Underground water level prediction method based on KAN network architecture

Abstract

The invention discloses an underground water level prediction method based on a KAN network architecture. The underground water level prediction method comprises the following steps: collecting underground water level historical data and underground water level influence factor historical data as original data; using LASSO regression to screen out relatively independent variables having influences on the underground water level for predicting the underground water level; obtaining a training set and a verification set; building an underground water level prediction model based on a KAN network architecture, wherein the underground water level prediction model comprises an LSTM layer, a Dropout layer and an output layer of the KAN network; training and optimizing an underground water level prediction model based on a KAN network structure to obtain an optimal parameter combination; and taking the optimal parameter combination as a model parameter to obtain a current underground water level prediction model based on the KAN network structure, inputting the fitted verification set data into the current underground water level prediction model based on the KAN network structure, and using the verified current underground water level prediction model based on the KAN network structure for underground water level prediction. According to the method, the underground water level is predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of water resource evaluation and management, and in particular to a groundwater level prediction method based on a KAN network architecture. Background Art

[0002] Groundwater resources are an important source of water resources for meeting the needs of agricultural irrigation, social and economic development in water-scarce areas, and are an important strategic resource for modern human development. The monitoring and prediction of groundwater levels play a vital role in the sustainable management of water resources, and the groundwater level prediction model is one of the key tools.

[0003] The fluctuation of groundwater level is affected by meteorological factors, geological factors and human activities, showing nonlinear dynamic changes, which makes the dynamic prediction of groundwater level face challenges. In the era of rapid development of artificial intelligence, building the relationship between external influencing factors and groundwater level changes based on data-driven models is one of the important technical means to achieve groundwater level prediction. However, the activation function of the deep learning model based on the MLP network architecture is fixed and fragile, which is easy to cause gradient disappearance or gradient explosion during the back propagation process. And the ability to process high-dimensional data and long-term dependencies is limited. In order to improve the ability and interpretability of the prediction model to handle long-term dependencies on the basis of achieving accurate and efficient prediction of groundwater level, in view of the problems existing in the existing prediction methods, Kolmogorov-Arnold Networks (KAN) is used as the basic network architecture, and the long short-term memory network is coupled to achieve the prediction of groundwater level fluctuations. Summary of the invention

[0004] The purpose of the present invention is to provide a groundwater level prediction method based on the KAN network architecture, aiming to utilize a more flexible network framework to obtain an optimized groundwater level prediction model by combining the KAN network architecture with B-spline curve interpolation fitting to achieve groundwater level prediction.

[0005] The present invention provides a groundwater level prediction method based on a KAN network architecture, which is characterized by comprising:

[0006] Collect historical data of groundwater levels and factors affecting groundwater levels from multiple observation wells within the study area as original data;

[0007] The historical data of groundwater level are used as the target variable for groundwater level prediction, and the factors affecting groundwater level are used as explanatory variables. LASSO regression is used to screen out relatively independent variables that have an impact on groundwater level for groundwater level prediction.

[0008] Normalize the groundwater level data and explanatory variables, generate multiple time series, combine the multiple time series into the data to be processed, divide the data to be processed into training sets and validation sets;

[0009] A groundwater level prediction model based on the KAN network architecture was built. The model includes two LSTM layers, a Dropout layer, and an output layer of the KAN network. The data processed by the two LSTM layers and the Dropout layer are input to the output layer of the KAN network. The B-spline curve activation function is used in the output layer of the KAN network to perform B-spline curve interpolation fitting of the training set subsequence data.

[0010] The training set subsequence data after B-spline curve interpolation fitting is input into the groundwater level prediction model based on KAN network structure for training to obtain the optimal parameter combination;

[0011] The optimized groundwater level prediction model based on the KAN network structure is obtained with the optimal parameter combination as the model parameters. The fitted validation set data is input into the optimized groundwater level prediction model based on the KAN network structure, and the groundwater level is predicted using the validated optimized groundwater level prediction model based on the KAN network structure.

[0012] Compared with the prior art, the advantages and positive technical effects achieved by the present invention are as follows:

[0013] 1) The current groundwater level prediction model based on the KAN network structure is obtained by taking the optimal parameter combination as the model parameters, and the current groundwater level prediction model based on the KAN network structure after verification is used for groundwater level prediction, which can effectively deal with the long-term dependence in the groundwater level sequence to realize the prediction of groundwater level;

[0014] 2) Different from the traditional MLP model which has a fixed activation function on the nodes, the constructed KAN network structure model sets a learnable B-spline curve activation function on the edges, which has better accuracy;

[0015] 3) Through steps such as sparse pruning, the KAN network has better interpretability, which helps to explore the basic numerical laws of groundwater level changes and provide groundwater management departments with an efficient, accurate and highly interpretable groundwater level prediction technology, which helps to improve the comprehensive understanding of the laws of groundwater level changes and enhance the planning and management capabilities of groundwater resources;

[0016] 4) A groundwater level prediction model with few trained parameters and capable of effectively handling long-term sequence dependencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1It is an overall flow chart of a groundwater level prediction method based on a KAN network architecture of the present invention;

[0018] Figure 2 It is an algorithm block diagram of a groundwater level prediction method based on a KAN network architecture of the present invention;

[0019] Figure 3 It is a schematic diagram of the structure of the groundwater level prediction model based on the KAN network structure constructed by the present invention;

[0020] Figure 4 It is a structural schematic diagram of the LSTM unit in the groundwater level prediction model of the present invention. DETAILED DESCRIPTION

[0021] The technical solution will be clearly described below in conjunction with the accompanying drawings and embodiments.

[0022] like Figure 1 As shown, a groundwater level prediction method based on the KAN network architecture of the present invention has the following specific steps:

[0023] Step 1: Data collection, including collecting historical groundwater level data and historical data of groundwater level influencing factors from multiple observation wells within the study area as original data; for example, obtaining groundwater level data and corresponding influencing factor data from 8 submersible observation wells in the study area from 2005 to 2017, including evapotranspiration, maximum temperature, minimum temperature, soil moisture, rainfall and normalized difference vegetation index (NDVI, an indicator for measuring vegetation growth), arranging the values ​​of historical groundwater level data and historical data of groundwater level influencing factors into a series in chronological order of occurrence to construct a time series of original data;

[0024] Step 2, data preprocessing, including screening and cleaning the original data, removing abnormal data values ​​from the original data time series, unifying the time scale of groundwater level data, setting the groundwater level data scale to 5-day data, and unifying the scales of other influencing factors; the time resolution of the influencing factor data is consistent with the groundwater level data; the commonly used groundwater level time series data scales include daily observation data, 5-day observation data, monthly observation data, and annual observation data. Among them, the monthly (annual) observation data takes the average value of the groundwater level observation of the current month (year);

[0025] Step 3: Use the LASSO regression algorithm to select the target variables that are relatively independent and have a significant impact on the groundwater level. The relevant equation is as follows:

[0026]

[0027] Where: X represents the explanatory variable matrix composed of the factors affecting groundwater level, Y represents the target variable for groundwater level prediction, β j represents the regression coefficient of the jth groundwater level influencing factor characteristics, represents the estimated value of the regression coefficient of the explanatory variable, λ represents the penalty factor, and p represents the total number of explanatory variables. Indicates the minimum function value of the calculated parameter;

[0028] The groundwater level prediction target variable Y is used to predict the groundwater level, and the groundwater level prediction data is obtained. According to the calculation results of LASSO regression, the explanatory variables used for groundwater level prediction are determined to be groundwater level influencing factors including at least evapotranspiration, maximum temperature, minimum temperature, soil moisture, rainfall and NDVI.

[0029] Step 4: normalize the groundwater level prediction data and the explanatory variables used for groundwater level prediction obtained in step 3, generate multiple time series accordingly, and combine the multiple time series into a data matrix X to be processed. * , the data is divided into a training set and a validation set in a ratio of 7:3 for groundwater level prediction model training and validation; specifically, each column of data is normalized based on the Min-Max method, and the data is processed to the (0, 1) interval. The calculation formula is as follows:

[0030]

[0031] Where: j′, j represent the data matrix to be processed X * Different column indexes in, that is, the j'th column data, the jth data, and Respectively represent the minimum and maximum values ​​in the j′th column data;

[0032] Step 5: Build a groundwater level prediction model based on the KAN network architecture. The model structure includes an LSTM layer, a Dropout layer, and an output layer of the KAN network. The specific description is as follows:

[0033] Step 5-1: Construct a groundwater level prediction model based on the KAN network structure. The specific structure is as follows: Figure 3 As shown. The training set and validation set are divided into subsequences according to the sliding window, where the sliding window length can be adjusted according to the model prediction needs; the training set and validation set subsequences are input into the LSTM layer located in the first layer of the model. The LSTM layer contains m neurons, and the relevant parameter formulas of the LSTM layer are as follows:

[0034] f t =σ(W f [x t ,h t-1 ]+bf ) (3)

[0035] i t =σ(W i [x t ,h t-1 ]+b i ) (4)

[0036]

[0037] o t =σ(W o [x t ,h t-1 ]+b o ) (6)

[0038]

[0039] In the formula, f t represents the forget gate, which chooses to forget information that is irrelevant to the prediction, i t Represents the input gate, which is used to input the information added to this processing unit, C t Represents the cell state, which is used to save long-term information during the prediction process. t represents the output gate, which is used to control the addition of new information and realize the output at the current moment, h t represents the hidden state, which is used to save the short-term output prediction information of the current time step, σ represents the gate activation function, W f , W i , W C , W o represents the weight matrix of different gates, b represents the bias vector, x t represents the input vector at time t, represents matrix multiplication, tanh(*) represents the activation function;

[0040] The model input is a 2D matrix consisting of the time window length × the number of input variables contained in the training set and validation set subsequences. The data enters the LSTM layer through the fully connected layer. The model has two LSTM layers, and the number of neurons is set to m and n respectively.

[0041] Step 5-2, in order to avoid overfitting in the simulation process, such as Figure 4 As shown in the figure, the groundwater level prediction model based on the KAN network structure has two LSTM layers. A Dropout layer is connected after each LSTM layer. The data input to the model at each time step is processed by the LSTM layer to form neurons and transmitted to the Dropout layer. The outputs of the two LSTM layers in the Dropout layer are respectively expressed as follows:

[0042]

[0043] Where x represents the input of the Dropout layer, W x represents the weight matrix of the Dropout layer, f() represents the activation function, m and n represent the total number of neurons in the two LSTM layers corresponding to the mask of the Dropout layer, p represents the probability of retaining neurons in the Dropout mask, the Bernoulli() function represents the generation of random variables to determine whether to retain or discard neurons, and i represents the neuron index;

[0044] In the Dropout layer, each neuron is retained with probability p and stops working with probability 1-p; the p value is set between 0 and 0.5, and the value needs to be adjusted according to the model prediction needs. y2 is the final output of the Dropout layer;

[0045] Step 5-3: The data processed by the LSTM layer and the Dropout layer is input to the output layer of the KAN network. The output layer of the KAN network uses the B-spline function as the activation function to output the training set subsequence data. The B-spline curve activation function formula is as follows:

[0046]

[0047] In the formula, C k represents the control point, k=0,1,...,K, by C k The polyline connected in sequence is the control polygon of the B-spline function, N k,p′ (d) is the B-spline basis function, k = 0, 1, ..., K, p′ represents the degree of the B-spline curve, and t represents the parameter of the B-spline curve, which is used to determine the point position on the spline curve;

[0048] Step 5-4, input the training set subsequence data after B-spline curve interpolation fitting in step 5-3 into the groundwater level prediction model based on the KAN network structure to complete multiple cycles of training, use the mean square error as the loss function evaluation index, automatically train and optimize the groundwater level prediction model based on the KAN network structure, and obtain the optimal parameter combination, that is, the optimal parameter combination corresponding to the minimum model operation loss; specifically, the MSE formula is as follows:

[0049]

[0050] In the formula, n′ represents the number of training samples, i′ represents the training sample index, and y i Indicates the actual value, represents the model prediction value;

[0051] Step 6, using the optimal parameter combination as the model parameter to obtain an optimized groundwater level prediction model based on the KAN network structure, inputting the fitted validation set data into the optimized groundwater level prediction model based on the KAN network structure, using the Nash efficiency coefficient as the model accuracy judgment index, and using the root mean square error as the model error judgment index. When the model accuracy and error meet the application requirements, the optimized groundwater level prediction model based on the KAN network structure is used for groundwater level prediction; the specific description is as follows:

[0052] Step 6-1, using the saved optimal parameter combination as the model parameter, inputting the fitted validation set data into the optimized groundwater level prediction model based on the KAN network structure, and performing prediction calculation on the groundwater level during the validation period. The validation set is input in the form of a subsequence, and the Nash efficiency coefficient (NSE) is selected as the model accuracy evaluation index, and the root mean square error (RMSE) is selected as the model error evaluation index; the calculation formula is as follows:

[0053]

[0054] In the formula, y i Indicates the actual value, represents the model prediction value, represents the mean of the observed values, n″ represents the number of validation samples, and i″ represents the validation sample index;

[0055] Step 6-2, adjust the model hyperparameters, that is, the optimal parameter combination obtained in step 5-4, and optimize the prediction results of the groundwater level prediction model based on the KAN network architecture until the prediction accuracy requirements of practical applications are met; through the above steps, save the hyperparameter combination with the best prediction performance for groundwater level prediction.

[0056] Table 1 shows the model simulation accuracy evaluation indicators of 8 submersible wells in the rate period and the verification period according to the embodiment of the present invention.

[0057] Table 1

[0058]

[0059] The above is an introduction to a groundwater level prediction method based on a KAN network architecture provided by the present application. The above implementation steps are only used to help understand the specific methods and core ideas of the present invention, and are not intended to limit the present invention. For some researchers in this field, according to the ideas of the present application, there will be changes in the specific implementation methods and application scopes.

[0060] Based on the embodiments of the present invention, all other embodiments and technical replacements and modifications of the embodiments obtained by ordinary technicians in the field without departing from the spirit of the present invention and without making creative work shall fall into the protection scope of the present invention.

Claims

1. A groundwater level prediction method based on KAN network architecture, It is characterized in that include: Collect historical data of groundwater levels and factors affecting groundwater levels from multiple observation wells within the study area as original data; The historical data of groundwater level are used as the target variable for groundwater level prediction, and the factors affecting groundwater level are used as explanatory variables. LASSO regression is used to screen out relatively independent variables that have an impact on groundwater level for groundwater level prediction. Normalize the groundwater level data and explanatory variables, generate multiple time series, combine the multiple time series into the data to be processed, divide the data to be processed into training sets and validation sets; A groundwater level prediction model based on the KAN network architecture was built. The model includes two LSTM layers, a Dropout layer, and an output layer of the KAN network. The data processed by the two LSTM layers and the Dropout layer are input to the output layer of the KAN network. The B-spline curve activation function is used in the output layer of the KAN network to perform B-spline curve interpolation fitting of the training set subsequence data. The training set subsequence data is input into the groundwater level prediction model based on the KAN network structure to obtain the optimal parameter combination; The optimized groundwater level prediction model based on the KAN network structure is obtained with the optimal parameter combination as the model parameters. The fitted validation set data is input into the optimized groundwater level prediction model based on the KAN network structure, and the groundwater level is predicted using the validated optimized groundwater level prediction model based on the KAN network structure.

2. According to claim 1, a groundwater level prediction method based on KAN network architecture, It is characterized in that Furthermore, the input of the groundwater level prediction model based on the KAN network structure is a two-dimensional matrix consisting of the time window length × the number of input variables contained in the training set and validation set subsequences, and the data enters the LSTM layer through the fully connected layer.

3. According to the method for predicting groundwater level based on KAN network architecture as described in claim 1, It is characterized in that The groundwater level prediction model based on the KAN network structure further sets two LSTM layers, and a Dropout layer is connected after each LSTM layer. The data input to the model at each time step is processed by the LSTM layer to form neurons and transmitted to the Dropout layer.

4. According to claim 1, a groundwater level prediction method based on KAN network architecture, It is characterized in that The groundwater level prediction model based on the KAN network structure further includes inputting the data processed by the LSTM layer and the Dropout layer into the output layer of the KAN network, and performing curve interpolation fitting of the subsequence data using a B-spline curve activation function.

5. According to claim 1, a groundwater level prediction method based on KAN network architecture, It is characterized in that Furthermore, the related equation based on which the LASSO regression is used to screen out relatively independent variables that have an impact on the groundwater level for groundwater level prediction is as follows: In the formula, X represents the explanatory variable matrix composed of the factors affecting groundwater level, Y represents the target variable for groundwater level prediction, β j represents the regression coefficient of the jth groundwater level influencing factor characteristics, represents the estimated value of the regression coefficient of the explanatory variable, λ represents the penalty factor, and p represents the total number of explanatory variables. Represents the minimum function value for which the parameter is calculated.

6. A method for predicting groundwater level based on KAN network architecture according to claim 1, It is characterized in that Furthermore, the output of the two LSTM layers in the Dropout layer is as follows: In the formula, x represents the input of the Dropout layer, y 1 ,y 2 represents the output of the two LSTM layers in the Dropout layer, W x Represents the weight matrix of the Dropout layer, f() represents the activation function, m and n represent the mask of the Dropout layer and correspond to the neurons in the LSTM layer, p represents the probability of retaining the neurons in the Dropout mask, and the Bernoulli() function is used to generate random variables to determine whether to retain or discard the neurons.

7. According to claim 1, a groundwater level prediction method based on KAN network architecture, It is characterized in that Furthermore, the B-spline curve activation function formula is as follows: In the formula, C k Represents the control point, C k The polyline connected in sequence is the control polygon of the B-spline function, N k,p′ (d) is the B-spline basis function, p′ represents the degree of the B-spline curve, and t represents the parameter of the B-spline curve, which is used to determine the point position on the spline curve.

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