Computer, method for generating time evolution paths, and program for generating time evolution paths

Abstract

In simulating the time evolution of the probability distribution of a system's state variables, arbitrary statistics can be obtained quickly. [Solution] The computer generates a first time evolution path based on the calculation condition parameters sampled from the prior probability distribution of the calculation condition parameters that specify the calculation conditions for the time evolution path, and a time evolution model. The computer then calculates the posterior probability distribution of the calculation condition parameters when the target statistic based on the first time evolution path and the newly generated second time evolution path is the correct statistic. The computer then generates a second time evolution path based on the calculation condition parameters sampled from the posterior probability distribution and a time evolution model such that the error between the correct statistic and the target statistic based on the second time evolution path generated based on the calculation condition parameters sampled from the posterior probability distribution is less than the target error.

Description

[Technical Field]

[0001] This invention relates to a computer, a method for generating time evolution paths, and a program for generating time evolution paths. [Background technology]

[0002] There is a technique called data assimilation that estimates the current and future state of complex systems based on system observations and simulations. In data assimilation, when simulating the time evolution of the probability distribution of the system's state, it is common to consider the uncertainty of the system's initial conditions, boundary conditions, and model parameters as probability distributions.

[0003] One method for simulating the time evolution of the probability distribution of a system state is Monte Carlo simulation, which involves extracting multiple samples from the probability distribution of uncertain parameters and performing a time evolution simulation for each sample. In Monte Carlo simulation, O(1 / ε) is used to reduce the error by a factor of ε. 2 This requires a massive amount of computation, resulting in an enormous computational cost.

[0004] For example, Non-Patent Document 1 discloses a method for simulating the time evolution of the probability distribution of a system state using a quantum computer, employing the Koopman-von Neumann (KvN) form. According to Non-Patent Document 1, by using a generalized KvN form, it becomes possible to simulate the classical dynamics of nonlinear, non-Hamiltonian systems using a quantum computer. Furthermore, Non-Patent Document 2 discloses that the computational efficiency of squaring is improved compared to classical Monte Carlo simulation by using amplitude estimation.

[0005] In other words, by combining the method disclosed in Non-Patent Document 1 with the amplitude estimation method disclosed in Non-Patent Document 2, the error can be reduced by a factor of ε with a computational complexity of O(1 / ε). [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Ilon Joseph, Koopman-von Neumann approach to quantum simulation of nonlinear classical dynamics, [online], PHYSICAL REVIEW RESEARCH 2, 043102(2020), [Accessed January 23, 2025], Internet [Non-Patent Document 2] Ashley Montanaro, Quantum speedup of Monte Carlo methods, [online], Proceedings of The Royal Society Series A, vol. 471 no. 2181, 20150301, 2015, [Accessed 2025.01.23], Internet [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] However, even combining the method disclosed in Non-Patent Document 1 with the method disclosed in Non-Patent Document 2 only yields information on a specific statistic at a certain future time (for example, the mean value of a certain state variable of the system). In other words, there was room to improve the simulation method so that arbitrary statistics could be obtained quickly, similar to Monte Carlo simulations, in the simulation of the time evolution of the probability distribution of the system's state variables.

[0008] This invention has been made in consideration of the above circumstances, and one of its objectives is to quickly obtain arbitrary statistics in the simulation of the time evolution of the probability distribution of the state variables of a system. [Means for solving the problem]

[0009] To achieve the above object, the present invention, as one aspect, provides a computer that generates a time evolution path representing the time evolution of a system with time-series variables, wherein a processor included in the computer calculates, for a target statistic based on the variables related to the time evolution path, a correct statistic indicating a value that the target statistic should take at a target time based on a time evolution model that models the time evolution, samples a calculation condition parameter from a prior probability distribution of the calculation condition parameter that specifies calculation conditions for the time evolution path, generates a first said time evolution path based on the calculation condition parameter sampled from the prior probability distribution and the time evolution model, assumes a newly generated second said time evolution path, calculates a posterior probability distribution of the calculation condition parameter when the target statistic based on the first time evolution path and the second time evolution path is the correct statistic, samples the calculation condition parameter from the posterior probability distribution such that an error between the correct statistic and the target statistic based on the second time evolution path generated based on the calculation condition parameter sampled from the posterior probability distribution is less than a target error, and generates the second time evolution path based on the calculation condition parameter sampled from the posterior probability distribution and the time evolution model. [Effects of the Invention]

[0010] According to the present invention, for example, in a simulation of the time evolution of the probability distribution of state variables of a system, an arbitrary statistic can be obtained at high speed. [Brief Description of the Drawings]

[0011] [Figure 1] Figure 1 is a block diagram illustrating an example of a functional configuration of a stochastic scenario generation device. [Figure 2] Figure 2 is an explanatory diagram illustrating an example of a weather scenario. [Figure 3A] Figure 3A is an explanatory diagram illustrating an example of sampling a new weather scenario. [Figure 3B] Figure 3B is an explanatory diagram illustrating an example of sampling a new weather scenario. [Figure 4] Figure 4 is an explanatory diagram showing an example of the data structure of the calculation condition parameter database. [Figure 5] Figure 5 is an explanatory diagram showing an example of the data structure of a time evolution path database. [Figure 6] Figure 6 is an explanatory diagram showing an example of the data structure of a statistics database. [Figure 7] Figure 7 is a flowchart showing an example of a probabilistic scenario generation process. [Figure 8] Figure 8 is an explanatory diagram showing an example of the user interface of the input section. [Figure 9] Figure 9 is an explanatory diagram showing an example of the user interface of the output unit. [Figure 10] Figure 10 is a block diagram showing an example of computer hardware. [Modes for carrying out the invention]

[0012] The embodiments of the present invention will be described in detail below with reference to Figures 1 to 9. However, the present invention is not limited to the following embodiments.

[0013] In this embodiment, we describe an example of generating time evolution paths (weather scenarios) sampled from prior probability distributions of calculation condition parameters using Monte Carlo simulation. Here, calculation condition parameters are parameters that specify the calculation conditions for time evolution paths, such as initial conditions, boundary conditions, and parameters of the weather time evolution model.

[0014] This embodiment is effective, for example, when predicting weather conditions for several hours from images captured by weather satellites. By using this embodiment, for example, by reducing the number of Monte Carlo simulation iterations required in a particle filter, which is a type of data assimilation method, it is expected that the computational resources and power consumption required for highly accurate weather forecasting will be reduced.

[0015] In this embodiment, we describe an example of generating weather scenarios, but it can also be applied to systems other than weather, such as human flow simulations, where the time evolution model can be expressed using differential equations, Hamiltonian formalisms, Lagrangian formalisms, etc.

[0016] Figure 1 is a block diagram showing an example of the functional configuration of the probabilistic scenario generation device 100.

[0017] The probabilistic scenario generation device 100 includes an interface 101, a DB (database) 102, a statistical calculation unit 103, a calculation condition parameter sampling unit 104, a path generation unit 105, and an error estimation unit 106.

[0018] Interface 101 has an input unit 111 and an output unit 112. Input unit 111 receives data including target statistics and target errors. Input unit 111 may also receive a function of the prior distribution of the calculation condition parameters.

[0019] DB102 includes calculation condition parameters DB121 (Figure 4), time evolution path DB122 (Figure 5), and statistics DB123 (Figure 6).

[0020] The statistics calculation unit 103 estimates the correct statistic for the specified target statistic based on the prior distribution of the calculation condition parameters and stores it in the statistics DB 123. The statistics calculation unit 103 is composed of a quantum computer or quantum computing device.

[0021] The calculation condition parameter sampling unit 104 samples calculation condition parameters from the prior distribution of calculation condition parameters input from the input unit 111 or from the posterior distribution of calculation condition parameters (described later), and stores them in the calculation condition parameter DB 121.

[0022] The path generation unit 105 generates weather scenarios by solving time evolution models such as differential equations that describe the time evolution of weather, and stores them in the time evolution path DB 122. The error estimation unit 106 calculates sample statistics (described later) from the weather scenarios stored in the time evolution path DB 122, and calculates the error against the ground truth statistics stored in the statistics DB 123.

[0023] The probabilistic scenario generation device 100 has a statistical calculation unit 103 which is composed of a quantum computer or quantum computing device. However, other processing units may also be composed of quantum computers or quantum computing devices, not just the statistical calculation unit 103. Alternatively, the probabilistic scenario generation device 100 may be configured such that the statistical calculation unit 103 performs statistical calculations using the computing resources of an external quantum computer or quantum computing device connected via a network.

[0024] Figure 2 is an explanatory diagram showing an example of a weather scenario.

[0025] Figure 2 shows the temporal evolution of temperature at a certain location as a representative example from among the various weather information that can be obtained, and shows five weather scenarios a1. In this embodiment, we consider the case where we want to quickly converge several statistics (called "target statistics") at a target time, for example, 24 hours later. Here, the target statistics can be expressed in the form of a real-valued function such as equation (1), which uses the expected value of functions f1(X), ..., fn(X) (where n is any natural number) of the random variable X.

number

[0026] Specific examples of target statistics include the mean of the random variable X represented by equation (2) and the standard deviation of the random variable X represented by equation (3).

number

number

[0027] Target statistics are specified by the user, and any number of one or more can be specified. Furthermore, all target statistics do not necessarily have to be values ​​at the same time; for example, various statistics at different times can be treated as target statistics simultaneously, such as the average temperature at time t1 and the standard deviation of humidity at time t2.

[0028] Figures 3A and 3B are explanatory diagrams illustrating an example of sampling a new weather scenario.

[0029] Figure 3A shows that three weather scenarios a2 have already been obtained through weather simulation. Figure 3B shows that, in addition to the three weather scenarios a2 in Figure 3A, one new weather scenario a3 is sampled, and compared to Figure 3A, the target statistic (sample statistic) is closer to the true statistic. Thus, in this embodiment, the next sampling of weather scenarios that causes the target statistic to converge to the true value at high speed can be performed by following the procedure below. However, Figures 3A and 3B are just examples, and the number of weather scenarios already obtained and the number of weather scenarios to be sampled next can also be arbitrary.

[0030] First, the statistics calculation unit 103 calculates the target statistics at the target time. According to Non-Patent Literature 1, the time evolution model of the vector x(t) representing the weather conditions at time t is expressed as shown in equation (4) using the vector-valued function v(x).

number

[0031] When the canonical conjugate momentum P of vector x is introduced, the KvN Hamiltonian H(x,P) can be expressed as shown in equation (5).

number

[0032] The probability distribution p(t,x) of x at time t can be obtained using the wave function φ(t,x) of the quantum system described by the KvN Hamiltonian H(x,P) as shown in equation (6) (Koopman-von Neumann form).

number

[0033] The time evolution of this quantum system can be computed, for example, by discretizing x and encoding it into qubits, and then implementing the time evolution operator in a quantum circuit using the Suzuki-Trotter decomposition. Furthermore, the target statistic can be estimated much faster than when performing Monte Carlo simulation by calculating the expectation value expressed by equation (7) using an amplitude estimation algorithm, such as the one shown in Non-Patent Document 2, for the quantum state at the target time for which the target statistic is to be obtained. The target statistic obtained here will be called the ground truth statistic.

number

[0034] The ground truth statistics obtained here are merely values ​​for specific statistics at a specific time, and this information alone does not allow us to know, for example, the probability distribution of temperature at other times. Therefore, in this embodiment, the sampling of weather scenarios is performed using a method that rapidly converges to the ground truth statistics. This makes it possible to obtain highly accurate weather scenarios, at least for the target statistics, even with a small number of samples.

[0035] In this embodiment, the prior probability distribution p(c) of the calculation condition parameter c is assumed to be sampleable, and the target statistic is expressed as a vector-valued function as shown in equation (8).

number

[0036] Here, the vector-valued function f(c) in equation (8) has its m-th component given by equation (9). Equation (9) explicitly expresses only the c-dependence. Tm is the target time for the target statistic specified by the user, and as mentioned above, it may be a different time depending on m.

number

[0037] Let S0 be the sample set of weather scenarios that have already been obtained, and let S1 be the sample set of weather scenarios to be sampled next. Here, the number of weather scenarios in S0 and S1, |S0| and |S1|, can be arbitrary.

[0038] In this case, the target statistic expressed as in equation (10) based on the expected value calculated using the sample set S will be called the "sample statistic using S".

number

[0039] Here c s is the computational condition parameter for the sample s∈S. Also, f(c s ) is the weather scenario x(t,c) in the calculation condition parameters of sample s∈S. s This is the vector-valued function f(c) (equation (8)) calculated using ).

[0040] The objective in this embodiment is to obtain the sample statistic g using all samples S0∪S1 for a new set of calculation condition parameters C1. S0∪S1 The correct statistic is g * The posterior probability distribution is determined assuming the above conditions. Then, the set of calculation condition parameters C1 is sampled from this posterior probability distribution. The set of calculation condition parameters C1 is defined by equation (11). The posterior probability distribution is expressed by equation (12).

number

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[0041] Sampling of the calculation condition parameter set C1 from the posterior probability distribution of Equation (12) is performed as follows. p(C1) can be written as in Equation (13). Sampling of the calculation condition parameter set C1 from Equation (13) is possible.

Equation

[0042] Therefore, if the value of p(g on the right side of Equation (12) S0∪S1 =g * |C1) is known, C1 can be sampled from the posterior probability distribution of Equation (12) by, for example, sampling importance resampling using this value as a weight.

[0043] Therefore, in the present embodiment, using the already obtained weather scenario {x(t,c s )} s∈S to model p(g S0∪S1 =g * |C1). As this modeling method, there are the following two methods, for example.

[0044] The first one is a method of modeling p(f(c)|c) by Gaussian process regression using the correspondence between c of each already obtained weather scenario {x(t,c s )} s∈S and f(c s ). Thereby, {f(c s )} can be sampled from C1. Also, by definition, from {f(c s )} s∈S1 and {f(c s )} s∈S0 and {f(c s )} s∈S1 , g S0∪S1 can be calculated. Therefore, for example, using kernel density estimation, p(g s )} s∈S1 obtained by multiple samplings of {f(c S0∪S1 =g* |C1) can be modeled.

[0045] The second is {x(t,c)} for each weather scenario that has already been obtained. s )} s∈S c s and f(c s This method uses the correspondence between the functions to deterministically model the approximate function f(c) using, for example, polynomial regression or neural networks. In this method, the exponential distribution L represented by equation (14) is used to calculate p(g S0∪S1 =g * Model |C1). Note that “A~” is equivalent to the symbol A with a “~” placed directly above it.

number

[0046] By the above method, p(C1|g S0∪S1 =g * C1 can be sampled from ), and by solving the weather time evolution model for this C1, a weather scenario {x(t,c)} in which the target statistic converges faster to the true value can be obtained. s )} s∈S You can obtain this.

[0047] The sampling procedure described above is merely one example. For instance, even if the time evolution model of the system is not given by differential equations and only the Hamiltonian is provided, the same procedure can be applied by converting it to a KdV Hamiltonian using the method shown in Non-Patent Document 1.

[0048] Figure 4 is an explanatory diagram showing an example of the data structure of the calculation condition parameter DB121.

[0049] The calculation condition parameter DB121 is a table that stores the calculation condition parameters for each weather scenario. Its column values ​​include the weather scenario ID 401 and the calculation condition parameters associated with weather scenario ID 401. The calculation condition parameters are real values ​​representing initial conditions, such as temperature (location A) initial condition 402, boundary conditions, such as humidity (location B, time 1) boundary condition 403, or model parameters, such as model parameter 404.

[0050] Figure 5 is an explanatory diagram showing an example of the data structure of the time evolution path DB122.

[0051] The Time Evolution Path DB122 is a three-dimensional data structure that stores the time evolution of each variable in each weather scenario. In other words, the Time Evolution Path DB122 represents the time evolution of the target system as a time series of each variable that indicates each state of the target system.

[0052] Each weather scenario stores the time (501) and a state variable associated with time (501) as column values. The state variable is a real value corresponding to each time (501), such as temperature (location A) 502, temperature (location B) 503, humidity (location A) 504, humidity (location B) 505, and there is no limit to the number of such variables, and missing values ​​are permitted.

[0053] Figure 6 is an explanatory diagram showing an example of the data structure of the statistics DB123.

[0054] The statistics DB123 is a table that stores values ​​related to the target statistics. Its column values ​​include the statistics ID 601, the statistics name 602 associated with statistics ID 601, the ground truth statistic 603, the sample statistic 604, and the target error 605. Not all columns are necessarily required; for example, the statistics name 602 and the target error 605 can be omitted.

[0055] Figure 7 is a flowchart showing an example of a probabilistic scenario generation process. The time evolution path generation program is read from memory resources and executed by the processor to perform at least one of the processes shown below.

[0056] (Step S701) Data input acceptance processing. The probabilistic scenario generation device 100 accepts data input including the type of target statistic (statistic name) and target error via the input unit 111, and proceeds to step S702. The type of target statistic (statistic name) and target error are stored in the statistics DB 123.

[0057] (Step S702) Calculation of the correct statistics. The probabilistic scenario generator 100 calculates the correct statistics using the statistics calculation unit 103 and proceeds to step S703. The correct statistics are stored in the statistics DB 123.

[0058] (Step S703) Sampling process from the prior distribution of calculation condition parameters. The probabilistic scenario generation device 100 samples calculation condition parameters from the prior distribution of calculation condition parameters using the calculation condition parameter sampling unit 104, and then proceeds to step S704. The sampled calculation condition parameters are stored in the calculation condition parameter DB 121.

[0059] (Step S704) The first time evolution path calculation process. The probabilistic scenario generator 100 generates weather scenarios for the calculation condition parameters sampled in step S703 using the path generation unit 105, and then proceeds to step S705. The generated weather scenarios are stored in the time evolution path DB 122.

[0060] (Step S705) Sampling process from the posterior distribution of calculation condition parameters. The probabilistic scenario generator 100 uses the calculation condition parameter sampling unit 104 to sample calculation condition parameters from the posterior distribution of calculation condition parameters obtained using the time evolution path DB 122, and then proceeds to step S706. The sampled calculation condition parameters are stored in the calculation condition parameter DB 121.

[0061] (Step S706) The second time evolution path calculation process. The probabilistic scenario generator 100 generates a weather scenario based on the calculation condition parameters and time evolution model sampled in step S705 by the path generation unit 105, and then proceeds to step S707. The generated weather scenario is stored in the time evolution path DB 122.

[0062] (Step S707) Error determination process. The probabilistic scenario generator 100 calculates sample statistics using weather scenarios stored in the time evolution path DB 122 and stores them in the statistics DB 123. From the ground truth statistics 603 and sample statistics 604 stored in the statistics DB 123, the error estimation unit 106 calculates the error for each statistic. If the error is not below the target error 605, the process returns to step S705; otherwise, the probabilistic scenario generation process terminates.

[0063] The above describes the process implemented by the time evolution path generation program. The generation process described above is just one example; for example, instead of using the error calculated by the error estimation unit 106 falling below the target error 605 as the termination condition in step S707, the termination condition may be set to the satisfaction of a predetermined number of iterations.

[0064] For example, steps S703 and S704 are performed using Monte Carlo simulation to generate multiple time evolution paths. Then, steps S705 to S707 are performed using the time evolution path generation method of this embodiment based on equations (8) to (14) described above, to obtain a weather scenario that converges quickly.

[0065] Figure 8 is an explanatory diagram showing an example of the input user interface U1 of the input unit 111. The input user interface U1 consists of a checkbox 801, a text box 802, input boxes 803 and 804, and an add button 805.

[0066] Checkbox 801 is used to select whether to use the target statistic; checking it selects that the target statistic will be used. Text box 802 is for entering the target error for the target statistic.

[0067] Input boxes 803 and 804 are for adding new target statistics, their formulas (definitions), and names. The formula for the target statistic is entered in input box 803, and the name is entered in input box 804. When the add button 805 is pressed, a checkbox 801 and a text box 802 corresponding to, for example, "temperature covariance between location A and location B" are added to the group of target statistics displayed on the screen.

[0068] Figure 9 is an explanatory diagram showing an example of the output user interface U2 of the output unit 112. The output user interface U2 consists of a state variable selection pull-down menu 901, a state variable display unit 902, a statistic selection unit 903, and a statistic display unit 904.

[0069] The state variable selection pull-down menu 901 is operated by the user to select the state variable for the relevant weather scenario. The selected state variable is read from the time evolution path DB 122 and displayed as a time-series graph in the state variable display unit 902.

[0070] Furthermore, the statistics selection unit 903 is operated by the user to select the statistics for the relevant weather scenario. For the selected statistics stored in the statistics DB 123, the sample statistics and ground truth statistics are displayed in a time-series graph on the statistics display unit 904.

[0071] In this case, regarding the sample statistic, in addition to the target statistic calculated using the value of x at time Tm given by equations (9) and (10), a sample statistic shifted by t to another time when the mth component is defined, as in equation (15), is also calculated. The temporal trajectory of this sample statistic tr may be displayed as shown in Figure 9.

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[0072] Furthermore, regarding the correct statistic st, it is not limited to the time Tm given by equations (9) and (10), but the statistic defined by equations (8) and (15) shifted to other times may also be estimated within a range where the absolute value of the shift time t from time Tm is small. This estimation result may be taken as the estimated correct statistic est and displayed as shown in Figure 9. This estimation method is as follows.

[0073] In other words, the time-shifted correct statistic st can be expressed by performing a Taylor expansion up to the first-order term with respect to the shift time t, as shown in equation (16).

number

[0074] Here, the mth component of V in equation (16) is given by equation (17).

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[0075] Here, V can be calculated using the statistical calculation unit 103, or it can be calculated more quickly by approximating it using the obtained sample set S as shown in equation (17).

[0076]

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[0077] Equation (16), which gives the estimated correct statistic est, is highly accurate when the absolute value of the shift time t is sufficiently small, and the error err increases as the absolute value of the shift time t increases. This error err is considered to be approximately equal to the difference between the time-shifted sample statistic tr and the first-order approximation for the shift time t expressed in equation (19).

[0078]

number

[0079] Therefore, by displaying the estimated correct statistics est on the statistics display unit 904 only within a predetermined range of target times where the absolute value of this error err is smaller than a pre-set threshold value, the estimated correct statistics est can be shown only within a range where a certain degree of accuracy is guaranteed.

[0080] Figure 10 is a block diagram showing an example of the hardware of Computer 1000.

[0081] Computer 1000 is an on-premise or cloud computing resource that implements each part of the probabilistic scenario generation device 100 by executing a predetermined program. The probabilistic scenario generation device 100 is constructed using one or more computers 1000.

[0082] The computer 1000 comprises a processor 1001, a main memory 1002, an auxiliary memory 1003, a network interface 1004, an input device 1005, and an output device 1006, all interconnected via an internal communication line 1007 such as a bus.

[0083] The processor 1001 consists of various semiconductor devices, including a CPU and GPU, which are responsible for controlling the overall operation of the computer 1000. The main memory 1002 is composed of, for example, volatile semiconductor memory and is used as the work memory of the processor 1001. The auxiliary storage device 1003 consists of a large-capacity non-volatile storage device such as a hard disk drive, SSD (Solid State Drive), or flash memory and is used to retain various programs and data for long periods of time.

[0084] The executable program 1003a stored in the auxiliary storage device 1003 is loaded into the main memory device 1002 when the computer 1000 is started or when necessary, and is executed by the processor 1001.

[0085] The executable program 1003a may be recorded on a non-temporary recording medium, read from the non-temporary recording medium by a media reader, and loaded into the main memory 1002. Alternatively, the executable program 1003a may be obtained from an auxiliary storage device of an external computer via a network and loaded into the main memory 1002.

[0086] The auxiliary storage device 1003 stores various executable programs 1003a. The main storage device 1002 and the auxiliary storage device 1003 may be collectively referred to as memory.

[0087] The network interface 1004 is an interface device for connecting the computer 1000 to various networks within the system or for communicating with other computers. The network interface 1004 consists of, for example, a NIC (Network Interface Card) such as a wired LAN (Local Area Network) or a wireless LAN.

[0088] The input device 1005 consists of a keyboard, a pointing device such as a mouse, and is used by the user to input various instructions and information into the computer 1000. The output device 1006 consists of a display device such as a liquid crystal display or an organic EL (Electro-Luminescence) display, or an audio output device such as a speaker, and is used to present necessary information to the user when needed.

[0089] (Effects of the embodiment) In the above embodiment, the probabilistic scenario generator 100 generates a first time evolution path based on the calculation condition parameters sampled from the prior probability distribution of the calculation condition parameters and the time evolution model. The probabilistic scenario generator 100 then calculates the posterior probability distribution of the calculation condition parameters when the target statistic based on the first time evolution path and a newly generated assumed second time evolution path is the correct statistic that indicates the value the target statistic should take at the target time. The probabilistic scenario generator 100 then samples the calculation condition parameters from the posterior probability distribution such that the error between the correct statistic and the target statistic based on the second time evolution path is less than the target error. The second time evolution path is a time evolution path generated based on the calculation condition parameters sampled from the posterior probability distribution. The probabilistic scenario generator 100 then generates the second time evolution path based on the calculation condition parameters sampled from the posterior probability distribution and the time evolution model.

[0090] Therefore, according to this embodiment, in the simulation of the time evolution of the probability distribution of the system's state variables, the desired statistic at the target time can be obtained quickly. Furthermore, according to this embodiment, even when the number of samples for the calculation condition parameters is small, the probability distribution of the system state at an arbitrary time and the desired statistic at the target time can be determined quickly and accurately.

[0091] Furthermore, in the above-described embodiment, the probabilistic scenario generator 100 calculates the correct statistics using a quantum computing device. In addition, in the above-described embodiment, the correct statistics are calculated using the Koopman-von Neumann formula and qubit amplitude estimation. Therefore, according to this embodiment, the correct statistics can be estimated at a faster speed compared to the case where Monte Carlo simulation is used.

[0092] Furthermore, in the above-described embodiment, the probabilistic scenario generation device 100 models the posterior probability distribution of the calculation condition parameters using the already generated first time evolution path and a Gaussian process or equation (14). Thus, according to this embodiment, sampling of the calculation condition parameters from the posterior probability distribution of the calculation condition parameters is done using the p(g) on ​​the right-hand side of equation (12) described above. S0∪S1 =g * This can be done by sampling importance resampling with |C1) as the weight.

[0093] Furthermore, in the above-described embodiment, the probabilistic scenario generator 100 repeatedly samples the calculation condition parameters from the posterior probability distribution of the calculation condition parameters until the error between the correct statistic and the target statistic falls below the target error. Therefore, according to this embodiment, when sampling the calculation condition parameters related to error determination, the sampling of the calculation condition parameters and the generation of the second time evolution path can be performed quickly by using the method of this embodiment based on equations (8) to (14) described above. Therefore, even when a strict numerical value is set for the target error and the number of sampling trials increases, the time evolution simulation can be converged quickly, so that the probability distribution of the system state at an arbitrary time and the target statistic at the target time can be determined quickly and accurately.

[0094] Furthermore, in the above-described embodiment, the true value of the ground truth statistic within a predetermined range of the target time is estimated based on the ground truth statistic and the target statistic based on the second time evolution path. Therefore, according to this embodiment, the true value of the ground truth statistic (estimated ground truth statistic) can be calculated quickly within a range where accuracy is guaranteed.

[0095] In the above-described embodiment, the user inputs the type of target statistic and the target error via an input user interface. In the above-described embodiment, the ground truth statistic, the first time evolution path, the second time evolution path, the target statistic based on the first time evolution path, the target statistic based on the second time evolution path, the true value of the ground truth statistic within a predetermined range of the target time, or the calculation condition parameters are output via an output user interface. Therefore, according to this embodiment, the user can perform a simulation of the time evolution of the probability distribution of the system's state variables and obtain a GUI display of various statistics, various time evolution paths, and calculation condition parameters simply by specifying the type of target statistic and the target error.

[0096] The present invention is not limited to the embodiments described above, and various modifications are included. For example, the embodiments described above are described in detail for the purpose of clearly illustrating the present invention, and are not necessarily limited to those having all the configurations described. Furthermore, it is possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment. Furthermore, it is possible to add, delete, or replace parts of the configuration of each embodiment with other configurations. In addition, some or all of the above-described configurations, functions, processing units, processing means, etc., may be realized in hardware, for example, by designing them as integrated circuits. Furthermore, the above-described configurations, functions, etc., may be realized in software by having a processor interpret and execute a program that realizes each function. [Explanation of Symbols]

[0097] 100: Probabilistic scenario generator, 1000: Computer, 1001: Processor

Claims

1. A computer that generates a time evolution path representing the time evolution of a system using time-series variables, The processor of the aforementioned computer is With respect to the target statistic based on the aforementioned variable relating to the time evolution path, the correct statistic that indicates the value the target statistic should take at the target time is calculated based on the time evolution model that models the time evolution. The calculation condition parameters that specify the calculation conditions for the aforementioned time evolution path are sampled from the prior probability distribution of the calculation condition parameters, A first time evolution path is generated based on the calculation condition parameters sampled from the prior probability distribution and the time evolution model. Assuming a newly generated second time evolution path, calculate the posterior probability distribution of the calculation condition parameters when the target statistic based on the first time evolution path and the second time evolution path is the correct statistic. The calculation condition parameters are sampled from the posterior probability distribution such that the error between the correct statistic and the target statistic based on the second time evolution path generated based on the calculation condition parameters sampled from the posterior probability distribution is less than the target error. The second time evolution path is generated based on the calculation condition parameters sampled from the aforementioned posterior probability distribution and the time evolution model. A computer characterized by the following features.

2. A computer according to claim 1, The processor calculates the correct statistics using a quantum computing device. A computer characterized by the following features.

3. A computer according to claim 2, The aforementioned processor, The correct statistics are calculated using the Koopman-von Neumann format and qubit amplitude estimation. A computer characterized by the following features.

4. A computer according to claim 1, The aforementioned processor, The aforementioned posterior probability distribution is modeled using the first time evolution path. A computer characterized by the following features.

5. A computer according to claim 1, The aforementioned processor, The calculation condition parameters are repeatedly sampled from the posterior probability distribution until the error falls below the target error. A computer characterized by the following features.

6. A computer according to claim 5, The aforementioned processor, Based on the aforementioned correct statistic and the aforementioned target statistic based on the second time evolution path, the true value of the correct statistic within a predetermined range of the target time is estimated. A computer characterized by the following features.

7. A computer according to claim 5, The aforementioned processor, The user inputs the type of the target statistic and the target error via an input user interface. A computer characterized by the following features.

8. A computer according to claim 6, The aforementioned processor, The correct statistics, the first time evolution path, the second time evolution path, the target statistics based on the first time evolution path, the target statistics based on the second time evolution path, the true value of the correct statistics within a predetermined range of the target time, or the calculation condition parameters are output via the output user interface. A computer characterized by the following features.

9. A method for generating a time evolution path, characterized by having each process performed by the computer described in any one of claims 1 to 8.

10. A time evolution path generation program for causing a computer to function as a calculator according to any one of claims 1 to 8.

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