Runoff prediction method fusing sparse neural network and quantum kernel function

Abstract

The invention relates to a runoff prediction method fusing a sparse neural network and a quantum kernel function, and the method comprises the steps: collecting day-by-day flow data of a watershed outlet hydrologic station as a prediction variable, collecting prediction variable impact factor data, and dividing a training set and a test set; and based on the sparse neural network, performing feature selection by adopting a neuron attribution method. And constructing a runoff prediction model based on a quantum kernel function, and carrying out model training and parameter optimization on the training set. And carrying out runoff prediction on the drainage basin outlet hydrological station on the test set by adopting a runoff prediction model fusing the sparse neural network and the quantum kernel function, and selecting an evaluation index to evaluate a runoff prediction effect of the drainage basin outlet hydrological station. According to the method, features can be efficiently selected, and memory and calculation cost are remarkably reduced. And rapid and accurate runoff prediction is realized based on potential acceleration provided by quantum calculation, meanwhile, prediction uncertainty is quantified, parameters are optimized based on a Bayesian method, and complexity and high calculation cost of a gradient descent optimization algorithm are avoided.

Description

Technical Field

[0001] The invention relates to the field of hydrological forecasting, and in particular to a runoff prediction method integrating a sparse neural network and a quantum kernel function. Background Art

[0002] Obtaining accurate runoff prediction results and the possible range of future runoff is of great significance for water resources management and utilization, flood and drought prevention, water conservancy project scheduling, and water ecological environment protection.

[0003] At present, the models used for runoff prediction are mainly divided into mechanism models and data-driven models. When using the two types of models for runoff prediction, screening the features that affect runoff is directly related to the prediction accuracy of runoff. Appropriate feature selection can reduce computation, memory and the resulting costs, improve interpretability, reduce data collection costs, and enhance model generalization. Traditional feature selection methods include filtering, packaging, and embedding. Filtering methods are prone to selecting irrelevant features, and packaging methods are computationally expensive. Embedding methods integrate feature selection into the learning process, so they can select relevant features and are cost-effective. Various techniques are used to perform embedded feature selection, including mutual information, SVM classifiers, and neural networks. Feature selection based on neural networks has attracted great attention in recent years in both supervised and unsupervised settings. These methods take advantage of the advantages of neural networks in capturing nonlinear dependencies and performing well on large data sets. However, many existing neural network-based feature selection methods suffer from over-parameterization, resulting in high computational costs, especially for high-dimensional data sets. After obtaining appropriate runoff impact characteristics, achieving fast and efficient runoff prediction is of great significance for water resources management. However, the traditional mechanism model takes a long time to calculate. Although the calculation efficiency of the data-driven model has been improved, the calculation cost is still relatively high for the runoff prediction of basins with complex characteristics and long sequence lengths, and the calculation accuracy needs to be further improved. In addition, the existing mechanism models and data-driven models tend to give future deterministic runoff point prediction results when predicting runoff, making it difficult to obtain the possible range of future runoff and unable to quantify the prediction risk. Summary of the invention

[0004] The purpose of the present invention is to provide a runoff prediction method that integrates sparse neural networks and quantum kernel functions. Through a new feature importance index based on neuron attribution, a sparse neural network with dynamic sparse training is used to perform efficient feature selection, thereby obtaining performance that is superior to dense neural network feature selection, while significantly reducing memory and computing costs. In addition, the runoff prediction model that further integrates sparse neural networks and quantum kernel functions uses quantum Hilbert space data encoding to enhance feature mapping using quantum exclusive resources, and provides advantages over classical mapping. Based on the potential acceleration provided by quantum computing, faster and more accurate runoff prediction can be achieved; at the same time, based on Bayesian reasoning, the uncertainty in runoff prediction is quantified, and future runoff expectations and their confidence intervals are fully displayed. In addition, Bayesian optimization is further used to optimize the hyperparameters of the model, avoiding the cumbersomeness and high computational cost of the gradient descent optimization algorithm.

[0005] The technical solution adopted by the present invention to solve its technical problem is: A runoff prediction method integrating sparse neural network and quantum kernel function comprises the following steps; Step S1: collect daily flow data of the basin outlet hydrological station as forecast variable data, and simultaneously collect forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the basin outlet hydrological station, and divide the collected data set containing the forecast variable data and the forecast influencing factor data into a training set and a test set; Step S2: Based on the dynamic sparse training strategy of the sparse neural network, the neural attribution method is used to perform feature selection on the forecast influencing factor data, and the forecast influencing factors with the top 50% influence on the forecast variable are determined as the feature set; Step S3: constructing a runoff prediction model integrating sparse neural network and quantum kernel function, and using the selected feature set and forecast variable data on the training set to perform model training and optimize the model parameters; Step S4: The runoff prediction model integrating sparse neural network and quantum kernel function is used on the test set to predict the runoff of the basin outlet hydrological station, and evaluation indicators are selected to evaluate its runoff prediction effect.

[0006] As a further technical solution of the present invention, the forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the basin outlet hydrological station in step S1 mainly include forecast influencing characteristic data such as rainfall, evaporation, daily maximum temperature, daily minimum temperature, daily average temperature, and upstream hydrological station flow.

[0007] As a further technical solution of the present invention, in step S2, the dynamic sparse training strategy based on sparse neural networks mainly optimizes the sparse connectivity of the network during the training process without using a dense network matrix. The dynamic sparse training strategy first initializes a complete neural network and then randomly sparsifies it, that is, creates a random topological network structure, and during the training process, maintains the sparsity of the network by removing low-importance neuron connections while optimizing the network weights.

[0008] As a further technical solution of the present invention, in step S2, when the neuron attribution method is used for feature selection, it is necessary to calculate the importance of the input neurons based on the attribution of the output neurons, wherein each input neuron of the first layer, that is, the importance score of each input neuron corresponding to each input neuron, is as shown in Formula 1: Formula 1: ; in, It is In the round iteration j The importance of input neurons, C is the number of output neurons, m is the number of samples, It is i The output neuron corresponds to Samples The j The neuron attribution value of the input feature. One input neuron can correspond to multiple output neurons. j The input neuron corresponds to j input features, where L is the number of network layers, including the sum of the total number of network layers including input layer, hidden layer and output layer, The layer corresponds to the output layer and represents the index value of the output layer. The larger the absolute value of the output neuron i For input features The more sensitive the change of , after deriving the importance of the input neurons corresponding to each input feature according to Formula 1, the features with the top 50% of the neuron attribution importance are selected as the feature set.

[0009] As a further technical solution of the present invention, when constructing the quantum enhanced runoff prediction model integrating the quantum kernel function in step S3, the model adopted is the Gaussian process regression prediction model, which establishes a non-parametric model that obeys the Gaussian process prior information by performing regression analysis on the data. Assume that a learning sample containing n pairs of independent observation data , is an input set consisting of n input vectors, Is n The output set consists of corresponding one-dimensional outputs, then the Gaussian process mean and variance It is expressed as Equation 2 and Equation 3: Formula 2: ; Formula 3: ; In the formula, represents any two random variables in the sample, E represents the mathematical expectation, Represents the prediction function.

[0010] As a further technical solution of the present invention, when constructing a runoff prediction model based on a Gaussian process regression prediction model in step S3, an instantaneous quantum polynomial time (IQP) feature map is used. The original classic time series data Converted into quantum state characteristic information , Indicates the first i A time series dataset with features. represents the number of features finally determined based on the sparse neural network, Indicates the first The time series data set with features is expressed as Equation 4: Formula 4: ; In the formula, Represents the W-dimensional real space where the classic time series data is located Convert to the Hilbert space where the quantum state characteristic information is located ; Representation using the instantaneous quantum polynomial time (IQP) feature graph The original classic time series data Converted into quantum state characteristic information ; is an adjustable hyperparameter introduced; Converting the original classical time series data into quantum state feature information through the instantaneous quantum polynomial time (IQP) feature map can nonlinearly reveal the complex temporal dynamics inherent in the sequence x, capturing not only the individual time contributions but also their interactive dynamics.

[0011] As a further technical solution of the present invention, in step S3, the original classical time series data x is mapped into quantum state characteristic information After that, by calculating the characteristic information of any two quantum states and Fidelity To quantify the corresponding sequence x and The similarity between them, the fidelity calculation formula is expressed as formula 5; Formula 5: .

[0012] As a further technical solution of the present invention, when optimizing and adjusting the hyperparameters of the Gaussian process model in step S3, the optimization algorithm adopts the Bayesian optimization method to avoid cumbersome gradient descent optimization and reduce the number of optimization iterations. The parameters to be optimized are set to , including the mean constant of the Gaussian process (GP) m , Noise Variance and bandwidth ,parameter From the specified parameter space , Used to optimize the function, the optimization goal is to find the best parameters , so that when the parameter The value is hour, Maximum, the best parameter after optimization It is expressed as formula 6; Formula 6: .

[0013] As a further technical solution of the present invention, after the runoff prediction model integrating the sparse neural network and the quantum kernel function is used to perform runoff prediction on the test set in step S4, the mean absolute percentage error MAPE is selected as the evaluation index of the runoff deterministic point prediction result of the model, and MAPE is expressed as Formula 7; Formula 7: ; In the formula, For the test period i The measured value of samples, For the i The predicted value of samples, C is the number of samples in the test set; The runoff probability prediction evaluation index of the model is selected as log likelihood (LL), which can be expressed as formula 8; Formula 8: ; In the formula, represents the variance of the prediction results, Represents the mean of the prediction results.

[0014] The beneficial effects of the present invention are: the method of the present invention can efficiently select features, significantly reduce memory and computing costs, and achieve fast and accurate runoff prediction based on the potential acceleration provided by quantum computing, while quantifying the prediction uncertainty and optimizing parameters based on the Bayesian method, avoiding the tediousness and high computing cost of the gradient descent optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flow chart of a runoff prediction method integrating a sparse neural network and a quantum kernel function is provided in an embodiment of the present invention.

[0016] Figure 2 A scatter plot of the measured water level and the predicted water level provided in an embodiment of the present invention.

[0017] Figure 3 A schematic diagram of probability interval prediction results provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] 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 creative work are within the scope of protection of the present invention.

[0019] See also Figure 1 , an embodiment of the present invention provides a runoff prediction method integrating sparse neural network and quantum kernel function, comprising the following steps; Step S1: collecting daily flow data of the basin outlet hydrological station as forecast variable data, and simultaneously collecting forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the basin outlet hydrological station, and dividing the collected data set containing the forecast variable data and the forecast influencing factor data into a training set and a test set, wherein the data set is composed of the forecast variable data and the forecast influencing factor data; Step S2: Based on the dynamic sparse training strategy of the sparse neural network, the neural attribution method is used to perform feature selection on the forecast influencing factor data, and the forecast influencing factors with the top 50% influence on the forecast variable are determined as the feature set; Step S3: constructing a runoff prediction model integrating sparse neural network and quantum kernel function, and using the selected feature set and forecast variable data on the training set to perform model training and optimize the model parameters; Step S4: The runoff prediction model integrating sparse neural network and quantum kernel function is used on the test set to predict the runoff of the basin outlet hydrological station, and evaluation indicators are selected to evaluate its runoff prediction effect.

[0020] In this embodiment, in step S1, the A basin is taken as the research object, and the forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the outlet hydrological station of the A basin are collected, mainly including rainfall, evaporation, daily maximum temperature, daily minimum temperature, daily average temperature, upstream hydrological station flow and other forecast influencing characteristic data. The length of the collected data time series is 2000-2023, of which the 2000-2015 data set is used as a training set, and the 2016-2023 data set is used as a test set.

[0021] In this embodiment, in step S2, the dynamic sparse training strategy based on the sparse neural network mainly optimizes the sparse connectivity of the network during the training process without using a dense network matrix. The dynamic sparse training strategy first initializes a complete neural network and then randomly sparsifies it, that is, creates a random topological network structure, and during the training process, maintains the sparsity of the network by removing low-importance neuron connections, while optimizing the network weights.

[0022] In this embodiment, in step S2, when the neuron attribution method is used for feature selection, the importance of the input neurons needs to be calculated based on the attribution of the output neurons, wherein each input neuron of the first layer, that is, the importance score of each input neuron corresponding to each input neuron, is as shown in Formula 1: Formula 1: ; in, It is In the round iteration j The importance of input neurons, C is the number of output neurons, m is the number of samples, It is i The output neuron corresponds to Samples The j The neuron attribution value of the input feature. One input neuron can correspond to multiple output neurons. j The input neuron corresponds to j input features, where L is the number of network layers, including the sum of the total number of network layers including input layer, hidden layer and output layer, The layer corresponds to the output layer and represents the index value of the output layer. The larger the absolute value of the output neuron i For input features After the importance of the input neurons corresponding to each input feature is derived according to Formula 1, the features with the top 50% of the neuron attribution importance are selected as the feature set, mainly including the four important features of upstream hydrological station flow, rainfall station precipitation, evaporation and daily average temperature.

[0023] In this embodiment, when constructing the quantum enhanced runoff prediction model integrating the quantum kernel function in step S3, the model adopted is the Gaussian process regression prediction model, which establishes a non-parametric model that obeys the Gaussian process prior information by performing regression analysis on the data. Assume that a learning sample containing n pairs of independent observation data , is an input set consisting of n input vectors, Is n The output set consists of corresponding one-dimensional outputs, then the Gaussian process mean and variance It is expressed as Equation 2 and Equation 3: Formula 2: ; Formula 3: ; In the formula, represents any two random variables in the sample, E represents the mathematical expectation, Represents the prediction function.

[0024] In this embodiment, when constructing the runoff prediction model based on the Gaussian process regression prediction model in step S3, the instantaneous quantum polynomial time (IQP) feature map is used. The original classic time series data Converted into quantum state characteristic information , Indicates the first i A time series dataset with features. represents the number of features finally determined based on the sparse neural network, Indicates the first The time series data set with features is expressed as Equation 4: Formula 4: ; In the formula, Represents the W-dimensional real space where the classic time series data is located Convert to the Hilbert space where the quantum state characteristic information is located ; Representation using the instantaneous quantum polynomial time (IQP) feature graph The original classic time series data Converted into quantum state characteristic information ; is the optimal bandwidth parameter; Converting the original classical time series data into quantum state feature information through the instantaneous quantum polynomial time (IQP) feature map can nonlinearly reveal the complex temporal dynamics inherent in the sequence x, capturing not only the individual time contributions but also their interactive dynamics.

[0025] In this embodiment, in step S3, the original classical time series data x is mapped into quantum state characteristic information. After that, by calculating the characteristic information of any two quantum states and Fidelity To quantify the corresponding sequence x and The similarity between them, the fidelity calculation formula is expressed as formula 5; Formula 5: .

[0026] In this embodiment, when optimizing and adjusting the hyperparameters of the Gaussian process model in step S3, the optimization algorithm adopts the Bayesian optimization method to avoid cumbersome gradient descent optimization and reduce the number of optimization iterations. The parameters to be optimized are set to , including the mean constant of the Gaussian process (GP) m , Noise Variance and bandwidth ,parameter From the specified parameter space , Used to optimize the function, the optimization goal is to find the best parameters , so that when the parameter The value is hour, Maximum, the best parameter after optimization It is expressed as formula 6; Formula 6: .

[0027] Based on the above Bayesian optimization algorithm, after parameter optimization, the optimal parameter values ​​of the Gaussian regression model based on the quantum kernel function in this embodiment are .

[0028] In this embodiment, after the runoff prediction model integrating the sparse neural network and the quantum kernel function is used to perform runoff prediction on the test set in step S4, the mean absolute percentage error (MAPE) is selected as the evaluation index of the runoff deterministic point prediction result of the model, and the MAPE is expressed as Formula 7; Formula 7: ; In the formula, For the test period i The measured value of samples, For the i The predicted value of samples, C is the number of samples in the test set; The runoff probability prediction evaluation index of the model is selected as log likelihood (LL), which can be expressed as formula 8; Formula 8: ; In the formula, represents the variance of the prediction results, Represents the mean of the prediction results.

[0029] In this example, the MAPE of the hydrological station at the outlet of basin A during the test period is 0.2036. LL The runoff prediction results are converted into water level prediction results according to the water level-flow relationship of the hydrological station. Figure 2 A scatter plot showing the observed and predicted values, Figure 2 In the above equation, the closer the scattered points are to the 1:1 line, the better the prediction effect. Figure 3 represents the interval prediction result of the water level during the test period, Figure 3 (a) is the line graph of the measured data during the test period. Figure 3 (b) in the figure is the 90% confidence interval diagram for the test period. The more measured data there are in the confidence interval, the narrower the confidence interval is, and the better the probability prediction effect is. Figure 2 It can be seen that the prediction effect of the model proposed in this invention is better than other models at hydrological station A. Figure 3 It can be seen that the method of the present invention can provide better interval prediction results.

[0030] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0031] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A runoff prediction method integrating sparse neural network and quantum kernel function, characterized in that: The steps include: Step S1: collect daily flow data of the basin outlet hydrological station as forecast variable data, and simultaneously collect forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the basin outlet hydrological station, and divide the collected data set containing the forecast variable data and the forecast influencing factor data into a training set and a test set; Step S2: Based on the dynamic sparse training strategy of the sparse neural network, the neural attribution method is used to perform feature selection on the forecast influencing factor data, and the forecast influencing factors with the top 50% influence on the forecast variable are determined as the feature set; Step S3: constructing a runoff prediction model integrating sparse neural network and quantum kernel function, and using the selected feature set and forecast variable data on the training set to perform model training and optimize the model parameters; Step S4: The runoff prediction model integrating sparse neural network and quantum kernel function is used on the test set to predict the runoff of the basin outlet hydrological station, and evaluation indicators are selected to evaluate its runoff prediction effect.

2. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 1, characterized in that: The forecast influencing factor data of the upstream basin rainfall station and hydrological station controlled by the basin outlet hydrological station in step S1 mainly include rainfall, evaporation, daily maximum temperature, daily minimum temperature, daily average temperature and upstream hydrological station flow.

3. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 1, characterized in that: In step S2, the dynamic sparse training strategy based on the sparse neural network optimizes the sparse connectivity of the network during the training process without using a dense network matrix. The dynamic sparse training strategy first initializes a complete neural network and then randomly sparsifies it, that is, creates a random topological network structure, and during the training process, maintains the sparsity of the network by removing low-importance neuron connections while optimizing the network weights.

4. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 3, characterized in that: In step S2, when the neuron attribution method is used for feature selection, the importance of the input neurons needs to be calculated based on the attribution of the output neurons, where each input neuron in the first layer corresponds to the importance score of each input neuron as shown in Formula 1: Formula 1: ; in, It is In the round iteration j The importance of input neurons, C is the number of output neurons, m is the number of samples, It is i The output neuron corresponds to Samples The j The neuron attribute value of the input feature, one input neuron corresponds to multiple output neurons, j The input neuron corresponds to j input features, where L is the number of network layers, including the sum of the total number of network layers including input layer, hidden layer and output layer, The layer corresponds to the output layer and represents the index value of the output layer. The larger the absolute value of the output neuron i For input features The more sensitive the change of , after deriving the importance of the input neurons corresponding to each input feature according to Formula 1, the features with the top 50% of the neuron attribution importance are selected as the feature set.

5. The runoff prediction method integrating sparse neural network and quantum kernel function according to claim 1, characterized in that: When constructing the quantum enhanced runoff prediction model integrating the quantum kernel function in step S3, the model used is the Gaussian process regression prediction model, which establishes a non-parametric model that obeys the Gaussian process prior information by performing regression analysis on the data. Assume that a learning sample containing n pairs of independent observation data , is an input set consisting of n input vectors, Is n The output set consists of corresponding one-dimensional outputs, then the Gaussian process mean and variance It is expressed as Equation 2 and Equation 3: Formula 2: ; Formula 3: ; In the formula, represents any two random variables in the sample, E represents the mathematical expectation, Represents the prediction function.

6. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 5, characterized in that: When constructing the runoff prediction model based on the Gaussian process regression prediction model in step S3, the instantaneous quantum polynomial time characteristic diagram is used The original classic time series data Converted into quantum state characteristic information , Indicates the first i A time series dataset with features. represents the number of features finally determined based on the sparse neural network, Indicates the first The time series data set with features is expressed as Equation 4: Formula 4: ; In the formula, Represents the W-dimensional real space where the classic time series data is located Convert to the Hilbert space where the quantum state characteristic information is located ; Representation using instantaneous quantum polynomial time characteristic graph The original classic time series data Converted into quantum state characteristic information ; is an adjustable hyperparameter introduced.

7. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 6, characterized in that: In step S3, the original classical time series data x is mapped into quantum state characteristic information After that, by calculating the characteristic information of any two quantum states and Fidelity To quantify the corresponding sequence x and The similarity between them, the fidelity calculation formula is expressed as formula 5; Formula 5: .

8. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 7, characterized in that: When optimizing and adjusting the hyperparameters of the Gaussian process regression prediction model in step S3, the optimization algorithm adopts the Bayesian optimization method and sets the parameters to be optimized as , including the average constant of the Gaussian process GP m , Noise Variance and bandwidth ,parameter From the specified parameter space , Used to optimize the function, the optimization goal is to find the best parameters , so that when the parameter The value is hour, Maximum, the best parameter after optimization It is expressed as formula 6; Formula 6: .

9. A runoff prediction method integrating sparse neural network and quantum kernel function according to claim 8, characterized in that: In step S4, after the runoff prediction model integrating sparse neural network and quantum kernel function is used to predict the runoff on the test set, the mean absolute percentage error MAPE is selected as the evaluation index of the runoff deterministic point prediction result of the model, and MAPE is expressed as formula 7; Formula 7: ; In the formula, For the test period i The measured value of samples, For the i The predicted value of samples, C is the number of samples in the test set; The runoff probability prediction evaluation index of the model is selected as the log likelihood LL, which is expressed as formula 8; Formula 8: ; In the formula, represents the variance of the prediction results, Represents the mean of the prediction results.

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