Chlorophyll a prediction method and system based on heterogeneity perception and equation embedding

Abstract

The present invention belongs to the field of ocean prediction technology, and discloses a chlorophyll a prediction method and system based on heterogeneity perception and equation embedding, step 1, obtaining input data related to chlorophyll a concentration prediction: step 2, spatial heterogeneity measurement: dividing the original input area into sub-areas to obtain the spatial heterogeneity level of the sub-areas; step 3, heterogeneity perception spatiotemporal evolution modeling: constructing a multi-layer adaptive heterogeneity perception network, and outputting heterogeneity perception spatiotemporal evolution characteristics; step 4, designing a physical constraint-guided prediction network embedded in the fluid motion equation, and calculating the future spatiotemporal evolution feature sequence of chlorophyll a; step 5, reshaping and aggregation decoding operations on the spatiotemporal evolution feature sequence, and merging the sub-area prediction sequences of the corresponding time period to obtain the final prediction result. The present invention realizes the spatiotemporal evolution modeling of spatial heterogeneity perception and equation physical knowledge embedding, and improves the accuracy and reliability of chlorophyll a concentration prediction.

Description

Technical Field

[0001] The present invention belongs to the field of ocean prediction technology and relates to a chlorophyll a prediction method based on deep learning, and in particular to a chlorophyll a prediction method and system based on heterogeneity perception and equation embedding. Background Art

[0002] Chlorophyll a concentration is an important indicator for reflecting the degree of eutrophication of water bodies and monitoring algal blooms, and is crucial to assessing the health of marine ecosystems. In recent years, data-driven methods based on deep learning have been widely used in the prediction of chlorophyll a concentration, such as LSTM, CNN-LSTM, ConvLSTM, and prediction networks improved by attention mechanisms. Compared with traditional numerical models and statistical methods that have high computational complexity and difficulty in fully modeling complex nonlinear relationships between data, this type of method achieves more accurate chlorophyll a concentration prediction by learning and mining the distribution patterns and high-dimensional evolution characteristics of a large amount of chlorophyll a spatiotemporal data. However, these advanced methods currently only focus on the simple application of basic deep learning models, and have not conducted in-depth research on the spatiotemporal distribution characteristics of chlorophyll a, and their long-term prediction accuracy is still limited. This type of method currently has the following problems:

[0003] First, when making large-scale spatiotemporal predictions of chlorophyll a concentrations, existing methods do not consider the spatial heterogeneity of chlorophyll a distribution in the entire study area. For example, the chlorophyll a concentrations in sub-areas of water far from the nearshore are very similar, with low fluctuation levels, and there is a high positive correlation between both adjacent points and distant points. In contrast, the chlorophyll a concentration values ​​in shallow water sub-areas close to the nearshore are usually significantly different, and vary significantly between seasons. The different correlations between these sub-areas reveal the phenomenon of spatial heterogeneity, which is defined as the uneven distribution of a trait, event, or relationship over a region.

[0004] Second, existing prediction methods usually rely on black-box deep learning network structures, which lack a solid physical foundation, resulting in reduced transparency and interpretability of chlorophyll a concentration prediction results. Specifically, most of the above-mentioned deep learning-based chlorophyll a concentration prediction methods use historical remote sensing data or buoy observation data to learn the complex spatiotemporal variation relationship of chlorophyll a, and do not require understanding of its underlying physical processes. However, this purely data-driven prediction method that relies solely on data for "black-box" network modeling requires a large amount of training data to achieve accurate long-term predictions. When the amount of data is small or the data is incomplete, it will be difficult for the model to mine the spatiotemporal evolution characteristics of chlorophyll a and produce prediction results that conform to the laws of physical mechanisms, thus limiting the stability and reliability of chlorophyll a concentration predictions. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a chlorophyll a prediction method and system based on heterogeneity perception and equation embedding, which realizes the spatiotemporal evolution modeling of spatial heterogeneity perception and equation physical knowledge embedding, and improves the accuracy and reliability of chlorophyll a concentration prediction. First, a multi-layer adaptive heterogeneity perception network is constructed to realize the spatiotemporal evolution modeling scheme of spatial heterogeneity perception. Specifically, the spatial heterogeneity level of the sub-region is measured, and the difference between it and the average heterogeneity level represented by different layers of the current network in the multi-layer adaptive heterogeneity perception network is judged, and then the optimal number of layers of the existing network is adaptively selected according to the heterogeneity clustering results. If the minimum difference is greater than the set threshold, the operation of adding one to the number of layers of the existing network is performed. This scheme ensures that the network retains the previously obtained spatial relationship while learning the new heterogeneity relationship, thereby better avoiding the catastrophic forgetting problem caused by spatial heterogeneity. Secondly, inspired by the design of a physical constraint-guided prediction network embedded in the fluid motion equation for air quality, the advection-diffusion equation that characterizes the mass transfer law of the flow system, that is, the basic physical process that controls the transport of chlorophyll a, is integrated into a framework with the graph neural network in the form of differential equations, thereby obtaining an advection-diffusion differential equation neural network function whose chlorophyll a concentration varies with space and time, and further calculating the future spatiotemporal evolution feature sequence of chlorophyll a based on the neural ordinary differential solver. This neural network architecture with physical constraint-guided differential equation embedding can generate accurate predictions with physical meaning, thereby improving the interpretability and reliability of chlorophyll a concentration predictions.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] The chlorophyll a prediction method based on heterogeneity perception and equation embedding includes the following steps:

[0008] Step 1: Obtain relevant input data for chlorophyll a concentration prediction:

[0009] Includes historical input series of chlorophyll a concentrations , wind speed and direction data;

[0010] Step 2: Spatial heterogeneity measurement: Divide the original input area into sub-areas, and then measure the spatiotemporal input sequence of each sub-area in turn. Perform heterogeneity measurement to obtain the spatial heterogeneity level of the sub-region ;

[0011] Step 3: Modeling the spatiotemporal evolution of heterogeneity perception: construct a multi-layer adaptive heterogeneity perception network to achieve dynamic network structure modeling of different sub-regional qualitative levels; including heterogeneity judgment and network adaptive training process, and finally train according to the selected optimal number of network layers and output the spatiotemporal evolution characteristics of heterogeneity perception;

[0012] Step 4: Design a physical constraint-guided prediction network embedded in the fluid motion equations;

[0013] The advection-diffusion equation that characterizes the mass transfer law of the chlorophyll a flow system is integrated with the graph neural network into a framework to obtain the neural network function of the advection-diffusion differential equation that describes the chlorophyll a concentration changing with space and time. Then, the future spatiotemporal evolution characteristic sequence of chlorophyll a is calculated through a multi-step predictive differential network.

[0014] Step 5: Reshape and aggregate the future chlorophyll a spatiotemporal evolution feature sequence obtained in step 4 to output the final prediction result. , and further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result .

[0015] Furthermore, in step 2, for each sub-region's spatiotemporal input sequence First, perform the weighted average within the time interval T to obtain ,in is the weight, z represents The selected time period is arrive time, Represents the sub-region spatiotemporal input sequence corresponding to the z time period;

[0016] Afterwards, To measure spatial heterogeneity, the following formula is used to measure heterogeneity:

[0017] (2);

[0018] in, Represents the normalized entropy of the chlorophyll a concentration value of the current input sub-region, Indicates the normalized standard deviation of the chlorophyll a concentration value of the current input sub-region. Represents the normalized mean of the chlorophyll a concentration values ​​in the current input sub-region.

[0019] Furthermore, in step 3, by measuring the spatial heterogeneity level of the sub-region, and using a multi-layer adaptive heterogeneity-aware network to determine the difference in average heterogeneity level represented by different layers of the current network, the optimal number of layers of the existing network is adaptively selected according to the heterogeneity clustering results; the details of step 3 are as follows:

[0020] Step 31: Randomly select a time , and then input the sequence according to its multiple sub-regions in time and space The heterogeneity level of the multi-layer adaptive heterogeneity perception network is initialized, that is, the number of network layers L and the average heterogeneity level of different layers are set and threshold TH;

[0021] Step 32: Whenever a sub-region space-time sequence is input When , the heterogeneity level of the current input sub-region is determined and the average heterogeneity level of different layers The difference between If the difference is less than the initialization threshold TH, then directly select If the difference is greater than the initialization threshold TH, the number of network layers needs to be increased to L+1; finally, training is performed based on the selected optimal number of network layers and the heterogeneity-aware spatiotemporal evolution features are output.

[0022] Further, in step 31, a time is randomly selected , we can get the input samples of P sub-regions , respectively, to measure spatial heterogeneity and obtain heterogeneity measurement values , and then through P sub-regions The maximum and minimum values ​​of the network are set to L=3, and each layer of the network uses the gated recurrent unit GRU; the minimum As the average heterogeneity level of the first layer , threshold , is the maximum value, As the average heterogeneity level of the second layer , H is the average heterogeneity level at level 3 .

[0023] Further, in step 32, if the current input sub-region spatiotemporal sequence The level of heterogeneity and the average heterogeneity level of different layers The difference is less than the threshold TH, and the best matching layer is found by formula (3) :

[0024] (3);

[0025] Represents the change in the number of layers of the network from 1 layer to L layers, where L is the total number of layers in the network;

[0026] In addition, the average heterogeneity level of the layer is updated:

[0027] (4);

[0028] in, It indicates that up to now The number of sub-region spatiotemporal sequences that match the layer, represents the average heterogeneity level of the layer before updating, represents the average heterogeneity level of the layer after updating;

[0029] If the current input sub-region spatiotemporal sequence The level of heterogeneity and the average heterogeneity level of different layers The difference between is greater than the threshold TH, the number of network layers is increased by 1 to handle this new level of sub-region heterogeneity, and the number of newly added network layers is The heterogeneity level is expressed as = .

[0030] Furthermore, step 4 is as follows:

[0031] Step 41: Use the fully connected layer to transform the heterogeneity-aware spatiotemporal evolution features output in step 3 to obtain the input of the multi-step prediction differential network The mean and variance of

[0032] Step 42: Construct an advection-diffusion equation that describes the mass transfer law of the chlorophyll a flow system, and characterize its differential process using the graph Laplace operator to obtain a neural network function for the advection-diffusion differential equation of chlorophyll a concentration that varies with space and time. ;

[0033] Step 43: Physical Constraint Guided Differential Equation Network Construction: Based on And the constructed advection-diffusion differential equation neural network function , construct a multi-step prediction differential network; use the multi-step prediction differential network to calculate the future Chlorophyll a feature sequence of time steps .

[0034] Further, in step 41, The mean and standard deviation It is expressed as:

[0035] (5);

[0036] Among them, g( ) represents the fully connected layer operation, MARH( ) represents the process of extracting features by multi-layer adaptive heterogeneity perception network, Represents the spatial and temporal evolution characteristics of heterogeneity perception;

[0037] Input to a multi-step predictive differential network ,in Sampled from a standard normal distribution.

[0038] Furthermore, in step 42, by defining the diffusion and advection differential processes in the chlorophyll a transmission process in the graph neural network, that is, by mapping the diffusion and advection differential processes in the chlorophyll a transmission process in the graph structure neural network, the equation of the variation of chlorophyll a concentration with space and time is obtained; specifically, the graph Laplacian operator The gradient divergence is expressed as ,in represents the gradient operator, div represents the divergence operator, therefore, the diffusion equation is expressed as follows:

[0039] (9);

[0040] Where C is the chlorophyll a concentration, D represents the diffusion coefficient, and L is a weighted adjacency matrix based on distance. Computed graph Laplacian;

[0041] The impact of the advection process is based on the flow field modeling based on wind speed and wind direction, using the flow field information as the graph. The weight of the edge; the wind speed and wind direction are input through a multi-layer perception to extract high-dimensional features and reconstruct the adjacency matrix To calculate the Laplace operator Q, the entire advection process is calculated by the following formula:

[0042] (11);

[0043] In order to simultaneously consider the effects of advection and diffusion processes on chlorophyll a concentration, a fusion process was constructed to generate the advection-diffusion differential equation function:

[0044] (12);

[0045] in, and are the outputs of the diffusion process and the advection process, respectively. Formula (12) describes the dynamic evolution of chlorophyll a concentration.

[0046] Furthermore, in step 43, the advection-diffusion differential equation of equation (12) is modeled as follows:

[0047] (13);

[0048] in, represents the parameters that need to be trained, is the neural network function constructed based on the physical differential equation of equation (12), defined as the neural network function of the advection-diffusion differential equation, Using the graph convolutional network representation in the graph neural network, its form is:

[0049] (14);

[0050] Among them, L and Q are graph Laplacian operators, and ReLU() is the activation function;

[0051] Based on step 41, input is obtained Neural network functions for advection-diffusion differential equations Based on the Neural ODE solver and graph neural network, a multi-step predictive differential network is constructed to obtain the future chlorophyll a characteristic sequence :

[0052] (15);

[0053] Among them, ODEsolver( ) represents the ODE solver, Represents the input of the multi-step prediction differential network The initial time, Represents the future of multi-step predictive differential network solutions time steps.

[0054] The present invention also provides a chlorophyll a prediction system based on heterogeneity perception and equation embedding, which is used to implement the chlorophyll a prediction method based on heterogeneity perception and equation embedding as described above, and the system includes an input preprocessing module, a spatial heterogeneity measurement module, a heterogeneity perception spatiotemporal evolution modeling module, a physical constraint guidance module embedded with fluid motion equations, and a chlorophyll a concentration prediction output module.

[0055] The input preprocessing module obtains a historical input sequence of chlorophyll a concentration based on the original data;

[0056] The spatial heterogeneity measurement module divides the area contained in the historical input sequence into sub-areas, and then measures the heterogeneity of the spatiotemporal input sequence of each sub-area in turn to obtain a metric representation of the spatial heterogeneity level of the sub-area.

[0057] The heterogeneity-aware spatiotemporal evolution modeling module uses a multi-layer adaptive heterogeneity-aware network to analyze the difference between the heterogeneity level of the input sub-region and the average heterogeneity level of different layers of the current network and perform sub-region clustering, and selects the optimal number of layers of the existing network according to the clustering results. If the minimum difference is greater than the set threshold, the number of layers of the existing network is increased by one;

[0058] The physical constraint guidance module embedded in the fluid motion equation includes a physical constraint guidance prediction network embedded in the fluid motion equation. First, the vector output by the heterogeneity perception spatiotemporal evolution modeling module is converted using a fully connected layer to obtain an initial state for the prediction module. The mean and variance of the advection-diffusion differential equation describing the mass transfer law of the chlorophyll a flow system are then constructed, and the differential process is characterized by the graph Laplace operator to obtain a neural network function of the advection-diffusion differential equation of chlorophyll a concentration varying with space and time. The neural ordinary differential solver is further used to calculate the future chlorophyll a characteristic sequence.

[0059] The chlorophyll a concentration prediction output module is used to embed the fluid motion equation into the output result of the module for reshaping and aggregation operations, and further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] 1. Construct a heterogeneity-aware spatiotemporal evolution modeling module, divide the original input large-scale area into sub-regions, measure the spatial heterogeneity level of the sub-regions, and use a multi-layer adaptive heterogeneity-aware network to judge the difference in the average heterogeneity level represented by different layers of the current network, and then adaptively select the optimal number of layers of the existing network according to the heterogeneity clustering results. Each layer in the network indirectly realizes the clustering of spatial sub-regions according to its heterogeneity level, where the average heterogeneity level of each layer is used as the cluster centroid. This ensures that the previously obtained spatial relationship is retained while learning new heterogeneous relationships, thereby effectively avoiding the catastrophic forgetting problem caused by the spatial heterogeneity distribution of chlorophyll a. In addition, the parameter update of the network is only performed on the selected optimal layer or the newly added layer. Therefore, only one layer participates in the network parameter update at a time during the training process, reducing the computational complexity of the model.

[0062] 2. A physical constraint-guided prediction network embedded in the equations of fluid motion was designed. The advection and diffusion equations that characterize the mass transfer law of the flow system, that is, the basic physical process that controls the transport of chlorophyll a, were integrated into a framework with the graph neural network in the form of differential equations, thereby obtaining an advection-diffusion differential equation neural network function whose chlorophyll a concentration varies with space and time. The future spatiotemporal evolution feature sequence of chlorophyll a was further calculated based on the neural ordinary differential solver. This neural network architecture with physical constraint-guided differential equation embedding can generate accurate predictions with physical meaning, thereby improving the interpretability and reliability of chlorophyll a concentration predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0064] Figure 1 is a system structure diagram of the present invention;

[0065] Figure 2 It is a schematic diagram of the structure of the spatial heterogeneity measurement module of the present invention;

[0066] Figure 3 This is a schematic diagram of the structure of the heterogeneity-aware spatiotemporal evolution modeling module of the present invention;

[0067] Figure 4 This is a schematic diagram of the structure of the physical constraint guidance module embedded in the fluid motion equation of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0069] Example 1

[0070] Combination Figure 1-Figure 4 This embodiment designs a chlorophyll a prediction method based on heterogeneity perception and equation embedding, including the following steps:

[0071] Step 1: Obtain relevant input data for chlorophyll a concentration prediction:

[0072] Step 11: Get the original chlorophyll a concentration data, and obtain the chlorophyll a concentration historical input sequence after data preprocessing =( ), where t represents the current time, T represents the time interval, They represent the input sequences at time t-T+1, t-T+2,...,t respectively. Represents the historical input sequence from time t-T+1 to time t;

[0073] Step 12: Obtain relevant variable wind speed and wind direction data for constructing an adjacency matrix in the graph structure.

[0074] Step 2: Spatial heterogeneity measurement: Divide the original input area into sub-areas, and then measure the spatiotemporal input sequence of each sub-area in turn. Perform heterogeneity measurement to obtain the spatial heterogeneity level of the sub-region ;in They represent the spatiotemporal input sequence of the i-th sub-region at time t-T+1, t-T+2, ..., t respectively, such as Figure 2 shown.

[0075] The size of the original input region is N*M. Assuming that each sub-region contains n grid points, P=N*M / n represents the number of sub-regions. Therefore, the input sequence at time t is and the sub-region spatiotemporal input sequence The relationship is expressed as follows:

[0076] (1);

[0077] Considering the computational efficiency and the temporal variation of the sub-regions, for each sub-region, the spatiotemporal input sequence First, perform the weighted average within the time interval T to obtain , z represents The selected time period is arrive The weighted average takes into account that the input closer to the prediction time has a greater impact on the prediction result, so the calculation The weight of each historical moment input is =1 / t-z+1, z represents The selected time period is arrive time.

[0078] Afterwards, To measure spatial heterogeneity, the following formula is used to measure heterogeneity:

[0079] (2);

[0080] in, Represents the normalized entropy of the chlorophyll a concentration value of the current input sub-region, Indicates the normalized standard deviation of the chlorophyll a concentration value of the current input sub-region. Represents the normalized mean of the chlorophyll a concentration values ​​in the current input sub-region.

[0081] Step 3: Modeling the spatiotemporal evolution of heterogeneity perception: construct a multi-layer adaptive heterogeneity perception network to achieve dynamic network structure modeling of different sub-regional qualitative levels; including heterogeneity judgment and network adaptive training process, and finally train according to the selected optimal number of network layers and output the spatiotemporal evolution characteristics of heterogeneity perception, such as Figure 3 As shown, this step is implemented through the heterogeneity-aware spatiotemporal evolution modeling module.

[0082] By measuring the spatial heterogeneity level of the sub-region and using a multi-layer adaptive heterogeneity-aware network to determine the difference in average heterogeneity levels represented by different layers of the current network, the optimal number of layers of the existing network is adaptively selected based on the heterogeneity clustering results.

[0083] The details of step 3 are as follows:

[0084] Step 31: Randomly select a time , and then input the sequence according to its multiple sub-regions in time and space The heterogeneity level of the multi-layer adaptive heterogeneity perception network is initialized, that is, the number of network layers L and the average heterogeneity level of different layers are set and threshold TH.

[0085] In step 31, a random time is selected , we can get the input samples of P sub-regions , and the spatial heterogeneity is measured according to formula (2) to obtain the heterogeneity measurement value , and then through P sub-regions The maximum and minimum values ​​of the network are set to L=3, and each layer of the network uses a gated recurrent unit (GRU). Minimum As the average heterogeneity level of the first layer , threshold is the maximum value, As the average heterogeneity level of the second layer , H is the average heterogeneity level at level 3 .

[0086] Step 32: Whenever a sub-region space-time sequence is input When , the heterogeneity level of the current input sub-region is determined and the average heterogeneity level of different layers The difference between If the difference is less than the initialization threshold TH, then directly select If the difference is greater than the initialization threshold TH, the number of network layers needs to be increased to L+1. Finally, training is performed based on the selected optimal number of network layers and the heterogeneity-aware spatiotemporal evolution features are output.

[0087] In step 32, if the current input sub-region spatiotemporal sequence The level of heterogeneity and the average heterogeneity level of different layers The difference is less than the threshold TH, and the heterogeneity processing unit finds the best matching layer , expressed by the following formula:

[0088] (3);

[0089] Represents the change in the number of network layers from 1 to L, where L is the total number of network layers.

[0090] In addition, the average heterogeneity level of the layer is updated:

[0091] (4);

[0092] in, It indicates that up to now The number of sub-region spatiotemporal sequences that match the layer, represents the average heterogeneity level of the layer before updating, Represents the average heterogeneity level of the layer after updating.

[0093] If the current input sub-region spatiotemporal sequence The level of heterogeneity and the average heterogeneity level of different layers The difference is greater than the threshold TH, and the number of network layers is increased by 1 to handle this new level of sub-region heterogeneity. The heterogeneity level can be expressed as = .

[0094] Each layer in the adaptive heterogeneity-aware network indirectly helps clustering of spatial sub-regions according to its heterogeneity level, where the average heterogeneity level of each layer is used as the cluster centroid; the parameter update of the adaptive heterogeneity-aware network is only for That is, the case where there is no layer growth and That is, the number of layers increases. Therefore, no matter how many layers the network has, only one layer of GRU participates in the network parameter update at a time during training, which reduces the computational complexity of the model.

[0095] Step 4: Design a physical constraint-guided prediction network embedded in the fluid motion equations;

[0096] The advection-diffusion equation that characterizes the mass transfer law of the chlorophyll a flow system is integrated with the graph neural network into a framework to obtain the neural network function of the advection-diffusion differential equation that varies with space and time for the chlorophyll a concentration. Then, the future spatiotemporal evolution characteristic sequence of chlorophyll a is calculated through a multi-step predictive differential network.

[0097] This step is achieved by embedding the physical constraints in the fluid motion equations to guide the prediction module, such as Figure 4 As shown, step 41: Use the fully connected layer to transform the heterogeneity-aware spatiotemporal evolution features output in step 3 to obtain the input of the multi-step prediction differential network The mean and variance of .

[0098] In step 41, The mean and standard deviation It is expressed as:

[0099] (5);

[0100] Among them, g( ) represents the fully connected layer operation, MARH( ) represents the process of extracting features by multi-layer adaptive heterogeneity perception network, Represents the spatial and temporal evolution characteristics of heterogeneity perception.

[0101] Next, we determine the input of the initial state of the multi-step prediction differential network based on a reparameterization technique. ,Right now ,in Sampled from a standard normal distribution.

[0102] Step 42: Construct an advection-diffusion equation that describes the mass transfer law of the chlorophyll a flow system, and characterize the differential process using the graph Laplace operator to obtain a neural network function of the advection-diffusion differential equation in which the chlorophyll a concentration varies with space and time.

[0103] In step 42, in physics, using the continuity equation, the chlorophyll a transport process is described as:

[0104] (6);

[0105] Where C is the chlorophyll a concentration, To describe the flux of chlorophyll a concentration transport, div is the divergence operator, Describes the changes in concentration at a particular point in space due to the flow of particles into and out of that point;

[0106] The diffusion process describes the random movement of particles from high concentration to low concentration in a medium. It is expressed by the continuity equation and Fick's law. Fick's law describes the flux of particles caused by diffusion and states that the magnitude of the flux is proportional to the concentration gradient, that is, , where D represents the diffusion coefficient, Represents the concentration gradient. Usually, when a substance moves from a high concentration area to a low concentration area, its amplitude is proportional to the concentration gradient, and the diffusion equation is as follows:

[0107] (7);

[0108] The advection process describes the horizontal transport of any variable resulting in local changes in that variable. Unlike the diffusion process, which explains the transport of particles due to differences in concentration gradients, advection explains the transport of particles due to the influence of external flow fields. In the advection process, It is represented by a vector field, that is, = , represents the fluid velocity, so the advection equation for chlorophyll a concentration can be obtained as follows:

[0109] =-div( ) (8);

[0110] The equations expressed by the above formulas (7) and (8) can be named as diffusion and advection differential equations for chlorophyll a transport. By defining the diffusion and advection differential processes in the chlorophyll a transport process in the graph neural network (i.e., by mapping the diffusion and advection differential processes in the chlorophyll a transport process in the graph neural network), an equation for the variation of chlorophyll a concentration with space and time is proposed. The graph neural network uses graph structure input for subsequent operations, including graph convolutional networks and graph attention networks. The graph structure Laplacian operator is mainly used here.

[0111] Specifically, the graph Laplacian operator The gradient divergence is expressed as ,in represents the gradient operator, div represents the divergence operator, therefore, the diffusion equation is expressed as follows:

[0112] (9);

[0113] Where L is a weighted adjacency matrix based on distance. Compute the graph Laplacian.

[0114] The impact of the advection process is based on the flow field modeling based on wind speed and wind direction. Following the formula proposed by Chapman, the discrete simulation of the advection process can be expressed as:

[0115] (10);

[0116] in, is a modified Laplace operator that uses flow field information as graph The wind speed and wind direction are input through a multi-layer perception to extract high-dimensional features and reconstruct the adjacency matrix To calculate the Laplace operator Q, the entire advection process is calculated by the following formula:

[0117] (11);

[0118] In order to simultaneously consider the effects of advection and diffusion processes on chlorophyll a concentration, a fusion process was constructed to generate the advection-diffusion differential equation function:

[0119] (12);

[0120] in, and are the outputs of the diffusion process and the advection process, respectively. Formula (12) describes the dynamic evolution of chlorophyll a concentration.

[0121] Step 43: Physical Constraint Guided Differential Equation Network Construction: Based on And the constructed advection-diffusion differential equation neural network function , using a multi-step prediction differential network to calculate the future Chlorophyll a feature sequence of time steps .

[0122] In step 43, inspired by the neural ordinary differential equation solver (neural ODEs), the advection-diffusion differential equation of equation (12) is modeled as follows:

[0123] (13);

[0124] in, represents the parameters that need to be trained, is the neural network function constructed based on the physical differential equation of equation (12), defined as the neural network function of the advection-diffusion differential equation, Using the graph convolutional network representation in the graph neural network, its form is:

[0125] (14);

[0126] Where L and Q are graph Laplacian operators, which are used to calculate how the concentration of the current node changes due to the diffusion and advection processes of its neighboring nodes. They are based on the weighted adjacency matrix of distance and the flow-based weighted adjacency matrix Get; ReLU() is the activation function.

[0127] Based on the input obtained in step 41 (i.e., the initial state input of the multi-step predictive differential network) and the advection-diffusion differential equation neural network function In our method, we build a multi-step prediction differential network based on the neural ODE solver and graph neural network. The multi-step prediction differential network uses graph convolutional network to build physical-based differential equations, and then iterates and updates the gradient of multi-step prediction features based on the neural ODE solver (neural ODEs). Finally, the future chlorophyll a feature sequence can be obtained through the multi-step prediction differential network. :

[0128] (15);

[0129] Among them, ODEsolver( ) represents the ODE solver, Represents the input of the multi-step prediction differential network The initial time, Represents the future of multi-step predictive differential network solutions time steps. Figure 4 In , They represent the use of ODE solvers to iteratively calculate and output future The prediction features of time steps are concatenated into .

[0130] Step 5: Perform reshaping and aggregation decoding operations to output the final prediction results , and further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result .

[0131] In step 5, the final prediction result Predicting sequences by subregions Merger income:

[0132] = (16).

[0133] Example 2

[0134] This embodiment designs a chlorophyll a prediction system based on heterogeneity perception and equation embedding, such as Figure 1-Figure 4 As shown, it is used to implement the chlorophyll a prediction method based on heterogeneity perception and equation embedding as described in Example 1. The system includes an input preprocessing module, a spatial heterogeneity measurement module, a heterogeneity perception spatiotemporal evolution modeling module, a physical constraint guidance module embedded with fluid motion equations, and a chlorophyll a concentration prediction output module.

[0135] The input preprocessing module obtains the historical spatiotemporal input sequence of chlorophyll a concentration based on the original data .

[0136] The spatial heterogeneity measurement module converts the original input sequence The included area is divided into sub-areas, and then the spatiotemporal input sequence of each sub-area is calculated in turn. Perform heterogeneity measurement to obtain the spatial heterogeneity level metric representation of the sub-region .

[0137] The heterogeneity-aware spatiotemporal evolution modeling module uses a multi-layer adaptive heterogeneity-aware network to analyze the heterogeneity level of the input sub-regions. The difference between the average heterogeneity level of different layers of the current network is used to cluster the sub-regions, and the optimal number of layers of the existing network is determined based on the clustering results. If the minimum difference is greater than the set threshold, the number of existing network layers is increased by one.

[0138] The physical constraint guidance module embedded in the fluid motion equation includes a physical constraint guidance prediction network embedded in the fluid motion equation. First, the vector output by the heterogeneity perception spatiotemporal evolution modeling module is converted using a fully connected layer to obtain an initial state for the prediction module. Then, by constructing the advection-diffusion equation that describes the mass transfer law of the chlorophyll a flow system and characterizing the differential process using the graph Laplace operator, a neural network function of the advection-diffusion differential equation of chlorophyll a concentration varying with space and time is obtained. The neural ordinary differential solver is further used to calculate the future chlorophyll a characteristic sequence. .

[0139] The chlorophyll a concentration prediction output module is used to embed the fluid motion equation into the output result of the module. Perform reshaping and aggregation operations, and further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result .

[0140] The same or similar parts between the various embodiments of the present invention specification can be referred to each other, and each embodiment focuses on the differences from other embodiments. In addition, the structure of the system embodiment is only schematic, and the program modules described by the detachable components may or may not be physically separated. In actual application, some or all modules can be selected as needed to achieve the purpose of the embodiment.

[0141] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary hardware platform, and of course can also be implemented entirely by hardware, but in many cases the former is a better implementation method. Based on such an understanding, all or part of the contribution of the technical solution of the present invention to the background technology can be embodied in the form of a software product, and the computer software product can be stored in a storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., including a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0142] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Any changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should fall within the protection scope of the present invention.

Claims

1. A chlorophyll a prediction method based on heterogeneity perception and equation embedding, characterized in that: The following steps are involved: Step 1: Obtain relevant input data for chlorophyll a concentration prediction: Contains the historical input sequence X of chlorophyll a concentration t-T+1：t , wind speed and direction data; Step 2: Spatial heterogeneity measurement: Divide the original input area into sub-areas, and then calculate the spatiotemporal input sequence S of each sub-area in turn. (i，t-T+1：t) Perform heterogeneity measurement to obtain the spatial heterogeneity level r1 of the sub-region; Step 3: Modeling the spatiotemporal evolution of heterogeneity perception: construct a multi-layer adaptive heterogeneity perception network to achieve dynamic network structure modeling of different sub-regional qualitative levels; including heterogeneity judgment and network adaptive training process, and finally train according to the selected optimal number of network layers and output the spatiotemporal evolution characteristics of heterogeneity perception; Step 4: Design a physical constraint-guided prediction network embedded in the fluid motion equations; The advection-diffusion equation that characterizes the mass transfer law of the chlorophyll a flow system is integrated with the graph neural network into a framework. Specifically, the advection-diffusion equation that describes the mass transfer law of the chlorophyll a flow system is constructed, and its differential process is characterized by the graph Laplace operator; by defining the diffusion and advection differential processes in the chlorophyll a transmission process in the graph neural network, that is, by mapping the diffusion and advection differential processes in the chlorophyll a transmission process in the graph structured neural network, the advection-diffusion differential equation neural network function of the chlorophyll a concentration changing with space and time is obtained. Then, the future spatiotemporal evolution characteristic sequence of chlorophyll a is calculated through a multi-step predictive differential network; Step 5: Reshape and aggregate the future chlorophyll a spatiotemporal evolution feature sequence obtained in step 4 to output the final prediction result. And further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result 2. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 1, characterized in that: In step 2, for each sub-region’s spatiotemporal input sequence S (i，t-T+1：t) First, perform the weighted average within the time interval T to obtain where α j is the weight, z represents S (i，z) The selected time period is from t-T+1 to time t, S (i，z) Represents the sub-region spatiotemporal input sequence corresponding to the z time period; Afterwards, To measure spatial heterogeneity, the following formula is used to measure heterogeneity: Among them, ENTR l Represents the normalized entropy of the chlorophyll a concentration value of the current input sub-region, STD l Indicates the normalized standard deviation of the chlorophyll a concentration value of the current input sub-region, MEAN l Represents the normalized mean of the chlorophyll a concentration values ​​in the current input sub-region.

3. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 1, characterized in that: In step 3, the spatial heterogeneity level of the sub-region is measured, and the multi-layer adaptive heterogeneity-aware network is used to determine the difference in the average heterogeneity level represented by different layers of the current network, and then the optimal number of layers of the existing network is adaptively selected according to the heterogeneity clustering results; the details of step 3 are as follows: Step 31: Randomly select time t0, and then input the sequence according to its multiple sub-regions in time and space The heterogeneity level of the multi-layer adaptive heterogeneity perception network is initialized, that is, the number of network layers L and the average heterogeneity level m of different layers are set k , k=1, 2, ..., L and threshold TH; Step 32: Whenever a sub-region space-time sequence S is input (i，t-T+1：t) When the heterogeneity level ri of the current input sub-region and the average heterogeneity level m of different layers are determined k The difference between best If the difference is less than the initialization threshold TH, l is directly selected. best If the difference is greater than the initialization threshold TH, the number of network layers needs to be increased to L+1; finally, training is performed based on the selected optimal number of network layers and the heterogeneity-aware spatiotemporal evolution features are output.

4. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 3 is characterized in that: In step 31, a time t is randomly selected a , we can get the input samples of P sub-regions The spatial heterogeneity is measured respectively to obtain the heterogeneity measurement value R j , then through P sub-regions R j The maximum and minimum values ​​of the network are set to L = 3, and each layer of the network uses the gated recurrent unit GRU; the minimum value r min As the average heterogeneity level m1 of the first layer, the threshold r max is the maximum value, r min +TH as the average heterogeneity level of the second layer m2,r min +2×TH as the average heterogeneity level m3 of layer 3.

5. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 3 is characterized in that: In step 32, if the current input sub-region spatiotemporal sequence S (i，t-τ+1：t) The heterogeneity level r i and the average heterogeneity level m in different layers k The difference is less than the threshold TH, and the best matching layer l is found by formula (3) best : l k Represents the change in the number of layers of the network from 1 layer to L layers, where L is the total number of layers in the network; In addition, the average heterogeneity level of the layer is updated: Among them, q best Indicates that up to now best The number of sub-region spatiotemporal sequences that match the layer, represents the average heterogeneity level of the layer before updating, represents the average heterogeneity level of the layer after updating; If the current input sub-region spatiotemporal sequence S (i，t-T+1：t) The heterogeneity level r i and the average heterogeneity level m in different layers k The difference between is greater than the threshold TH, the number of network layers is increased by 1 to handle this new level of sub-region heterogeneity, and the number of newly added network layers is l L+1 The heterogeneity level is denoted as m L+1 =r i .

6. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 1, characterized in that: Step 4 also includes the following steps: The fully connected layer is used to transform the heterogeneity-aware spatiotemporal evolution features output in step 3 to obtain the input of the multi-step prediction differential network. The mean and variance of Physical constraint-guided differential equation network construction: based on And the constructed advection-diffusion differential equation neural network function Construct a multi-step prediction differential network; use the multi-step prediction differential network to calculate the chlorophyll a feature sequence for the next τ time steps 7. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 6, characterized in that: The mean and standard deviation It is expressed as: Among them, g() represents the fully connected layer operation, MARH() represents the process of extracting features from the multi-layer adaptive heterogeneity perception network, and MARH(S (i，t-T+1：t)) Represents the spatial and temporal evolution characteristics of heterogeneity perception; Input to a multi-step predictive differential network where ∈ i Sampled from a standard normal distribution.

8. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 1, characterized in that: In step 4, specifically, the graph Laplacian Δ is expressed as the divergence of the gradient: in represents the gradient operator, div represents the divergence operator, therefore, the diffusion equation is expressed as follows: Where C is the chlorophyll a concentration, D represents the diffusion coefficient, and L is the weighted adjacency matrix W based on the distance. d Computed graph Laplacian; The impact of the advection process is based on the flow field modeling based on wind speed and wind direction, using the flow field information as the graph. The wind speed and wind direction are input through a multi-layer perception system to extract high-dimensional features and reconstruct the adjacency matrix W. p To calculate the Laplace operator Q, the entire advection process is calculated by the following formula: In order to simultaneously consider the effects of advection and diffusion processes on chlorophyll a concentration, a fusion process was constructed to generate the advection-diffusion differential equation function: Among them, H diff and H adv are the outputs of the diffusion process and the advection process, respectively. Formula (12) describes the dynamic evolution of chlorophyll a concentration.

9. The chlorophyll a prediction method based on heterogeneity perception and equation embedding according to claim 8, characterized in that: The advection-diffusion differential equation of equation (12) is modeled as follows: Among them, φ represents the parameters that need to be trained, is the neural network function constructed based on the physical differential equation of equation (12), defined as the neural network function of the advection-diffusion differential equation, Using the graph convolutional network representation in the graph neural network, its form is: Among them, L and Q are graph Laplacian operators, and ReLU() is the activation function; Based on the input Neural network functions for advection-diffusion differential equations Using the Neural Ordinary Differential Equation Solver, a multi-step predictive differential network is constructed to obtain the future chlorophyll a characteristic sequence. Among them, ODEsolver() represents the ODE solver, and t0 represents the input of the multi-step predictive differential network. The initial time, t1, ..., t τ represents the future τ time steps solved by the multi-step prediction differential network.

10. A chlorophyll a prediction system based on heterogeneity perception and equation embedding, characterized in that: The system is used to implement the chlorophyll a prediction method based on heterogeneity perception and equation embedding as described in any one of claims 1 to 9, the system comprising an input preprocessing module, a spatial heterogeneity measurement module, a heterogeneity perception spatiotemporal evolution modeling module, a physical constraint guidance module embedded with fluid motion equations, and a chlorophyll a concentration prediction output module. The input preprocessing module obtains a historical input sequence of chlorophyll a concentration based on the original data; The spatial heterogeneity measurement module divides the area contained in the historical input sequence into sub-areas, and then measures the heterogeneity of the spatiotemporal input sequence of each sub-area in turn to obtain a metric representation of the spatial heterogeneity level of the sub-area; The heterogeneity-aware spatiotemporal evolution modeling module uses a multi-layer adaptive heterogeneity-aware network to analyze the difference between the heterogeneity level of the input sub-region and the average heterogeneity level of different layers of the current network and perform sub-region clustering, and selects the optimal number of layers of the existing network according to the clustering results. If the minimum difference is greater than the set threshold, the number of layers of the existing network is increased by one; The physical constraint guidance module embedded in the fluid motion equation includes a physical constraint guidance prediction network embedded in the fluid motion equation. First, the vector output by the heterogeneity perception spatiotemporal evolution modeling module is converted using a fully connected layer to obtain an initial state for the prediction module. The mean and variance of the advection-diffusion differential equation describing the mass transfer law of the chlorophyll a flow system are then constructed, and the differential process is characterized by the graph Laplace operator to obtain a neural network function of the advection-diffusion differential equation of chlorophyll a concentration varying with space and time. The neural ordinary differential solver is further used to calculate the future chlorophyll a characteristic sequence. The chlorophyll a concentration prediction output module is used to embed the fluid motion equation into the output result of the module for reshaping and aggregation operations, and further merge the sub-region prediction sequences of the corresponding time period to obtain the final prediction result.

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