CN117494862B - Data-driven runoff forecasting model optimization method under limited sample based on hypothesis test - Google Patents

Abstract

The invention provides a data-driven runoff forecasting model optimization method under a limited sample based on hypothesis test, which comprises the following steps: establishing a mapping relation between runoff and a forecasting factor, selecting a plurality of data driving models to describe the mapping relation, and establishing an alternative model set; calibrating model parameters for the selected model hypothesis to be used as overall estimation of a real model; sampling the overall model, dividing a sample set into a training set and a test set, and performing model calibration and inspection on each group of dividing schemes to obtain sampling distribution of prediction precision; determining an optimal sample set partitioning capacity; calculating the prediction precision and the observation value of statistics of the test set; judging whether to reject the original assumption according to whether the observed value of the statistic falls in a reject domain; if a plurality of alternative models pass the hypothesis test, model optimization is performed based on a criterion of minimum rejection rate. The method can verify the reliability of the prediction model on the unknown overall inference prediction, and provides decision basis for the optimization of the prediction model.

Description

A data-driven runoff forecast model optimization method based on hypothesis testing under finite samples

Technical Field

The invention relates to the technical field of runoff forecasting, and in particular to a method for optimizing a data-driven runoff forecasting model under limited samples based on hypothesis testing.

Background technique

Medium- and long-term runoff forecasting is a classic and difficult problem in hydrological forecasting. Reliable runoff forecast information is an important decision-making basis for guiding the scientific planning and utilization of water resources and the safe and economic operation of water conservancy projects. Seeking high-precision forecasting models through model optimization and providing reliable runoff forecast information for management decision makers has always been one of the key tasks of current hydrological forecasting research.

Annual runoff forecasts with long forecast periods often use statistical data-driven models to mine the inherent laws contained in sample data to achieve inference and prediction of unknown samples. The essence of this type of forecast modeling method is to select a suitable mathematical model to fit the laws of finite samples, and then predict unknown samples based on the fitted model, hoping to minimize the prediction error of random uncertainty. In terms of model selection, due to the unknown nature of the sample population, traditional modeling methods usually select multiple alternative models from a large number of models based on empirical cognition for modeling, use training sets to calibrate model parameters, and then compare and select models with higher prediction accuracy on the test set for actual runoff forecasting.

However, according to the theory of mathematical statistical inference, the measured runoff samples are a set of observations from the population that occur with probability, and they are not certain to occur in the future. The shorter the measured sample sequence, the greater the probability of deviation from the overall distribution. Since the annual runoff observation sequence is relatively short, usually decades, the prediction accuracy index obtained by model calibration and prediction accuracy test based on finite measured samples with shorter observation sequences also occurs with probability. Therefore, the model selected by the traditional modeling method based on the prediction accuracy of the test set is difficult to verify the prediction uncertainty of the unknown population, and there is still a lack of effective verification methods. Although the hypothesis testing theory in statistics provides a theoretical basis for the statistical inference problem of finite samples, how to combine the key links of data-driven forecast modeling to construct a hypothesis testing method for the runoff forecast model that focuses on the prediction accuracy of the model for unknown samples is still a technical difficulty that needs to be solved urgently.

Summary of the invention

In response to the above-mentioned problems and technical difficulties, the present invention provides a data-driven runoff forecast model optimization method under finite samples based on hypothesis testing, which is used to verify the reliability of the forecast model's inference prediction of the unknown population and provide a decision-making basis for the optimization of the forecast model.

The present invention is implemented by the following technical solution: a method for optimizing a data-driven runoff forecast model under a limited sample based on hypothesis testing, comprising the following steps:

Step 1: Screen prediction factors based on historical runoff data and meteorological data, establish a mapping relationship between runoff and prediction factors, select multiple data-driven models to describe the mapping relationship, and establish a candidate model set;

Step 2: Based on the alternative model set in step 1, select a model as the model hypothesis, and define the null hypothesis H ₀ and the alternative hypothesis H ₁ to test the authenticity of the forecast model; where:

H ₀ : Model y = f(X; ω ^* ) + ε, ε ~ g(θ ^* ) is assumed to be true, and the prediction model obtained by calibration using the training set is the true model, whose prediction accuracy σ(n,m) on the test set _DL,m =( _Xm , _ym ) is equal to the model's true accuracy σ ^* ;

H ₁ : Forecast model is not true, that is, σ(n,m) is not equal to σ ^* ;

If the prediction model is true, then σ(n,m) approaches σ ^* within a certain allowable deviation range, and the constructed statistic is:

Z＝σ(n,m)-σ ^* (2)

When σ(n,m) makes the absolute value |z| of the observed value z ₀ of the statistic Z too large, the hypothesis H ₀ is rejected, otherwise the hypothesis H ₀ is accepted;

Step 3: For a model hypothesis selected in step 2, use a measured sample with a sample size of L The model parameters are calibrated as the overall estimate of the true model. The overall model is recorded as y = f(X; ω ^* ) + ε, ε ~ g(θ ^* ), and the true accuracy of the model is estimated as σ ^* ;

Step 4: Use the Monte Carlo method to sample the overall model y＝f(X；ω ^* )+ε,ε～g(θ ^* ) with a sample size of L. The number of samplings is denoted as C, and the sample size of C times is L. One sampling is denoted as sample set _DL . For each sampling, the sample set _DL is divided into a training set _DL,n ＝( _Xn , _yn ) and a test set _DL,m ＝( _Xm , _ym ) with sample sizes of n and m respectively. The sample set partitioning scheme is denoted as L(n,m). The training set _DL,n is used for model parameter calibration, and the test set DL _,m is used for model prediction accuracy testing. For each group of partitioning schemes L(n,m), C samplings are used for model calibration and testing to obtain the sampling distribution of prediction accuracy.

Step 5: Determine the optimal sample set partition capacity L(n ^r ,m ^r ) based on the principle of minimum average distance, so that the sampling distribution of the statistic Z is as close to the true H ₀ as possible. The smaller the average distance index between the sampling distribution of Z and the true accuracy of the model, the smaller the sampling distribution of the statistic Z is close enough to the true H ₀ , that is, the closer the sampling distribution of the prediction accuracy σ(n,m) of the optimal sample set partition capacity L(n ^r ,m ^r ) is to the true accuracy σ ^* of the model, the greater the probability that the original hypothesis H ₀ is true;

Step 6: Construct the sampling distribution of the statistic Z according to the prediction accuracy σ(n,m) sample set of the optimal sample set partition capacity L(n ^r ,m ^r ) in step 5, and determine the rejection region of the sampling distribution of the statistic Z according to the sampling distribution of the statistic Z and the given significance level α;

Step 7: Based on the measured samples Construct a prediction model with a sample partition capacity of L(n ^r ,m ^r ) and calculate the prediction accuracy of the test set/> and the observed value z ₀ of the statistic Z;

Step 8: Determine whether to reject the null hypothesis H ₀ based on whether the observed value z ₀ of the statistic Z falls within the rejection region of the sampling distribution of the statistic Z. If the null hypothesis H ₀ is rejected, the current model fails the hypothesis test and is not suitable as the preferred model. If there are multiple alternative models that pass the hypothesis test, the p-value method is further used to give the minimum significance level at which the null hypothesis H ₀ can be rejected. The calculation formula for the p-value is:

p＝P{|z|≥z ₀ }

The model with the smallest rejection rate 1-p for the null hypothesis H ₀ is considered to be closest to the true model, and the model optimization is performed based on the "minimum rejection rate" criterion.

Furthermore, the data-driven model described in step 1 is composed of a model structure, parameters, input variables, and output variables, and the model expression is as follows:

y＝f(X；ω)+ε，ε～g(θ)

Wherein, the input variable X is a predictor correlated with runoff; the output variable y is runoff; f(X; ω) is a model form with certain structural characteristics; ω is a model parameter obtained through historical sample training; ε is a random term with a distribution function of g(θ).

Furthermore, the true accuracy index σ ^* of the model in step 3 includes root mean square error, mean absolute error, and correlation coefficient

Furthermore, the objective function of the model solution in step 3 consists of a fitting error function and a penalty function. The general expression of the objective function is as follows:

Where L(y ⁱ ,f(X ⁱ ;ω)) is the fitting error of the model, which means that the model fits the training samples as much as possible; n is the training sample capacity; λΩ(ω) is the penalty function introduced to constrain the overfitting of the model to improve the generalization ability of the model in unknown sample sets.

Furthermore, step 5 specifically includes:

Step 5.1: Use the average deviation d(n,m,σ ^* ) as the discriminant index for sample set partitioning. Let the number of sampling times of the forecast model statistical test with the sample set partitioning capacity L(n,m) be C, let the test set prediction accuracy sample set of C sampling times be σ _m , where the cth sample is σ _m (c), and use the root mean square distance index to quantify the average deviation between σ _m (c∈C) and the true accuracy σ ^* . Define the average deviation index d(n,m,σ ^* ), and the calculation formula is as follows:

Step 5.2: If d(n,m,σ ^* ) obtains the minimum value in the multi-group sample set partitioning scheme L(n,m), it is the sample set partitioning capacity, called the "optimal sample set capacity"L(nr,mr); at this time, the deviation between the distribution of prediction accuracy σ(n,m) and the true σ ^* is as small as possible, that is, the distribution of the statistic Z is close enough to _H0 .

The present invention has the following advantages.

(1) In step 2, the present invention provides a hypothesis testing method for a runoff forecast model under a finite sample based on the principle of the actual impossibility of small probability events in hypothesis testing theory; in steps 4-5, the Monte Carlo method is used to simulate the distribution of prediction accuracy to obtain a sampling distribution with the lowest risk of deviating from the true model; in steps 7-8, a model optimization criterion based on the minimum rejection rate is proposed to maximize the probability of ensuring the credibility of the optimal model for the prediction of the unknown population inference. As shown in the results of Figure 6 in the embodiment, the credibility of the mean model selected by the hypothesis testing method is 0.91, which is 0.89 and 0.61 higher than the credibility of the model selected by the traditional optimization method (2:1 and 4:1), respectively, which verifies the superiority of the hypothesis testing optimization method proposed by the present invention.

(2) The forecast model optimization method provided can be extended to prediction problems in different fields, providing a reliability-based optimization method for the construction of data-driven forecast models under finite samples.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the probability distribution of the prediction accuracy of the model and the rejection region of the two-sided test in an embodiment of the present invention;

FIG2 is a flow chart of a method for optimizing a data-driven runoff forecast model under finite samples based on hypothesis testing according to an embodiment of the present invention;

FIG3 is a diagram showing the change process of the mid-year runoff series and the anomaly and first-order difference series according to an embodiment of the present invention;

FIG4 is a diagram showing the change process of the 95% confidence interval and the average deviation index of the prediction accuracy of the six alternative models such as the mean model in the embodiment of the present invention with the sample size n of the training set;

Figure 5 shows the 95% confidence interval of the sampling distribution of the statistic Z and the distribution position of z ₀ for the six alternative models including the mean model;

FIG6 is a comparison diagram of the prediction model optimization results of the hypothesis testing method of the present invention and the traditional optimization method.

Detailed ways

In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

As shown in FIG2 , the present embodiment provides a method for optimizing a data-driven runoff forecast model under limited samples based on hypothesis testing, comprising the following steps:

Step 1: Screen forecasting factors based on historical runoff data and meteorological data, select multiple data-driven models to establish a mapping relationship between runoff and forecasting factors, and establish a set of alternative models.

The data-driven model consists of model structure, parameters, input variables and output variables. The model expression is as follows:

y＝f(X；ω)+ε，ε～g(θ) (1)

Wherein, the input variable X is a prediction factor correlated with runoff, such as an autocorrelation factor or an external cause-related factor; the output variable y is the runoff; f(X; ω) is a model form with certain structural characteristics; ω is a model parameter obtained through historical sample training; ε is a random term with a distribution function of g(θ).

The annual runoff data collected in this embodiment from 1956 to 2010 has a sample size of 55. The runoff sequence and its first-order difference sequence are shown in Figure 3. Linear and nonlinear autocorrelation analysis was performed on the 55-year measured runoff sequence and difference sequence, and the prediction factors were screened and the autocorrelation model was established. Since the linear autocorrelation of the measured runoff sequence is not significant, the mean model can be used for modeling; the autocorrelation of the first-order difference sequence is significant when the order is p = 1 to 2, and the first-order difference autoregression model ARI (1, 1) and ARI (2, 1) can be used; the "mutual information" is used to quantify the autocorrelation of the measured runoff sequence. The results show that there is a certain nonlinear autocorrelation when the order is p = 1 to 3, and the support vector regression model SVR (1), SVR (2) and SVR (3) can be used for modeling. Therefore, the candidate model set is constructed as follows: 6 models: mean model, ARI (1, 1), ARI (2, 1), SVR (1), SVR (2) and SVR (3).

Step 2: Based on the candidate model set in step 1, select a model as the model hypothesis.

The sample set _DL = {(X, y) | X∈RL ^×d , y∈RL} with a known sample size of L ^is a sample from the population D = (X, y). Since the actual population is unknown, the known sample _DL is used to construct the model y = f(X; ω ^* ) + ε, ε ~ g(θ ^* ) to infer the population D = (X, y). The known sample set _DL is divided into a training set _DL,n = ( _Xn , _yn ) and a test set _DL,m = ( _Xm , _ym ) with sample sizes of n and m respectively. The sample set division scheme is denoted as L(n, m). The training set _DL,n is used for model parameter calibration, and the test set _DL,m is used to test the model prediction accuracy. The empirical model calibrated using the training set _DL,n is denoted as ω( _DL,n ) is the estimated value of the parameter ω ^* .

In order to test the authenticity of the forecast model, the null hypothesis H ₀ and the alternative hypothesis H ₁ are defined.

H ₀ : The model hypothesis is true, and the prediction model is calibrated using the training set is the true model, whose prediction accuracy σ(n,m) in the test set is equal to the model's true accuracy σ ^* .

H ₁ : Forecast model is not true, that is, its prediction accuracy σ(n,m) in the test set is not equal to the model's true accuracy σ ^* . Construct statistics:

Z＝σ(n,m)-σ ^* (2)

When σ(n,m) makes the absolute value z of the observed value of the statistic Z too large, the hypothesis H ₀ is rejected, otherwise the hypothesis H ₀ is accepted.

The schematic diagram of the sampling distribution and rejection region of Z and the observed value z ₀ of Z is shown in Figure 1.

Step 3: For a model hypothesis selected in step 2, use the measured sample with a sample size of L = 55 to calibrate the model parameters as the overall estimate of the true model. The model is recorded as y = f(X; ω ^* ) + ε, ε ~ g(θ ^* ), and the true accuracy estimate of the model is σ ^* ;

The objective function of the model solution in step 3 is generally composed of a fitting error function and a penalty function. The general expression of the objective function is as follows:

In the formula, L( ^yi , f( ^Xi ; ω)) is the fitting error of the model, which means that the model fits the training samples as much as possible; n is the training sample capacity; λΩ(ω) is the penalty function introduced to constrain the model from overfitting, so as to improve the generalization ability of the model in unknown sample sets. Traditional linear regression models often use the mean squared error (MSE) as the objective function and use the least squares method to solve it; machine learning models such as support vector regression (SVR) often use the objective function of parameter optimization that includes an error function and a penalty function. The objective function is also called a loss function and is solved using optimization algorithms such as gradient descent.

In step 3, the model's true accuracy index σ ^* can be selected from different indicators such as root mean square error, mean absolute error, correlation coefficient, etc. Taking the root mean square error (RMSE) as an example, the calculation formula for the prediction accuracy evaluation index of the test set is as follows:

Where σ is the root mean square error, which is the square root of the mean square error (MSE), m is the test sample size, ^yi is the measured value of runoff, is the predicted value of runoff by the empirical model.

Fitting the model The parameters of are estimated according to the objective function and solution method of formula (3); the residual sequence ε is determined by KS test to determine whether the residual sequence satisfies the normal distribution. The residual root mean square error estimates σ ^* of the six alternative models, mean model, ARI (1,1), ARI (2,1), SVR (1), SVR (2) and SVR (3) are 698, 804, 775, 679, 599 and 534 respectively.

Step 4: Based on the population estimated by the mean model, ARI (1,1), ARI (2,1), SVR (1), SVR (2) and SVR (3), the Monte Carlo method is used to perform C = 500 random samplings with a sample size of L = 55 from the population. Each sampling is recorded as the sample set _DL . The sample set _DL is divided into a training set and a test set with a sample size of L (n, m) in time sequence.

46 sets of L(n,m) schemes are set: n is between 5 and 50, and correspondingly m varies between 50 and 5. For each set of L(n,m) schemes, the forecast model training and testing are performed with C=500 samplings, and the test set prediction accuracy sample sets σ _m of the 46 sets of schemes are obtained in turn.

Step 5: If the average distance index between the prediction accuracy sampling distribution and the model's true accuracy is smaller, it means that the sampling distribution of the statistic Z is close enough to the true H ₀ , that is, the sampling distribution of σ(n,m) is close to the model's true accuracy σ ^* , and the probability that the original hypothesis H ₀ is true is greater. Determine the optimal sample set partition capacity L(n ^r ,m ^r ) based on the principle of minimum average distance, so that the sampling distribution of the statistic Z is as close to the true H ₀ as possible. The specific steps include:

Step 5.1: Use the average deviation d(n,m,σ ^* ) of formula (5) as the discriminant index for sample set partitioning. Let the number of sampling times of the forecast model statistical test with the sample set partitioning capacity L(n,m) be C, let the test set prediction accuracy (root mean square prediction error) sample set of C sampling times be σ _m , where the cth sample is σ _m (c). The root mean square distance index is used to quantify the average deviation degree of σ _m (c∈C) from the true accuracy σ ^* , and the average deviation index d(n,m,σ ^* ) is defined, and the calculation formula is as follows:

Step 5.2: If d(n,m,σ ^* ) obtains the minimum value in the multi-group sample set partitioning scheme L(n,m), it is the sample set partitioning capacity, called the "optimal sample set capacity" L(nr,mr). At this time, the deviation between the distribution of the prediction accuracy σ(n,m) and the true σ ^* is as small as possible, that is, the distribution of the statistic Z in formula (2) is close enough to H ₀ .

According to the test set prediction accuracy sample set of 46 groups of L(n,m) schemes in step 4, the following formula (5) is used to calculate

Calculate the average deviation d(n,m,σ ^* ) between the σ _m samples and σ ^* under each L(n,m) scheme. Plot the 95% confidence intervals and average deviation index results of the prediction accuracy of the six alternative models, including the mean model, ARI(1,1), ARI(2,1), SVR(1), SVR(2) and SVR(3), as the training set sample size n changes, as shown in Figure 4.

The average deviation d(n,m,σ ^* ) of the six models in Figure 4(a) to (f) is analyzed: as the training set n increases (m decreases), the d(n,m,σ ^* ) of each model first decreases and then increases, and the minimum value is obtained under a certain n and m. Based on this, the best sample set division for each model can be determined. The training sample capacity is n=15, 21, 24, 26, 26, 25, and the test set capacity is 55-n.

Step 6: Construct a sampling distribution of the statistic Z based on the prediction accuracy σ(n,m) sample set of the sample partition capacity L(n ^r ,m ^r ) in step 5, and determine the rejection region based on the sampling distribution and the given significance level α.

The prediction accuracy σ _m of the test set under the optimal sample size partition is adopted, and the statistic Z is constructed according to formula (5). The confidence interval with a significance level of α = 0.05 is obtained according to the sampling distribution of Z. The lower and upper limits of the interval of the two-sided test are respectively taken as the α/2 = 2.5% and 1-α/2 = 97.5% quantiles of the sampling distribution of Z.

Step 7: According to steps 4.1 and 4.2, calculate the prediction accuracy of the test set of the measured samples under the optimal sample size The observed value z ₀ of the statistic Z is further calculated according to formula (2).

Taking the significance level as 0.05, the 95% confidence interval of the sampling distribution of the statistic Z and the distribution position of z ₀ of the six alternative models are plotted, as shown in Figure 5.

Step 8: According to the quantile of z ₀ in the Z sampling distribution, the p-value is calculated using formula (6) to quantify the credibility of the six model assumptions. The credibility p-value and the rejection rate 1-p are shown in Table 1.

Table 1. Hypothesis test results of forecast model under optimal sample size division

Comparing and analyzing the test results of the six models in Table 1, we can see that the rejection rates of the six models show that the mean model and SVR(1) have the highest credibility, followed by ARI(2,1), ARI(1,1) and SVR(2) have lower credibility, and SVR(3) is an unreliable model at a significance level of 0.05. Therefore, it is recommended to select the mean model and SVR(1) as the optimal models, and the optimal sample sizes of the two models are (15,40) and (26,29), respectively.

Furthermore, the forecast model optimization method provided above is compared with the existing methods:

The hypothesis testing method is the method proposed in the present invention, which performs model optimization based on the minimum rejection rate criterion under the optimal sample set division; the traditional optimization method divides the measured samples into training set and test set according to the empirical ratio (2:1 and 4:1), and performs model optimization based on the highest prediction accuracy of the test set.

The corresponding relationships between the test accuracy σ and the rejection rate 1-p of the measured samples of the six models under the hypothesis testing method, the traditional optimization method (2:1) and the traditional optimization method (4:1) are given respectively, as shown in Figure 6.

In Figure 6(a), the optimal mean model and the suboptimal model SVR(1) selected by the hypothesis testing method (minimum rejection rate criterion) not only have higher test accuracy than the other four models on the measured samples, but also have the lowest rejection rate of the model being true, which are 0.09 and 0.1 respectively; while in Figure 6(b), the traditional optimization method (2:1) recommends SVR(3) as the best model with the highest accuracy, but the model rejection rate is 0.98, rejecting the hypothesis that the model is true at the 95% confidence level; in Figure 6(c), the traditional optimization method (4:1) recommends ARI(2,1) as the optimal model with the highest accuracy and SVR(3) as the suboptimal model, but the rejection rates reach 0.7 and 0.85, and the credibility of the model being true is low. It can be seen that the model selected based only on the test accuracy of the traditional optimization method (2:1 and 4:1) may lead to unreasonable model selection results due to the sampling uncertainty of the prediction accuracy statistics.

The credibility of the mean model selected by the hypothesis testing method is 0.91, which is 0.89 and 0.61 higher than the credibility of the model selected by the traditional optimization method (2:1 and 4:1), respectively, which verifies the superiority of the proposed hypothesis testing optimization method.

The above is only a specific implementation of a case of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (4)

1. A method for optimizing a data-driven runoff forecast model under finite samples based on hypothesis testing, characterized in that it comprises the following steps: Step 1: Screen the prediction factors according to the historical runoff data and meteorological data, establish the mapping relationship between runoff and prediction factors, select multiple data-driven models to describe the mapping relationship, and establish a candidate model set; the data-driven model consists of model structure, parameters, input variables and output variables, and the model expression is as follows: y＝f(X；ω)+ε，ε～g(θ) In the formula, the input variable X is a predictor correlated with runoff; the output variable y is runoff; f(X; ω) is a model form with certain structural characteristics; ω is a model parameter obtained through historical sample training; ε is a random term with a distribution function of g(θ); Step 2: According to the alternative model set in step 1, select each alternative model as the model hypothesis in turn; the sample set _DL with a known sample size of L is a sample from the population D, and the known sample _DL is used to construct the model y=f(X;ω ^* )+ε,ε~g(θ ^* ) to infer the population D, ω ^* is the model parameter used to infer the population D using the sample _DL , and the distribution function is g(θ ^* ) at this time, which is the overall estimate of the true model, and the true accuracy of the model is estimated to be σ ^* ; the known sample set _DL is divided into a training set _DL,n and a test set DL _,m with sample sizes of n and m respectively, and the sample set division scheme is denoted as L(n,m); the training set _DL,n is used for model parameter calibration, and the test set DL _,m is used for testing the model prediction accuracy; the forecast model calibrated using the training set DL _,n is denoted as ω( _DL,n ) is the estimated value of parameter ω ^* ; The null hypothesis H ₀ and the alternative hypothesis H ₁ are defined to test the authenticity of the forecast model; where: H ₀ : Model y = f(X; ω ^* ) + ε, ε ~ g(θ ^* ) is assumed to be true, and the prediction model is obtained by calibration using the training set _DL,n is the true model, whose prediction accuracy σ(n,m) on the test set _DL,m is equal to the true model accuracy σ ^* ; H ₁ : Forecast model is not true, that is, the prediction accuracy σ(n,m) is not equal to σ ^* ; If the prediction model is true, then σ(n,m) approaches σ ^* within a certain allowable deviation range, and the constructed statistic is: Z = σ(n,m)-σ ^* ; When σ(n,m) makes the absolute value of the observed value z ₀ of the statistic Z too large, the hypothesis H ₀ is rejected, otherwise the hypothesis H ₀ is accepted; Step 3: For a model hypothesis selected in step 2, use the measured sample D _L ⁰ with a sample size of L to calibrate the model parameters as the overall estimate of the true model. The true accuracy of the model is estimated as σ ^* ; Step 4: Use the Monte Carlo method to sample the overall model y = f (X; ω ^* ) + ε, ε ~ g (θ ^* ) with a sample size of L. The number of samplings is C, and the sample size of C times is L. For each group of partitioning schemes L (n, m), use C samplings to calibrate and test the model to obtain the sampling distribution of prediction accuracy; Step 5: Determine the optimal sample set partition capacity L(n ^r ,m ^r ) based on the principle of minimum average distance, so that the sampling distribution of the statistic Z is as close to the true H ₀ as possible. The smaller the average distance index between the sampling distribution of Z and the true accuracy of the model, the smaller the sampling distribution of the statistic Z is close enough to the true H ₀ , that is, the closer the sampling distribution of the prediction accuracy σ(n,m) of the optimal sample set partition capacity L(n ^r ,m ^r ) is to the true accuracy σ ^* of the model, the greater the probability that the original hypothesis H ₀ is true; Step 6: Construct the sampling distribution of the statistic Z according to the prediction accuracy σ(n,m) sample set of the optimal sample set partition capacity L(n ^r ,m ^r ) in step 5, and determine the rejection region of the sampling distribution of the statistic Z according to the sampling distribution of the statistic Z and the given significance level α; Step 7: Based on the measured samples Construct a prediction model with a sample set partition capacity of L(n ^r ,m ^r ) and calculate the prediction accuracy of the test set/> and the observed value z ₀ of the statistic Z; Step 8: Determine whether to reject the null hypothesis H ₀ based on whether the observed value z ₀ of the statistic Z falls within the rejection region of the sampling distribution of the statistic Z. If the null hypothesis H ₀ is rejected, the current model fails the hypothesis test and is not suitable as the preferred model. After performing the hypothesis test on each alternative model, if there are multiple alternative models that pass the hypothesis test, the p-value method is further used to give the minimum significance level at which the null hypothesis H ₀ can be rejected. The calculation formula for the p-value is: p＝P{|z|≥z ₀ }; The model with the smallest rejection rate 1-p for the null hypothesis H ₀ is considered to be closest to the true model, and the model optimization is performed based on the "minimum rejection rate" criterion. 2. The method for optimizing the data-driven runoff forecast model under finite samples based on hypothesis testing as described in claim 1 is characterized in that: the model true accuracy indicator σ ^* in step 3 includes root mean square error, mean absolute error, and correlation coefficient. 3. The method for optimizing the data-driven runoff forecast model under finite samples based on hypothesis testing according to claim 1 is characterized in that the objective function of the model solution in step 3 is composed of a fitting error function and a penalty function, and the general expression of the objective function is as follows: Where F(y ⁱ , f(X ⁱ ; ω)) is the fitting error of the model, which means that the model fits the training samples as much as possible; n is the training sample capacity; λΩ(ω) is the penalty function introduced to constrain the overfitting of the model to improve the generalization ability of the model in unknown sample sets. 4. The method for optimizing the data-driven runoff forecast model under finite samples based on hypothesis testing according to claim 1, characterized in that: step 5 specifically comprises: Step 5.1: Use the average deviation d(n,m,σ ^* ) as the discriminant index for sample set partitioning. Let the number of sampling times of the forecast model statistical test with the sample set partitioning capacity L(n,m) be C, let the test set prediction accuracy sample set of C sampling times be σ _m , where the cth sample is σ _m (c), and use the root mean square distance index to quantify the average deviation between σ _m (c∈C) and the true accuracy σ ^* . Define the average deviation index d(n,m,σ ^* ), and the calculation formula is as follows: Step 5.2: If d(n,m,σ ^* ) obtains the minimum value in the multi-group sample set partitioning scheme L(n,m), the sample set partitioning capacity at this time is called the "optimal sample set partitioning capacity" L( ^nr , ^mr ); at this time, the distribution of the prediction accuracy σ(n,m) deviates sufficiently from the true σ ^* , that is, the distribution of the statistic Z is close enough to _H0 .