform; a velocity estimation unit that estimates the velocity of each of the particles so that the variance of the velocity of each of the particles is minimized; an output unit that outputs the estimated position and velocity of each of the particles; An information processing device comprising:

[0068] (Appendix 2) the position estimation unit calculates an average density of the particle flow using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further calculates a total number of the particles from the calculated average density of the particle flow, and estimates a position of each of the particles using the calculated total number of particles so that the assumption is established. 2. The information processing device according to claim 1.

[0069] (Appendix 3) the velocity estimation unit uses the acquired average velocity to estimate a plurality of types of velocities that are assumed to be the velocity of the particles in accordance with a predetermined rule, and determines which of the estimated plurality of types of velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value; 2. The information processing device according to claim 1.

[0070] (Appendix 4) The particle flow to be simulated is a flow of moving objects in a traffic flow. 2. The information processing device according to claim 1.

[0071] (Appendix 5) a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; An information processing method comprising:

[0072] (Appendix 6) In the position estimation step, an average density of the particle flow is calculated using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further, a total number of the particles is calculated from the calculated average density of the particle flow, and the position of each of the particles is estimated using the calculated total number of particles so that the assumption is established. 1. The information processing method described in Appendix 5.

[0073] (Appendix 7) In the velocity estimation step, a plurality of types of velocities that are assumed to be the velocities of the particles are estimated in accordance with a predetermined rule using the acquired average velocity, and it is determined which of the plurality of estimated velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value. 1. The information processing method described in Appendix 5.

[0074] (Appendix 8) The particle flow to be simulated is a flow of moving objects in a traffic flow. 1. The information processing method described in Appendix 5.

[0075] (Appendix 9) On the computer, a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; A program that executes.

[0076] (Appendix 10) In the position estimation step, an average density of the particle flow is calculated using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further, a total number of the particles is calculated from the calculated average density of the particle flow, and the position of each of the particles is estimated using the calculated total number of particles so that the assumption is established. 10. The program described in Appendix 9.

[0077] (Appendix 11) In the velocity estimation step, a plurality of types of velocities that are assumed to be the velocities of the particles are estimated in accordance with a predetermined rule using the acquired average velocity, and it is determined which of the plurality of estimated velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value. 10. The program described in Appendix 9.

[0078] (Appendix 12) The particle flow to be simulated is a flow of moving objects in a traffic flow. 10. The program described in Appendix 9. [Industrial Applicability]

[0079] As described above, according to the present disclosure, it is possible to efficiently optimize the initial conditions in a particle flow simulation. The present disclosure is useful for systems that perform various simulations. [Explanation of symbols]

[0080] 10. Information processing equipment 11 Data Acquisition Section 12 Position estimation part 13 Speed ​​estimation part 14 Output section 20 Terminal equipment 30 Computer Systems 110 Computer 111 CPU 112 main memory 113 Storage device 114 Input Interface 115 Display Controller 116 Data Reader / Writer 117 Communication Interface 118 Input Devices 119 Display Device 120 Recording Media 121 Pass

Claims

1. a data acquisition unit for acquiring an average velocity of the particle flow to be simulated; a position estimation unit that estimates a position of each of the particles by using the obtained average velocity, assuming that the intervals between the particles constituting the particle stream are uniform; a velocity estimation unit that estimates the velocity of each of the particles so that the variance of the velocity of each of the particles is minimized; an output unit that outputs the estimated position and velocity of each of the particles; An information processing device comprising:

2. the position estimation unit calculates an average density of the particle flow using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further calculates a total number of the particles from the calculated average density of the particle flow, and estimates a position of each of the particles using the calculated total number of particles so that the assumption is established. The information processing device according to claim 1 .

3. the velocity estimation unit uses the acquired average velocity to estimate a plurality of types of velocities that are assumed to be the velocity of the particles in accordance with a predetermined rule, and determines which of the estimated plurality of types of velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value; The information processing device according to claim 1 .

4. The particle flow to be simulated is a flow of moving objects in a traffic flow. The information processing device according to claim 1 .

5. a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; An information processing method comprising:

6. In the position estimation step, an average density of the particle flow is calculated using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further, a total number of the particles is calculated from the calculated average density of the particle flow, and the position of each of the particles is estimated using the calculated total number of particles so that the assumption is established. The information processing method according to claim 5 .

7. In the velocity estimation step, a plurality of types of velocities that are assumed to be the velocities of the particles are estimated in accordance with a predetermined rule using the acquired average velocity, and it is determined which of the plurality of estimated velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value. The information processing method according to claim 5 .

8. The particle flow to be simulated is a flow of moving objects in a traffic flow. The information processing method according to claim 5 .

9. On the computer, a data acquisition step of acquiring an average velocity of the particle flow being simulated; a position estimation step of estimating a position of each of the particles using the obtained average velocity, assuming that the particles constituting the particle stream are spaced equally apart; a velocity estimation step of estimating the velocity of each of the particles such that the variance of the velocity of each of the particles is minimized; an output step of outputting the estimated position and velocity of each of the particles; A program that executes.

10. In the position estimation step, an average density of the particle flow is calculated using a relationship between an average velocity of the particle flow and an average density of the particle flow that has been calculated in advance, and further, a total number of the particles is calculated from the calculated average density of the particle flow, and the position of each of the particles is estimated using the calculated total number of particles so that the assumption is established. The program according to claim 9.

11. In the velocity estimation step, a plurality of types of velocities that are assumed to be the velocities of the particles are estimated in accordance with a predetermined rule using the acquired average velocity, and it is determined which of the plurality of estimated velocities the velocity of each of the particles corresponds to so that the variance of the particle velocities in the particle flow takes a minimum value. The program according to claim 9.

12. The particle flow to be simulated is a flow of moving objects in a traffic flow. The program according to claim 9.

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