A method for optimizing layout of a watershed monitoring network based on mutual information active learning

Abstract

The application discloses a kind of based on inter-information active learning's watershed monitoring network layout optimization method, comprising: data processing;Integrated learning prediction model is built by multiple LSTMs, each LSTM model parameter is initialized by setting different random seed, and model parameter is iteratively updated;The covariance matrix of the prediction result of potential monitoring point is constructed using the integrated learning prediction model trained;Based on the active learning algorithm of inter-information maximization, the inter-information gain of all candidate sites joining the current monitoring network is calculated, the candidate point with the maximum inter-information gain is selected, and the information value of potential monitoring point is sorted according to the size of inter-information gain;Output monitoring site optimization suggestion list.The application uses integrated learning method to scientifically quantify uncertainty, uses inter-information maximization strategy to evaluate global information value, so that site selection decision is no longer dependent on subjective experience, but based on data and rigorous calculation of information theory, significantly improve the scientific nature of decision-making.

Description

Technical Field

[0001] This invention relates to a method for optimizing the layout of a watershed monitoring network, and more particularly to a method for optimizing the layout of a watershed monitoring network based on mutual information active learning. Background Technology

[0002] Watershed water quality monitoring is the foundation of water environment protection and scientific management. A scientific and efficient monitoring network can provide crucial data for environmental decision-making.

[0003] Currently, the layout of monitoring networks largely relies on traditional methods. For example, sites are typically selected based on administrative divisions, the distribution of major pollution sources, or expert experience, sometimes employing simple spatial uniformity or random placement strategies. However, these traditional methods have significant limitations. First, their decision-making process is highly subjective and lacks data-driven quantitative scientific basis. Second, this "blind" deployment often leads to irrational allocation of monitoring resources. This results in a situation where information redundancy and monitoring gaps coexist: redundant stations may be deployed in areas with simple hydrological processes, causing resource waste; while key nodes with complex hydrological and hydrochemical processes (such as tributary confluences and areas with multiple pollution sources) may lack station coverage. Ultimately, these problems lead to overall inefficiency of the entire monitoring network.

[0004] In recent years, with the development of artificial intelligence technology, some studies have begun to explore using water quality prediction models to guide the optimization of monitoring networks. The basic idea is to train a prediction model using existing data and suggest adding monitoring stations in areas where the model's prediction error is large. However, this approach has a fundamental flaw: simply equating "high model prediction uncertainty" with "high information value at that point" is inaccurate. For example, a remote tributary completely unknown to the model may have extremely high prediction uncertainty, but setting up a station there may contribute very little to improving the understanding of the entire watershed system. Conversely, a key node located at the confluence of multiple pollution sources may have only moderate uncertainty in the model's predictions, but obtaining observational data at that point could significantly reduce the prediction uncertainty of the entire downstream river network.

[0005] Therefore, existing technologies generally lack a solution that can intelligently assess and differentiate the "information value" of each potential monitoring point from the perspective of global information gain. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to propose a method for optimizing the layout of a watershed monitoring network based on mutual information active learning, so as to realize the intelligent identification and priority ranking of watershed monitoring stations.

[0007] Technical solution: This invention includes the following steps:

[0008] S1: Collect time-series driving data, water quality target data, and static attribute data of the study watershed, and preprocess them;

[0009] S2: Construct an integrated learning prediction model for watershed water quality composed of multiple LSTMs, initialize the parameters of each LSTM model by setting different random number seeds, and iteratively update the model parameters;

[0010] S3: Within the scope of the river network in the research basin, the covariance matrix of the prediction results of potential monitoring points is constructed using the trained ensemble learning prediction model;

[0011] S4: Based on the active learning algorithm of maximizing mutual information, calculate the mutual information gain of all candidate sites joining the current monitoring network, select the candidate points that maximize the mutual information gain, and sort the potential monitoring points by information value according to the size of the mutual information gain.

[0012] S5: Output a list of optimization suggestions for monitoring sites, and verify the optimization effect through simulation experiments using the observation system.

[0013] In step S2, multiple benchmark models are trained independently using a training dataset, where the loss function is:

[0014] in, The loss value used during the training phase; This represents the total number of paired predictions and observations within a calculation window. For the index of the sample pair, ; For the first The model prediction value corresponding to each sample; For the first The measured values ​​of the model corresponding to each sample.

[0015] In step S2, the gradient is calculated through backpropagation and based on the learning rate. Update parameters:

[0016]

[0017] in, The parameter value after one parameter update; The parameter values ​​before the last parameter update; The learning rate; θ represents the loss value used during the training phase; θ is the set of trainable parameters for the model.

[0018] In S3, the method for constructing the covariance matrix of the potential monitoring point prediction results is as follows:

[0019] For the A baseline LSTM model, at potential monitoring points Place, No. The prediction output at each time step is defined as:

[0020]

[0021] in, Indicates the first A benchmark model at point Location, Time Step The predicted value, It is the output gate weight matrix. For the corresponding hidden state, It is the output gate bias vector;

[0022] Define the ensemble prediction mean as:

[0023]

[0024] in, as potential monitoring points The mean of the ensemble predictions at point M is the number of baseline LSTM models in the ensemble learning;

[0025] Constructing the prediction results of potential monitoring points covariance matrix , where matrix elements Defined as:

[0026]

[0027] in, as potential points and The predicted covariance, Indicates the first A benchmark model at point Location, Time Step The predicted value, as potential monitoring points The ensemble prediction mean at the location.

[0028] The mutual information gain consists of the difference between two conditional entropy terms:

[0029]

[0030] in, Candidate sites Join the current monitoring network The resulting information gain In order to know the current network Under the conditions of observation information, the station Conditional entropy; In the case of known division In addition to the information of other undeployed points, the site The conditional entropy.

[0031] The The calculation formula is:

[0032]

[0033]

[0034] in, Pi is a constant. It is a natural constant; In order to know the current monitoring network Under information conditions, the site conditional variance; Covariance matrix China and the site The corresponding variance scalar; For the site With sets The row vector of covariance among all stations in the data; Represents the inverse of a submatrix; for The transpose of .

[0035] The The calculation formula is:

[0036]

[0037]

[0038] in, In a known set Under information conditions, the site The conditional variance of Covariance matrix China and the site The corresponding variance scalar, For the site With sets The row vectors of covariance among the stations within the site, For set The inverse of the internal covariance submatrix, for The transpose of .

[0039] The formula for calculating the candidate point that maximizes mutual information gain is:

[0040]

[0041] in, For the first The optimal candidate site selected in the next iteration. It is the independent variable that maximizes the objective function. It is a set of potential monitoring points. This is the current monitoring network.

[0042] The method for ranking information value is as follows: ... As the kth suggested addition site, its ranking is recorded, and the network is updated. Repeat this iterative process until all potential monitoring points have been selected and ranked, forming the final information value ranking list.

[0043] The preprocessing in S1 includes: data cleaning and format unification, data transformation and standardization, dataset partitioning and data reshaping.

[0044] Beneficial effects: This invention has the following advantages:

[0045] (1) The ensemble learning method is used to scientifically quantify uncertainty and the mutual information maximization strategy is used to evaluate the value of global information, so that the point selection decision no longer depends on subjective experience, but is based on rigorous calculation of data and information theory, which significantly improves the scientific nature of the decision.

[0046] (2) By outputting a priority list, it is possible to guide the limited monitoring funds and equipment to be invested in the most valuable information points, so as to improve the understanding and control of the water environment of the entire basin with less investment and faster, and maximize the monitoring benefits.

[0047] (3) For the first time, robust uncertainty quantification methods in the field of deep learning are combined with efficient decision-making strategies in information theory, and innovatively applied to solve the classic environmental science problem of optimizing large-scale watershed monitoring networks;

[0048] (4) The output priority list contains key information such as geographic coordinates, which can directly guide engineering practice, achieve the goal of capturing more watershed information with fewer stations, and provide a scientific decision-making basis for the planning and optimization of watershed water quality monitoring network. Attached Figure Description

[0049] Figure 1 This is a flowchart of the present invention;

[0050] Figure 2 Heatmap of the covariance matrix of the prediction results from the integrated model;

[0051] Figure 3 This is a comparison chart showing the reduction in global error between the method of this invention and the control location method. Detailed Implementation

[0052] The invention will now be further described with reference to the accompanying drawings.

[0053] Example 1

[0054] like Figure 1 As shown in the figure, the watershed monitoring network layout optimization method based on mutual information active learning in this embodiment includes the following steps:

[0055] S1: Collect time-series driving data, water quality target data, and static attribute data of the study watershed, and preprocess them. Specifically, this includes:

[0056] S11, Data Acquisition

[0057] This embodiment collected observational data from 979 stations covering the continental United States and Central Europe. The data covers the period from January 1, 1981 to December 31, 2023. The collected data are mainly divided into the following three categories:

[0058] Time series driven data: Acquire daily meteorological forcing data and hydrological observation data, specifically including precipitation, surface air pressure, snow water equivalent, shortwave radiation, daily average temperature, daily maximum temperature, daily minimum temperature, U-direction wind speed, V-direction wind speed, and standardized flow observations.

[0059] Water quality target variable data: Obtain daily water quality observation data that will serve as the model prediction target, preferably dissolved oxygen (DO) concentration and water temperature. Raw water quality observation data typically have a low observation frequency, discontinuous data sequences, and contain many missing values.

[0060] Watershed static attribute data: Obtain static attribute data that describes each watershed and does not change over time, specifically divided into categories such as climate attributes, hydrogeological attributes, land use attributes, soil attributes, and topographic attributes.

[0061] S12. Preprocess the collected data, including:

[0062] S121. Data Cleaning and Format Standardization: For the original water quality observation data, replace missing values ​​('NA') in text format with standard missing values ​​(NaN) used in numerical calculations, ensuring that all time series data files are formatted in a uniform format: behavior is time step, columns are different stations. Constant attribute data files are formatted as: behavior is station, columns are different attribute features.

[0063] S122. Data Transformation and Standardization: For variables with significant skewed distributions (such as flow rates Q, DO, and WT), logarithmic transformation is performed before standardization.

[0064]

[0065] in, The values ​​of the variables after logarithmic transformation. These are the original variable values ​​before the logarithmic transformation. It is a constant;

[0066] Perform the following on all input features (transformed time-series driving data, constant watershed attribute data) and target variable (transformed water quality data) Standardization. Standardized mean. and standard deviation Calculated based on data from the training period. The standardized formula is:

[0067]

[0068] in, For the standardized variable values, The values ​​of the variables after logarithmic transformation. For the standardized mean, Standard deviation;

[0069] Record the mean and standard deviation of all variables (e.g., ...). ), used for subsequent reverse normalization.

[0070] S123. Dataset partitioning: Divide the entire time series into a training set (e.g., 1981-2009) and a test set (e.g., 2010-2023).

[0071] S124. Data Reshaping: The preprocessed and partitioned data is reorganized into a three-dimensional tensor format suitable for LSTM model input. The preferred tensor dimension order is [number of time steps, number of stations, number of features].

[0072] S2: Construct an integrated learning prediction model for watershed water quality composed of multiple LSTMs. Initialize the parameters of each LSTM model by setting different random number seeds, and use the root mean square error as the loss function to iteratively update the model parameters.

[0073] This embodiment selects the Long Short-Term Memory (LSTM) network as the baseline prediction model. LSTM units control the information flow through forget gates, input gates, and output gates. Its core computation process is defined by the following formula:

[0074] Forgotten Gate:

[0075]

[0076] in, This represents the activation vector of the forget gate. yes function, It is the weight matrix of the forget gate. It is the hidden state of the previous time step. It is the input at the current time step, i.e., the standardized features after S1 preprocessing. At time step The value of , It is the bias term of the forget gate;

[0077] Input Gate:

[0078]

[0079] in, This represents the activation vector of the input gate. yes function, It is the input gate weight matrix. It is the hidden state of the previous time step. It is the input at the current time step, i.e., the standardized features after S1 preprocessing. At time step The value of , It is the input gate bias vector;

[0080] Candidate cell status:

[0081]

[0082] in, It represents the candidate cell state, indicating the amount of new information added to the cell state through the input gate. It is the weight matrix of the candidate unit states. It is the hidden state of the previous time step. It is the input at the current time step, i.e., the standardized features after S1 preprocessing. At time step The value of , It is the bias vector of the candidate unit state;

[0083] Cell status update:

[0084]

[0085] in, and This indicates the cell state at the current time step and the previous time step. This represents the activation vector of the forget gate. This represents element-wise multiplication. It is the candidate cell state;

[0086] Output gate:

[0087]

[0088] in, It is the output gate activation vector. yes function, It is the output gate weight matrix. It is the hidden state of the previous time step. It is the input at the current time step, i.e., the standardized features after S1 preprocessing. At time step The value of , It is the output gate bias vector;

[0089] Hidden state:

[0090]

[0091] in, It is the hidden state or output of the current time step. It is the output gate activation vector. Indicates the cell state at the current time step;

[0092] The baseline LSTM model contains at least one hidden layer with 60 hidden units and a Dropout rate of 0.2. The model can be implemented using the PyTorch framework.

[0093] The ensemble learning prediction model consists of M independent LSTM baseline models, where M is an integer greater than 1. In this embodiment, M=5. The model diversity is ensured by setting different random number seeds for the M baseline models to initialize the weights.

[0094] In a server environment, M baseline models are trained independently using the training dataset. The root mean square error (RMSE) loss function is preferred.

[0095] in, The loss value used during the training phase is preferably the root mean square error (RMSE), which measures the overall deviation between the prediction and the observation. The total number of paired predictions and observations within a calculation window. : Index of sample pairs ( ), For the first The model prediction value for each sample For the first The measured values ​​of the model corresponding to each sample;

[0096] The Adam optimizer is used, and the gradient is calculated through backpropagation and based on the learning rate. Update parameters:

[0097]

[0098] in, This refers to the set of trainable parameters for the model, specifically the adjustable parameters in the LSTM model described above. The parameter value after one parameter update. The parameter values ​​before the last parameter update. For learning rate, The loss value used during the training phase;

[0099] Set the batch size to 40, the time step to 360 days, and the training period to 100 until the model converges.

[0100] S3: Within the study area of ​​the river network, construct the covariance matrix of the prediction results of potential monitoring points using the trained ensemble learning prediction model.

[0101] To obtain the predicted water quality value at each time step, the hidden state is obtained in LSTM based on step S2. Then, a linear output layer is used to map the hidden state to the predicted value of the target variable. For the ... A baseline LSTM model, at potential monitoring points Place, No. The prediction output at each time step is defined as:

[0102]

[0103] in, Indicates the first A benchmark model at point Location, Time Step The predicted value, It is the output gate weight matrix. For the corresponding hidden state, It is the output gate bias vector;

[0104] Define the ensemble prediction mean as:

[0105]

[0106] in, as potential monitoring points The mean of the ensemble predictions at point M, where M is the number of baseline LSTM models in the ensemble learning. Indicates the first A benchmark model at point Location, Time Step The predicted value;

[0107] Furthermore, the prediction results of potential monitoring points are constructed. covariance matrix , where matrix elements Defined as:

[0108]

[0109] in, as potential points and The predicted covariance, where M is the number of baseline LSTM models in the ensemble learning. Indicates the first A benchmark model at point Location, Time Step The predicted value, as potential monitoring points The ensemble prediction mean at the location, Indicates the first A benchmark model at point Location, Time Step The predicted value, as potential monitoring points The ensemble prediction mean at the location.

[0110] S4: Based on the active learning algorithm that maximizes mutual information, calculate the mutual information gain of all candidate sites joining the current monitoring network, select the candidate points that maximize mutual information gain, and rank the potential monitoring points according to the magnitude of mutual information gain.

[0111] Information gain is quantified using mutual information, and its calculation relies on the N×N covariance matrix Σ obtained above. For each candidate site y ∈ Calculate its inclusion in the current monitoring network The resulting mutual information gain This gain consists of the difference between the two conditional entropy terms:

[0112]

[0113] in, Candidate sites Join the current monitoring network The resulting information gain In order to know the current network Under the conditions of observation information, the station Conditional entropy; In the case of known division In addition to the information of other undeployed points, the site The conditional entropy.

[0114] The calculation process is as follows:

[0115] Assume that the predicted values ​​of potential monitoring points follow a multivariate Gaussian distribution defined by the covariance matrix Σ. Within this framework, a single Gaussian variable... Entropy and its variance The relationship is:

[0116]

[0117] in, The entropy of a single Gaussian variable X, Let π be the constant value of pi, taken as 3.14159. is the natural constant, taken as 2.71828. For random variables The variance;

[0118] Conditional entropy Then with the corresponding conditional variance Related. Quantified in the current monitoring network under conditions The remaining uncertainty. First, extract the relationship between the covariance matrix Σ and... and set Related blocks: variance ,gather covariance submatrix ,as well as and The covariance vector between and its transpose Based on the properties of the multivariate Gaussian distribution, the conditional variance is calculated as follows:

[0119]

[0120] in, In order to know the current monitoring network Under information conditions, the site The conditional variance of Covariance matrix China and the site The corresponding variance scalar, For the site With sets The row vector of covariance among all stations in the middle, Denotes the inverse of a submatrix. for Transpose of;

[0121] Then, calculate the conditional entropy:

[0122]

[0123] in, In order to be in the current monitoring network Under the conditions, the site conditional entropy, Let π be the constant value of pi, taken as 3.14159. is the natural constant, taken as 2.71828. In order to know the current monitoring network Under information conditions, the site conditional variance;

[0124] Quantified the number of all other known undeployed sites. Information conditions The remaining uncertainty. The calculation method is the same as above, only the condition set needs to be replaced with :

[0125]

[0126] in, In a known set Under information conditions, the site The conditional variance of Covariance matrix China and the site The corresponding variance scalar, For the site With sets The row vectors of covariance among the stations within the site, For set The inverse of the internal covariance submatrix, for Transpose of;

[0127]

[0128] in, In the case of known division In addition to the information of other undeployed points, the site conditional entropy, Let π be the constant value of pi, taken as 3.14159. is the natural constant, taken as 2.71828. In a known set Under information conditions, the site conditional variance.

[0129] In the k-th iteration, by calculating all candidate sites Given the mutual information gain ΔMI(y), select the candidate point that maximizes ΔMI(y).

[0130]

[0131] in, For the first The optimal candidate site selected in the next iteration. It is the independent variable that maximizes the objective function. It is a set of potential monitoring points. For the current monitoring network, Candidate sites Join the current monitoring network The resulting information gain;

[0132] Will As the kth suggested addition site, its ranking is recorded, and the network is updated. Repeat this iterative process N-n0 times, where N is the number of potential monitoring points and n0 is the number of existing monitoring stations, until all potential monitoring points are selected and sorted to form the final information value ranking list.

[0133] S5: Output a list of optimization suggestions for monitoring sites, and verify the optimization effect through simulation experiments using the observation system.

[0134] The information value ranking results obtained in step S4 are organized into a decision list containing information such as site priority ranking, geographical coordinates, and optional information value scores. The optimization effect is verified through observation system simulation experiments (OSSEs): a small number of sites (e.g., 20%) are retained as the initial sparse network, and the data of the remaining sites are hidden; a baseline model is trained using the initial network data, and sites are added sequentially according to both this method and a random site placement strategy. After each addition, the model is updated through incremental training to predict the water quality data of the remaining hidden sites, and the following baseline performance indicators are calculated:

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] in, This represents the model's predicted value. The model represents the observed values, where n represents the total number of paired predictions and observations within a computation window; Pbias is the percentage bias; NSE is the Nash efficiency coefficient; RMSE is the root mean square error; and Pcorr is the Pearson correlation coefficient between the model's predicted sequence and the observed sequence. The sample mean of the observations during the test period; This represents the sample mean of the model's predicted values ​​during the testing period.

[0141] The percentage deviation (Pbias) ranges from negative infinity to positive infinity; a lower absolute value indicates a more accurate model simulation. The Nash efficiency coefficient (NSE) ranges from negative infinity to 1. Traditionally, 1 indicates a perfect match between the model prediction and the observed value, NSE < 0 indicates an unreliable model, and NSE ≥ 0.5 is considered a good water quality model. The root mean square error (RMSE) ranges from 0 to infinity; a lower value indicates a better model performance. Pcorr ranges from -1 to 1, representing the absolute negative and positive correlations between simulated and observed values, respectively.

[0142] Example 2

[0143] This embodiment uses data from a total of 796 river basins in the United States and Central Europe, spanning from 1981 to 2019.

[0144] Figure 2 A heatmap of the covariance matrix of the ensemble model prediction results is presented, with the diagonal lines representing the prediction variance of each site and the off-diagonal lines representing the covariance between sites. This result indicates a significant information correlation structure among different sites, providing a basis for subsequent mutual information-based site selection based on statistical structure in this invention. This allows for the identification of redundant areas and the prioritization of new sites with higher information gain.

[0145] Figure 3 The results show a comparison of the root mean square error (RMSE) reduction between the mutual information location method and the control location method under the same number of new sites. The results show that the mutual information location method has a lower overall error curve throughout the entire process, with a final relative improvement of 19.5%. Furthermore, under the condition of reaching the same error threshold, the mutual information location method can save 54 new sites (22.5%), reducing the construction and maintenance costs of the monitoring network while ensuring the effectiveness.

Claims

1. A method for optimizing the layout of a watershed monitoring network based on mutual information active learning, characterized in that, Includes the following steps: S1: Collect time-series driving data, water quality target data, and static attribute data of the study watershed, and preprocess them; S2: Construct an integrated learning prediction model for watershed water quality composed of multiple LSTMs, initialize the parameters of each LSTM model by setting different random number seeds, and iteratively update the model parameters; S3: Within the scope of the river network in the research basin, the covariance matrix of the prediction results of potential monitoring points is constructed using the trained ensemble learning prediction model; S4: Based on the active learning algorithm that maximizes mutual information, calculate the mutual information gain of all candidate sites joining the current monitoring network, select the candidate points that maximize the mutual information gain, and rank the potential monitoring points according to the magnitude of the mutual information gain. The mutual information gain is composed of the difference between two conditional entropy terms. in, Candidate sites Join the current monitoring network The resulting information gain In order to know the current network Under the conditions of observation information, the station Conditional entropy; In the case of known division In addition to the information of other undeployed points, the site Conditional entropy; The The calculation formula is: in, Pi is a constant. It is a natural constant; In order to know the current monitoring network Under information conditions, the site conditional variance; Covariance matrix China and the site The corresponding variance scalar; For the site With sets The row vector of covariance among all stations in the data; Represents the inverse of a submatrix; for Transpose of; The The calculation formula is: in, In a known set Under information conditions, the site The conditional variance of Covariance matrix China and the site The corresponding variance scalar, For the site With sets The row vectors of covariance among the stations within the site, For set The inverse of the internal covariance submatrix, for Transpose of; S5: Output a list of optimization suggestions for monitoring sites, and verify the optimization effect through simulation experiments using the observation system.

2. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 1, characterized in that, In step S2, multiple benchmark models are trained independently using a training dataset, where the loss function is: in, The loss value used during the training phase; This represents the total number of paired predictions and observations within a calculation window. For the index of the sample pair, ; For the first The model prediction value corresponding to each sample; For the first The measured values ​​of the model corresponding to each sample.

3. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 2, characterized in that, The gradient is calculated through backpropagation and based on the learning rate. Update parameters: in, The parameter value after one parameter update; The parameter values ​​before the last parameter update; The learning rate; The loss value used during the training phase; This is the set of trainable parameters for the model.

4. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 1, characterized in that, In S3, the method for constructing the covariance matrix of the potential monitoring point prediction results is as follows: For the first A baseline LSTM model, at potential monitoring points Place, No. The prediction output at each time step is defined as: in, Indicates the first A benchmark model at point Location, Time Step The predicted value, It is the output gate weight matrix. For the corresponding hidden state, It is the output gate bias vector; Define the ensemble prediction mean as: in, as potential monitoring points The mean of the ensemble predictions at point M is the number of baseline LSTM models in the ensemble learning; Constructing the prediction results of potential monitoring points covariance matrix , where matrix elements Defined as: in, For potential points and The predicted covariance, Indicates the first A benchmark model at point Location, Time Step The predicted value, as potential monitoring points The ensemble prediction mean at the location.

5. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 1, characterized in that, The formula for calculating the candidate point that maximizes mutual information gain is: in, For the first The optimal candidate site selected in the next iteration. It is the independent variable that maximizes the objective function. It is a set of potential monitoring points. This is the current monitoring network.

6. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 5, characterized in that, The method for ranking information value is as follows: ... As the kth suggested addition site, its ranking is recorded, and the network is updated. Repeat this iterative process until all potential monitoring points have been selected and ranked, forming the final information value ranking list.

7. The method for optimizing the layout of a watershed monitoring network based on mutual information active learning according to claim 1, characterized in that, The preprocessing in S1 includes: data cleaning and format unification, data transformation and standardization, dataset partitioning and data reshaping.

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