Model creating device, estimating device, and model creation method

Abstract

This model creating device comprises: a calculating unit (251) that estimates a probability distribution of each piece of time-series data and a joint probability distribution of the plurality of pieces of time-series data on the basis of the plurality of pieces of time-series data and basis function candidates of a model equation; an analyzing unit (252) that, on the basis of the probability distribution and the joint probability distribution, calculates a movement entropy indicating the strength of a causal relationship for a combination of a cause and a result for each piece of time-series data; a basis function determining unit (253) that extracts primary causal relationships in which the movement entropy (T) is equal to or greater than a predetermined threshold value, and determines a basis function of the model equation from the basis function candidates on the basis of the combination of primary causal relationships; an estimation processing unit (26) that estimates a parameter value included in the basis function on the basis of the time-series data; and a model determining unit (27) that creates a model on the basis of the basis function and the parameter value.

Description

Model Creation Apparatus, Estimation Apparatus, and Model Creation Method

[0001] The present disclosure relates to a model creation apparatus, an estimation apparatus, and a model creation method.

[0002] In order to predict phenomena that will occur in the future, it is common practice to create models based on time-series data of various physical quantities, and further perform simulations for various cases (initial values, parameters, etc.). Since simulations are executed as time evolution of models expressed by differential equations, their accuracy depends on the performance of the model. For model creation, a method of performing machine learning using time-series data and constructing a model in a data-driven manner is widely adopted.

[0003] Non-Patent Document 1 discloses that a model is generated by acquiring time-series data of a plurality of elements and estimating by analogy the relationships between the plurality of elements based on their correlations.

[0004] Fama, E. F. (1970).“Efficient Capital Markets:A Review of Theory and Empirical Work.” The Journal of Finance, 25(2),383-417. [Searched on March 14, 2025], Internet <URL:https: / / www.jstor.org / stable / <2325486>

[0005] However, for highly nonlinear phenomena such as meteorological phenomena and oceanic phenomena, the instantaneous fluctuation process of physical quantities is important. Therefore, the method of estimating by analogy the relationships between a plurality of elements and the model based on the correlation of time-series data may not sufficiently capture the instantaneous fluctuation process of physical quantities in nonlinear phenomena and the causal relationship between a plurality of data. For this reason, there has been a problem that a model created by the method disclosed in Non-Patent Document 1 cannot achieve sufficient performance when used for simulating highly nonlinear phenomena such as meteorological phenomena.

[0006] This disclosure is made in view of the above circumstances, and its purpose is to provide a model creation device, an estimation device, and a model creation method that can create a model capable of performing highly accurate simulations even for phenomena with strong nonlinearity where the model equations are unknown.

[0007] A model creation apparatus according to one aspect of the present disclosure includes: a calculation unit that estimates the probability distribution of each time series data and the joint probability distribution of the multiple time series data based on a plurality of time series data and candidate basis functions of the model equation; an analysis unit that calculates a moving entropy indicating the strength of the causal relationship for each cause-and-effect combination of the time series data based on the probability distribution and the joint probability distribution; a basis function determination unit that extracts major causal relationships in which the moving entropy is greater than or equal to a predetermined threshold and determines the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; an estimation processing unit that estimates the parameter values ​​included in the basis functions based on the time series data; and a model determination unit that creates a model based on the basis functions and the parameter values.

[0008] An estimation device according to one aspect of the present disclosure includes: a calculation unit that estimates the probability distribution of each time series data and the joint probability distribution of the multiple time series data based on a plurality of time series data and candidate basis functions of a model equation; an analysis unit that calculates a moving entropy indicating the strength of the causal relationship for each cause-and-effect combination of the time series data based on the probability distribution and the joint probability distribution; a basis function determination unit that extracts major causal relationships in which the moving entropy is greater than or equal to a predetermined threshold and determines the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; an estimation processing unit that estimates the parameter values ​​included in the basis functions based on the time series data; a model determination unit that determines a model based on the basis functions and the parameter values; a time evolution module that estimates each physical quantity based on the created model and the time interval, the calculation end time, and the initial values ​​of the elements included in the model function; and an output unit that outputs the estimated physical quantities.

[0009] A model creation method according to one aspect of the present disclosure is a model creation method in which a model creation device creates a model, the method comprising: estimating the probability distribution of each time series data and the joint probability distribution of the multiple time series data based on a plurality of time series data and candidate basis functions of the model equation; calculating a moving entropy indicating the strength of the causal relationship for each cause-and-effect combination of the time series data based on the probability distribution and the joint probability distribution; extracting major causal relationships in which the moving entropy is greater than or equal to a predetermined threshold; determining the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; estimating the parameter values ​​included in the basis functions based on the time series data; and creating a model based on the basis functions of the model equation and the estimated parameters.

[0010] According to this disclosure, it becomes possible to perform highly accurate simulations even for phenomena with strong nonlinearity where the model equations are unknown.

[0011] Figure 1 is a schematic diagram of the estimation device according to the embodiment. Figure 2 is a block diagram showing the detailed configuration of the estimation unit of the estimation device according to the embodiment. Figure 3 is a block diagram showing the detailed configuration of the model creation device of the estimation device according to the embodiment. Figure 4 is an explanatory diagram showing the joint probability distribution and the histogram of the probability distribution. Figure 5 is a diagram showing the cause and effect matrix and the moving entropy T(X→Y). Figure 6 is a diagram showing the cause and effect matrix, the moving entropy T(X→Y), and the data that exceeds the threshold θ. Figure 7 is a graph showing a portion of the time series data created by "Lorenz63," a simplified model of meteorological phenomena, as time series data to be input to the third input unit, and the results obtained by evolving the model created by the model creation device according to this embodiment over time in the estimation unit. Figure 8 is a graph showing the results equivalent to the time series data of "Lorenz63" obtained when a model created by a conventional method is adopted and evolves over time. Figure 9 is a block diagram showing the hardware configuration of this embodiment.

[0012] The embodiments will be described below with reference to the drawings. Figure 1 is an explanatory diagram showing the schematic configuration of the estimation device 100 according to the embodiment. As shown in Figure 1, the estimation device 100 comprises an estimation unit 1 and a model creation device 2. Figure 2 is a block diagram showing the detailed configuration of the estimation unit 1, and Figure 3 is a block diagram showing the detailed configuration of the model creation device 2.

[0013] As shown in Figure 2, the estimation unit 1 comprises a first input unit 11, a second input unit 12, a time evolution module 13, and an output unit 14.

[0014] The first input unit 11 accepts input of parameters used for time evolution calculations when performing simulations of future predictions, such as future weather forecasts, using a model created by the model creation device 2. For example, it accepts input of parameters such as the time interval Δt and the calculation end time tend when estimating the phenomenon to be predicted in the future, and acquires these parameters. The first input unit 11 acquires the above data, for example, through input operations by the user. The first input unit 11 outputs the acquired data to the time evolution module 13.

[0015] The second input unit 12 accepts input of initial values ​​for each physical quantity in the basis functions created by the model creation device 2 (the basis functions determined by the basis function determination unit 253, which will be described later). The second input unit 12 acquires the input data. As initial values, virtual numerical values ​​that simulate the situation to be estimated may be set. It is also possible to set numerical values ​​at any time from multiple time series data input to the model creation device 2 (time series data input to the third input unit 21, which will be described later) as initial values. For example, the second input unit 12 acquires the initial values ​​a(t0), b(t0), and c(t0) at the initial time t0 and outputs them to the time evolution module 13. "a, b, c" are the basis functions used in the model equations, and their details will be described later.

[0016] The time evolution module 13 acquires a model (a differential equation type model) described by a time differential equation created by the model determination unit 27 of the model creation device 2 (details will be described later). As a differential equation type model that shows the time evolution of physical quantities a, b, and c, the differential equations shown in equations (1) to (3) below are acquired, for example.

[0017] da / dt = -10a + 10b ... (1) db / dt = 28a - b - ac ... (2) dc / dt = ab - (8 / 3)c ... (3) The a, b, c, ab, and ac shown in equations (1) to (3) are basis functions.

[0018] The time evolution module 13 acquires the model created by the model creation device 2. Using the acquired model, the time evolution module 13 calculates each physical quantity at time intervals Δt, based on a general time evolution scheme of differential equations, with the initial value at initial time t0 as the reference, up to the calculation end time tend. The initial values ​​of the physical quantities are, for example, a(t0), b(t0), and c(t0). The time evolution module 13 has the function of estimating each physical quantity based on the model created by the model creation device 2, the time interval Δt, the calculation end time tend, and the initial values ​​of the elements included in the model function.

[0019] The output unit 14 outputs physical quantities, such as a(t), b(t), and c(t), at time intervals Δt from the initial time t0 to the calculation end time tend, as discrete time series data, as estimated values ​​from the simulation. In other words, the output unit 14 outputs the estimated physical quantities.

[0020] On the other hand, as shown in Figure 3, the model creation device 2 includes a third input unit 21, a fourth input unit 22, a fifth input unit 23, a preprocessing unit 24, a causal analysis module 25, an estimation processing unit 26, and a model determination unit 27. Based on multiple time series data, candidate basis functions for the model equations, and a threshold θ for determining causal relationships, the model creation device 2 determines each basis function of the model equations in the causal analysis module 25 and creates a model described by differential equations.

[0021] The third input unit 21 accepts input of multiple time-series data. For example, when time-series data A, B, C, ... are input, the third input unit 21 acquires this data. Each time-series data A, B, C ... can be represented by N elements with a fixed time interval. N is an integer indicating the number of time-series data.

[0022] The preprocessing unit 24 applies preprocessing such as interpolation of missing values, correction of outliers, seasonal adjustment, and trend removal to each element included in each time series data input by the third input unit 21. "Interpolation of missing values" refers to interpolating missing values ​​when some elements included in the time series data are missing, using a well-known interpolation process. "Correction of outliers" refers to correcting abnormal values ​​when the numerical values ​​of elements are clearly abnormal. "Seasonal adjustment" refers to adjusting each time series data according to the season. "Trend removal" refers to removing data that is affected by temporary trends.

[0023] By applying preprocessing to the time series data, preprocessed time series data such as "A = (a0, ..., aN), B = (b0, ..., bN), ..." are generated. The preprocessing unit 24 outputs the preprocessed time series data A, B, ... to the causal analysis module 25.

[0024] The fourth input unit 22 accepts input of candidate basis functions (basis function candidates) for an arbitrarily determined model equation. For example, when "a, b, c, aa, ab, ac, bb, bc, cc, ..." is input as a basis function candidate, the fourth input unit 22 acquires this basis function candidate. The fourth input unit 22 outputs the acquired basis function candidate to the causal analysis module 25.

[0025] The fifth input unit 23 receives input of a threshold θ used in the causal analysis module 25 to determine whether or not a causal relationship exists. The threshold θ is a numerical value used to determine whether or not a causal relationship between a cause and effect combination is a major causal relationship. In other words, the threshold θ is the criterion for deciding whether or not to incorporate the basis function candidates input in the fourth input unit 22 into the model equation. The fifth input unit 23 obtains the input threshold θ and outputs it to the causal analysis module 25.

[0026] The causal analysis module 25 comprises a calculation unit 251, an analysis unit 252, and a basis function determination unit 253.

[0027] The calculation unit 251 estimates the joint probability distributions "p(Y+, Y, X)", "p(Y, X)", "p(Y+, Y)", and the probability distribution "p(Y)" from the plurality of time series data (A, B, ...) input via the third input unit 21 and preprocessed by the preprocessing unit 24, based on a histogram described later. Here, (X, Y) respectively correspond to (cause, effect) in a causal relationship. The suffix "+" indicates the time one step later. For example, for Y = (y1, y2, ..., yN), Y+ = (y2, y3, ..., yN+1).

[0028] Hereinafter, the process of estimating the aforementioned "joint probability distribution" and "probability distribution" will be specifically described. Let the multi-element time series data input via the third input unit 21 and preprocessed by the preprocessing unit 24 be A = (a0, ... aN), B = (b0, ... bN), C = (c0, ... cN). "N" is an integer indicating the number of time series data. Furthermore, let the basis function candidates input via the fourth input unit 22 be "a, b, c, aa, ab, ac, bb, bc, cc, ...".

[0029] When calculating the probability distribution p(Yt) from time series data, a histogram of the probability distribution p(Yt) is generated by counting situations that meet the conditions shown in the following example. The expression "p(Y+, Y, X)" representing the joint probability distribution is represented by the following formula (4).

[0030] p(Y+, Y, X) = count(yt+1, yt, xt) / N ··· (4) The function "count" shown in formula (4) counts sets that satisfy the following conditions for N points of discrete time series data when t = ta+1 to ta+N. Here, "a" is an arbitrary count starting step, and N is a finite value.

[0031] As the counting condition, it is assumed that the set of two variables (yt, xt) at an arbitrary time t in the time series data and the value yt+1 at time t+1, (yt+1, yt, xt), simultaneously satisfies the following formulas (5a) to (5c).

[0032] (yi+)−(Δy) / 2 ≦ yt+1 < (yi+)+(Δy) / 2 ・・・(5a) (yi)−(Δy) / 2 ≦ yt < (yi)+(Δy) / 2 ・・・(5b) (xi)−(Δx) / 2 ≦ xt < (xi)+(Δx) / 2 ・・・(5c) In addition, in the above formulas (5a) to (5c), (yi+) ∈ [ymin to ymax], (yi) ∈ [ymin to ymax], (xi) ∈ [xmin to xmax], and (Δy) = (ymax − ymin) / (nbin), (Δx) = (xmax − xmin) / (nbin), as defined. As a result, for example, as shown in FIG. 4, a histogram with three mutually orthogonal axes for "cause X", "result Y", and "result Y+" can be generated. "nbin" is the number of bars of the histogram shown in FIG. 4, and normally an appropriate value of "nbin" between 50 and 100 is set.

[0033] For example, for time series data of (yt+1, yt, xt) = (20.76, 20.20, 15.52), in the example shown in FIG. 4, the histogram is set as "nbin = 20", which means a histogram with a width of approximately "Δ = 2" is created. Under this condition, the count for (yi+) = 20, (yi) = 20, (xi) = 16 is increased.

[0034] Hereinafter, in addition to the formula "p(Y+, Y, X)" representing the joint probability distribution p shown in the above-mentioned formula (4), the joint probability distributions "p(Y, X)", "p(Y+, Y)", and the probability distribution "p(Y)" are calculated by the following formulas (6a), (6b) and (6c).

[0035]

[0036] The calculation unit 251 outputs the data of the above-mentioned joint probability distributions "p(Y+, Y, X)", "p(Y, X)", "p(Y+, Y)", and the probability distribution "p(Y)" to the analysis unit 252.

[0037] The analysis unit 252 quantitatively calculates the strength of the causal relationship for all combinations of cause (X) and effect (Y) as a transfer entropy T(X→Y) based on the joint probability distribution and probability distribution calculated by the calculation unit 251. In this embodiment, an example using all combinations of cause and effect is described, but only some combinations may be used instead of all of them.

[0038] The procedure for calculating the transfer entropy T(X→Y) is described below. The analysis unit 252 receives the joint probability distributions "p(Y+, Y, X)", "p(Y, X)", "p(Y+, Y)", and the probability distribution "p(Y)" for all combinations of X (cause) and Y (effect) calculated by the calculation unit 251.

[0039] The analysis unit 252 calculates the transfer entropy T(X→Y), which indicates the strength of the causal relationship, using the following equation (7).

[0040]

[0041] In this case, X (cause) is set to a candidate function (a, b, c, aa, ab, ac, ...) that can serve as the basis function of the model, and Y (effect) is set to the quantity one step ahead of cause X (a+, b+, c+), thereby helping to analyze causal relationships that have a temporal sequence.

[0042] The analysis unit 252 generates corresponding data, expressed as a cause-and-effect matrix, based on the transfer entropy T(X→Y), as shown in Figure 5. In Figure 5, darker shades indicate a larger transfer entropy T(X→Y). The analysis unit 252 outputs the corresponding data shown in Figure 5 to the basis function determination unit 253.

[0043] The basis function determination unit 253 extracts the main causal relationships that affect the simulation results based on the corresponding data of the moving entropy T(X→Y) calculated by the analysis unit 252. Based on the extracted combinations, the basis function determination unit 253 determines the basis functions of the model equations. This will be explained in detail below.

[0044] The basis function determination unit 253 determines, based on the threshold θ input in the fifth input unit 23, the combination of X (cause) → Y (effect) such that the moving entropy T(X→Y) is "T(X→Y) > θ" as the main causal relationship. Figure 6 is an explanatory diagram showing data in which the moving entropy T(X→Y) is greater than or equal to the threshold θ. As shown in Figure 6, the data indicated by symbols q1 to q7 are greater than or equal to the threshold θ. Therefore, the combination of these data q1 to q7 is determined as the main causal relationship.

[0045] The threshold θ used for comparison with the moving entropy T(X→Y) may be the threshold input in the fifth input unit 23 described above, or it may be set arbitrarily. For example, the threshold θ may be set to a value (reference value) that is midway between the maximum and minimum values ​​of the moving entropy T(X→Y). That is, it may be set to "θ = {(max T(X→Y)) - min T((X→Y))} / 2". The basis function determination unit 253 determines the basis function candidates that have the main causal relationship combinations as basis functions.

[0046] By setting the threshold value θ to a value greater than the above-mentioned standard value, the number of combinations determined as major causal relationships decreases, thus reducing the basis functions and, consequently, the number of terms in the model equations, resulting in a simpler model. On the other hand, by setting the threshold value θ to a value smaller than the above-mentioned standard value, the number of basis functions increases and the model becomes more complex, resulting in a model that allows for more accurate simulations.

[0047] The basis function determination unit 253 creates a difference equation representing the time evolution of the result from the causes extracted as the main causal relationships to the result of equation (7) above. Specifically, it creates the difference equation shown in equation (8) below.

[0048]

[0049] In equation (8), P1 to P7 are parameter values.

[0050] The following explains in detail. In Figure 6, result a ｎ＋１By extracting only the rows, the causes (each element in the n-th step) affecting a in the (n+1)-th step are linearly combined using the basis of the function. That is, the following formula (8a) is obtained.

[0051] a ｎ＋１ =f ａ (a ｎ , b ｎ )=P １ a ｎ +P ２ b ｎ ...(8a) By rearranging the right-hand side of formula (8a), the difference equation of the following formula (8b) is obtained.

[0052] a ｎ＋１ -a ｎ =(P １ -1)a ｎ +P ２ b ｎ ...(8b) Since the time interval Δt is constant, dividing both sides by Δt gives the following formula (8c).

[0053] (a ｎ＋１ -a ｎ ) / Δt={(P １ -1)a ｎ +P ２ b ｎ} / Δt ...(8c) In formula (8c), by taking the limit as Δt approaches infinitesimal, an ordinary differential equation is obtained. That is, by redefining P １ =(P １ -1) / Δt, P ２ =P ２ / Δt, the following formula (8d) is obtained.

[0054] da / dt=P １ a+P ２ b ...(8d) By implementing this for each row, the functional form of the model equation shown in the following formula (9) is finally obtained.

[0055]

[0056] The basis function determining unit 253 outputs the created differential equation to the estimation processing unit 26.

[0057] The estimation processing unit 26 shown in Figure 3 employs a general parameter estimation method and estimates parameter values ​​for each basis function of the model equation based on multiple time-series data input at the third input unit 21. Specifically, the estimation processing unit 26 estimates the parameters P1 to P7 in the differential equation shown in equation (9). As a result, for example, the parameter values ​​P(P1, P2, P3, P4, P5, P6, P7) = (-10, 10, 28, -1, -28, 1, -8 / 3) are calculated. These parameter values ​​are output to the model determination unit 27.

[0058] The model determination unit 27 determines the model by combining the basis functions of the model equation determined by the basis function determination unit 253 with the corresponding parameter values. The determined model is a differential equation type model described by time differential equations. The model determination unit 27 outputs this model to the time evolution module 13 shown in Figure 2.

[0059] Specifically, the estimation unit 1 performs simulations of each phenomenon using a time differential equation type model created by the model determination unit 27 of the model creation device 2. Since the model created by the model creation device 2 is created using basis functions that utilize data with strong causal relationships between multiple time series data, it becomes possible to obtain highly accurate simulation results even for phenomena with high nonlinearity.

[0060] Next, we will explain the processing when the estimation device 100 described above is applied to a simplified weather model, weather forecast, ocean forecast, earthquake forecast, and mechanical device forecast.

[0061] [Example of application to a simplified weather model] An example of applying the estimation device 100 according to this embodiment to the "Lorenz63" model (a model with three variables a, b, and c), which is a simplified weather model, will be described.

[0062] Let (A, B, C) be the time series data input at the third input unit 21, and let time t ∈ [0 to 100]. Let (a, b, c) be the candidate basis for the model function input at the fourth input unit 22, and let (a, b, c) be the candidate for a nonlinear basis function formed by any combination of these (for example, aa, ab, ac, bb, bc, cc). Let θ be the threshold input at the fifth input unit 23 be θ = {(max T(X→Y)) - min T((X→Y))} / 2 ≈ 1.

[0063] Furthermore, the time interval Δt for time evolution is set to Δt = 0.05 (>0, forward calculation), the calculation end time tend = 50 (>0, future time), and the initial values ​​of a, b, and c at time t0 are set to (a(t0), b(t0), c(t0)) = (1, 1, 1). In addition, the predicted values ​​of the time series Asim = (a(t0), ..., a(tend)) are output at time intervals Δt. Predicted values ​​of the time series Bsim and Csim are also obtained secondarily. Note that "sim" is a suffix indicating the simulation result.

[0064] By using the causal analysis module 25 according to this embodiment, the model equations shown in equations (10a) to (10c) below can be obtained.

[0065] da / dt = -10a + 10b ... (10a) db / dt = 28a - b - ac ... (10b) dc / dt = ab - (8 / 3)c ... (10c) The third term "ac" on the right-hand side of equation (10b) and the first term "ac" on the right-hand side of equation (10c) are nonlinear elements.

[0066] By performing a time-evolution simulation on the model equations (10a) to (10c) described above, the results shown in Figure 7 were obtained. As shown in Figure 7, the predicted values ​​match the time series of the weather model "Lorenz63" used as input.

[0067] Next, we will describe a comparative example that does not use the causal analysis module 25 shown in Figure 3. In the comparative example, the model equations do not include nonlinear elements and are given by equations (11a) to (11c) below.

[0068] da / dt = -10a + 10b ... (11a) db / dt = -13a + 9.5b - 2.2c + 1 ... (11b) dc / dt = -a + 2b - 0.5c + 28 ... (11c) Using the above model equations (11a) to (11c), when a time progression similar to the original "Lorenz63" simulation is performed, the result shown in Figure 8 is obtained. The average value is reproduced, but the chaotic time evolution of the input time series is not reproduced for instantaneous fluctuations.

[0069] In other words, it is understood that by using the model creation device 2 according to this embodiment, highly accurate prediction results can be obtained for weather forecasts with a high degree of nonlinearity.

[0070] [Example of use in predicting sudden changes in precipitation] Next, an example of predicting sudden changes in precipitation, which is an example of weather forecasting, will be described using the estimation device 100 according to this embodiment.

[0071] In the third input unit 21, time-series data (A, B, C, D, E, F, G, H, I, J) = (precipitation, temperature, wind speed, wind direction, atmospheric pressure, humidity, cloud cover, sunshine, sea surface temperature, ice temperature) are input. (a, b, c, d, e, f, g, h, i, j) and any combination thereof (for example, ab, ehj, log(a), sin(b), ...) are used as candidate basis for the model function.

[0072] Furthermore, the time interval Δt for time evolution is set to Δt > 0 (forward calculation), and the calculation end time is set to tend (> 0, future time). The initial values ​​are the numerical values ​​of "a, b, c, d, e, f, g, h, i, j" as described above at time t0.

[0073] The output is a time series of predicted precipitation values, Asim = (a(t0), ..., a(tend)). Additionally, time series data of predicted values ​​for other variables (Bsim, Csim, Dsim, Esim, ...) can be obtained as a secondary result.

[0074] [Examples of use in ocean forecasting] Next, we will explain the prediction of primary production by photosynthesis of marine microorganisms, which is an example of ocean observation, using the estimation device 100 according to this embodiment. Here, we predict the oxygen concentration in the ocean, which affects the improvement of marine ecosystems and fish catches, and the primary production of microorganisms, which influences ocean acidification, from time-series data of physical quantities that can be observed with ocean observation devices (buoys, etc.).

[0075] In the third input unit 21, time-series data is input: (A, B, C, D, E, F, G, H, I, J, K, L) = (primary production by marine microorganisms, total primary production, salinity, oxygen concentration, acidification degree, nutrient concentration, light intensity, chlorophyll concentration, pH, number or density of predators in the microbial community, number or density of predators in the microbial community, and concentration of pollutants).

[0076] In the fourth input unit 22, candidate bases for the model function (a, b, c, d, e, f, g, h, i, j, k, l), and any combination thereof (for example, ab, ehj, log(a), sin(b), ...) are input.

[0077] Furthermore, the time interval Δt for time evolution is set to Δt > 0 (forward calculation), and the calculation end time is set to tend (> 0, future time). The initial values ​​are the numerical values ​​of "a, b, c, d, e, f, g, h, i, j" as described above at time t0.

[0078] The output is a time series Asim = (a(t0), ..., a(tend)) of predicted primary production by marine microorganisms. Furthermore, as a secondary effect, time series of predicted values ​​for other variables (Bsim, Csim, Dsim, Esim, ...) can be obtained.

[0079] [Example of use in earthquake prediction] Next, we will explain how to predict the epicenter of an earthquake using the estimation device 100 according to this embodiment. Here, the epicenter is identified as being near the location with the earliest start time of vibration among multiple observation points xi. In particular, in the case of an anomalous seismic zone, vibrations may be stronger at observation points far from the epicenter, so it is necessary to analyze the details of the time series of vibrations at multiple points by going back in time. Therefore, by simulating a model based on the observed time series, it is possible to obtain time series data with higher temporal resolution for past vibrations.

[0080] In the third input unit 21, time-series data (A, B, C, D, E, F, G, H, I, J) = (vibration at position x1, vibration at position x2, vibration at position x3, ..., geothermal temperature at position x1, geothermal temperature at position x2, geothermal temperature at position x3, ...) is input. Position xi is set to an arbitrary position in three-dimensional space.

[0081] In the fourth input unit 22, candidate bases for the model function (a, b, c, d, e, f, g, h, i, j) and any combination thereof (for example, af, log(f), sin(a), ...) are input.

[0082] Furthermore, the time interval Δt for time evolution is set to Δt > 0 (forward calculation), and the calculation end time is set to tend (< 0, past time). The initial values ​​are the numerical values ​​of "a, b, c, d, e, f, g, h, i, j" as described above at time t0.

[0083] The output is obtained as the oscillation Xsim = (x(t0), ..., x(tend)) at position xi (where tend is a past time). Additionally, the time series of predicted values ​​for other variables (Bsim, Csim, Dsim, Esim, ...) can be obtained as a secondary result.

[0084] [Example of use in predicting mechanical failures] Next, as an example of predicting mechanical failures using the estimation device 100 according to this embodiment, we will describe an example of identifying parts that generate strong vibrations and heat that lead to mechanical failures.

[0085] In the third input unit 21, time-series data (A, B, C, D, E, F, G, H, I, J) = (vibration at part x1, vibration at part x2, vibration at part x3, ..., surface temperature at part x1, geothermal temperature at part x2, geothermal temperature at part x3, ...) is input.

[0086] In the fourth input unit 22, candidate bases for the model function (a, b, c, d, e, f, g, h, i, j) and any combination thereof (for example, af, log(f), sin(a), ...) are input. The time interval Δt for time evolution is set to Δt > 0 (forward calculation), and the calculation end time is set to tend (> 0, future time). The initial values ​​are the numerical values ​​of "a, b, c, d, e, f, g, h, i, j" at time t0.

[0087] The output is the vibration Xsim = (x(t0), ..., x(tend)) at component xi. Additionally, the time series of predicted values ​​for other variables (Bsim, Csim, Dsim, Esim, ...) can be obtained as a secondary result.

[0088] [Example of use for identifying faulty parts in machinery] Next, we will describe how the estimation device 100 according to this embodiment can be used to identify faulty parts in machinery.

[0089] In the third input unit 21, time-series data (A, B, C, D, E, F, G, H, I, J) = (vibration at part x1, vibration at part x2, vibration at part x3, ..., surface temperature at part x1, geothermal temperature at part x2, geothermal temperature at part x3, ...) is input.

[0090] In the fourth input unit 22, candidate bases for the model function (a, b, c, d, e, f, g, h, i, j) and any combination thereof (for example, af, log(f), sin(a), ...) are input. The time interval Δt for time evolution is set to Δt < 0 (forward calculation), and the calculation end time is set to tend (< 0, past time). The initial values ​​are the numerical values ​​of "a, b, c, d, e, f, g, h, i, j" as described above at time t0.

[0091] The output is the vibration Xsim = (x(t0), ..., x(tend)) at component xi, where "tend" is a past time. Additionally, the time series of predicted values ​​for other variables (Bsim, Csim, Dsim, Esim, ...) can be obtained as a secondary result.

[0092] As described above, the model creation device 2 according to this embodiment includes a calculation unit 251 that estimates the probability distribution of each time series data and the joint probability distribution of the multiple time series data based on a plurality of time series data and candidate basis functions of the model equation; an analysis unit 252 that calculates moving entropy, which indicates the strength of the causal relationship for each cause-and-effect combination of time series data, based on the probability distribution and the joint probability distribution; a basis function determination unit 253 that extracts major causal relationships in which the moving entropy T is greater than or equal to a predetermined threshold and determines the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; an estimation processing unit 26 that estimates the parameter values ​​included in the basis functions based on the time series data; and a model determination unit 27 that creates a model based on the basis functions and parameter values.

[0093] In this embodiment, the moving entropy T(X→Y) in information theory is calculated using time-series data of multiple input elements. This makes it possible to identify causal relationships between multiple elements. As a result, it is possible to extract, in a data-driven manner, the causal relationships of physical phenomena involving instantaneous interactions between multiple elements that cannot be captured by the average value of time-series data alone. Furthermore, it becomes possible to extract basis functions for model equations quantitatively and comprehensively.

[0094] In this embodiment, the performance of the model that takes into account the causal relationships of physical phenomena is improved, making it possible to improve the prediction accuracy of physical processes that change over time in simulations of highly nonlinear phenomena that cannot be discussed using only average values ​​as in the past.

[0095] By exploring causal relationships important to the phenomenon being simulated from time-series data, it becomes possible to quantitatively extract the functions and elements included in the model equations without any excess or omission, and generate a model.

[0096] Furthermore, as shown in Figure 4, the calculation unit 251 generates a histogram with three mutually orthogonal axes based on cause X, result Y, and result Y+, and estimates the probability distribution and joint probability distribution using the histogram. This makes it possible to create a model that can simulate highly nonlinear phenomena in a simpler way.

[0097] As shown in Figure 9, the model creation device 2 and estimation device 100 of this embodiment described above can use a general-purpose computer system that includes, for example, a CPU (Central Processing Unit, processor) 901, memory 902, storage 903 (HDD: Hard Disk Drive, SSD: Solid State Drive), communication device 904, input device 905, and output device 906. The memory 902 and storage 903 are storage devices. In this computer system, the functions of the model creation device 2 and estimation device 100 are realized when the CPU 901 executes a predetermined program loaded onto the memory 902.

[0098] The model creation device 2 and the estimation device 100 may be implemented on a single computer or on multiple computers. Furthermore, the model creation device 2 and the estimation device 100 may be virtual machines implemented on a computer.

[0099] The programs for the model creation device 2 and the estimation device 100 can be stored on computer-readable recording media such as HDDs, SSDs, USB (Universal Serial Bus) memory, CDs (Compact Discs), and DVDs (Digital Versatile Discs), or they can be distributed via a network. Computer-readable recording media are, for example, non-transitory recording media.

[0100] This disclosure is not limited to the embodiments described above, and numerous modifications are possible within the scope of its essence.

[0101] 1 Estimation Unit 2 Model Creation Device 11 First Input Unit 12 Second Input Unit 13 Time Evolution Module 14 Output Unit 21 Third Input Unit 22 Fourth Input Unit 23 Fifth Input Unit 24 Preprocessing Unit 25 Causal Analysis Module 26 Estimation Processing Unit 27 Model Determination Unit 100 Estimation Device 251 Calculation Unit 252 Analysis Unit 253 Basis Function Determination Unit

Claims

1. A model creation device comprising: a calculation unit that estimates the probability distribution of each time series data and the joint probability distribution of multiple time series data based on multiple time series data and candidate basis functions of the model equation; an analysis unit that calculates moving entropy indicating the strength of the causal relationship for each cause-and-effect combination of the time series data based on the probability distribution and the joint probability distribution; a basis function determination unit that extracts major causal relationships for which the moving entropy is above a predetermined threshold and determines the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; an estimation processing unit that estimates the parameter values ​​included in the basis functions based on the time series data; and a model determination unit that creates a model based on the basis functions and the parameter values.

2. The model creation device according to claim 1, wherein the calculation unit generates a histogram with cause X, result Y, and result Y+ as three mutually orthogonal axes, and estimates the probability distribution and the joint probability distribution using the histogram.

3. An estimation device comprising: a calculation unit that estimates the probability distribution of each time series data and the joint probability distribution of multiple time series data based on multiple time series data and candidate basis functions of a model equation; an analysis unit that calculates moving entropy, which indicates the strength of the causal relationship for each cause-and-effect combination of the time series data, based on the probability distribution and the joint probability distribution; a basis function determination unit that extracts major causal relationships for which the moving entropy is above a predetermined threshold and determines the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; an estimation processing unit that estimates the parameter values ​​included in the basis functions based on the time series data; a model determination unit that determines a model based on the basis functions and the parameter values; a time evolution module that estimates each physical quantity based on the created model, time intervals, calculation end time, and initial values ​​of elements included in the model function; and an output unit that outputs the estimated physical quantities.

4. A model creation method in which a model creation device creates a model, comprising: estimating the probability distribution of each time series data and the joint probability distribution of the multiple time series data based on a plurality of time series data and candidate basis functions of the model equation; calculating a moving entropy indicating the strength of the causal relationship for each cause-and-effect combination of the time series data based on the probability distribution and the joint probability distribution; extracting major causal relationships in which the moving entropy is greater than or equal to a predetermined threshold; determining the basis functions of the model equation from the candidate basis functions based on the combination of major causal relationships; estimating the parameter values ​​included in the basis functions based on the time series data; and creating a model based on the basis functions of the model equation and the estimated parameters.

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