Global and Local Koopman's PM 2.5 Prediction methods and systems

Abstract

The present invention discloses a PM prediction method and system based on global and local Koopman, belonging to the field of geographic information technology (GIS). 2.5 For a large amount of PM monitoring data, the method converts a one-dimensional time series into a two-dimensional tensor to capture multi-period time information, and uses a graph convolution method to capture the spatial information between PM concentration monitoring stations. 2.5 In the encoder part, a global and local Koopman network is adopted to capture the changes within a period, and a self-attention mechanism is used to capture the information between periods. Through the decoding of the model, hourly prediction of the PM station concentration can be realized. 2.5 The present invention can realize the time series prediction of the PM station concentration and has important significance in the fields of atmospheric environment monitoring and the like. 2.5 The present invention can achieve the time series prediction of the PM station concentration and has important significance in the fields such as atmospheric environment monitoring. 2.5 The present invention can realize the time series prediction of the PM station concentration and has important significance in fields such as atmospheric environment monitoring.

Description

Technical Field

[0001] The present invention belongs to the field of neural network technology, and in particular relates to a global and local Koopman PM 2.5 Prediction methods and systems. Background Art

[0002] Atmospheric PM 2.5 Refers to suspended particulate matter with a diameter less than or equal to 2.5 microns. High concentrations of PM 2.5 It can cause haze and low visibility, and harmful substances in it can increase respiratory diseases. Deeply understand and accurately predict PM 2.5 The dynamic changes of pollution, the exploration of the internal mechanism of its evolution pattern, and the establishment of an air pollution prediction model are of great significance for public health management and the formulation of environmental protection measures.

[0003] Existing PM 2.5 Spatiotemporal prediction methods are mainly divided into theory-driven methods and data-driven methods. At present, both methods have certain shortcomings, which affect PM 2.5 Prediction accuracy. Deeply understand and accurately predict PM 2.5 The dynamic change law of pollution, and the exploration of the internal mechanism of its evolution pattern, and then the establishment of air pollution prediction model are of great significance for public health management and the formulation of environmental protection measures. Koopman operator theory provides an effective mathematical tool for complex nonlinear dynamic modeling. Its core idea is to map complex nonlinear dynamic systems into linear state space to predict the state of the system. Koopman operator is a set of infinite-dimensional linear operators used to describe the time evolution of observable quantities of the system under dynamics. The basic characteristics of complex systems can be explained by the spectral properties of Koopman operator, and its characteristic function provides an intrinsic coordinate system for global linearized nonlinear dynamics. However, when dealing with PM with spatial attribute information 2.5 The existing Koopman method fails to fully capture PM in mapping the system state space. 2.5 The geospatial correlation between concentration monitoring sites is not conducive to the in-depth understanding and accurate prediction of spatiotemporal data. In addition, existing time series models usually rely only on historical data and fail to fully capture the characteristics of spatiotemporal data, which may lead to rapid accumulation of prediction errors. Summary of the invention

[0004] The present invention aims to solve the above problems in the prior art and provides a global and local Koopman PM 2.5 Prediction methods and systems.

[0005] The specific technical solutions adopted by the present invention are as follows:

[0006] In a first aspect, the present invention provides a global and local Koopman PM 2.5 Prediction methods, including:

[0007] S1. Obtain the historical PM of each monitoring station in the target area 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in the form of a matrix;

[0008] S2. By means of a fast Fourier transform (FFT), the one-dimensional time series data structure is transformed from the time domain to the frequency domain, a plurality of characteristic frequencies are selected based on the amplitude of the frequency component and the period length corresponding to each characteristic frequency is determined, so that each one-dimensional time series in the one-dimensional time series data structure is reshaped into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure;

[0009] S3, all k characteristic frequencies The corresponding two-dimensional time series data structure input consists of a PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector Evolution, evolution results The input is reconstructed in the decoder with self-attention mechanism to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

[0010] As a preferred embodiment of the first aspect, in S1, the historical PM of each monitoring station in the target area is obtained. 2.5 After monitoring the data, the historical PM of each monitoring station is 2.5 The monitoring data is encoded in time series format to obtain the PM corresponding to each monitoring station. 2.5 Concentration time series and calculation of PM 2.5 Missing rate of concentration time series data, excluding PM 2.5 The PM concentration time series of the monitoring stations with missing data exceeding the threshold are then interpolated using the linear interpolation method for the remaining monitoring stations. 2.5 The concentration time series is completed, and each monitoring station obtains the time length Continuous PM in the range 2.5 The concentration time series, as the one-dimensional time series.

[0011] As a preferred embodiment of the first aspect, the specific implementation steps of S2 are:

[0012] S21, performing a fast Fourier transform (FFT) on the one-dimensional time series data structure along the time series direction, taking the amplitude of each frequency component obtained by the transformation, calculating the average amplitude of all frequency components along the station direction, and obtaining the average amplitude of each frequency component at all stations; sorting the average amplitudes of all frequency components, taking the frequencies corresponding to the k frequency components with the largest average amplitudes as the characteristic frequencies ;

[0013] S22, for each characteristic frequency , the length of the one-dimensional time series Divide by the characteristic frequency Get the corresponding period length , reshape each one-dimensional time series in the one-dimensional time series data structure into a period length is the number of rows with characteristic frequency is a two-dimensional time series with the number of columns; finally, the characteristic frequency is formed by the two-dimensional time series of all N monitoring stations The corresponding two-dimensional time series data structure in the form of a three-dimensional tensor.

[0014] As a preferred embodiment of the first aspect, the PM 2.5 In each prediction branch of the spatiotemporal prediction model, the adaptive graph convolution network includes an adaptive graph relation network and a graph convolution network;

[0015] In the adaptive graph relationship network, for the two-dimensional time series data structure of the input current prediction branch, it is constructed into a graph with monitoring sites as nodes, and based on the spatial distance between the monitoring sites With minimum threshold The Gaussian kernel function method is used to construct the initial adjacency matrix, and the weights directly calculated by the Gaussian kernel function method do not exceed the minimum threshold At the same time, the high-level representation vector corresponding to the two-dimensional time series of each monitoring station is extracted from the two-dimensional time series data structure of the current prediction branch using the time convolution network. , and then the high-level representation vector corresponding to all monitoring sites Constructing a high-level representation matrix , the high-level representation matrix The product of the conjugate transposed matrix of and the original matrix is ​​outputted by the ReLU activation function and the Softmax function in turn to obtain an adaptive adjacency matrix;

[0016] The input of the graph convolution network is the graph constructed in the adaptive graph relational network and the adaptive adjacency matrix. The graph convolution network is composed of multiple layers of graph convolution layers cascaded together, and each layer of graph convolution layer performs feature propagation and node update on the basis of the previous layer of graph convolution layer. The adjacency matrix during feature propagation is the sum of the standardized adjacency matrix and the adaptive adjacency matrix. The standardized adjacency matrix is ​​obtained by adding the self-loop to the initial adjacency matrix and performing degree matrix normalization. The output of the last layer of graph convolution layer in the graph convolution network is used as the spatial information embedded in the adaptive graph convolution network extracted from the two-dimensional time series data structure. .

[0017] As a preferred embodiment of the first aspect, the encoder is implemented by a multi-layer perceptron, and its input is the spatial information embedded in the adaptive graph convolutional network. , the output is the measurement vector in the Koopman invariant subspace .

[0018] As a preferred embodiment of the first aspect, the decoder is implemented by a multi-layer perceptron, and its input is the evolution result under the Koopman invariant subspace. The output is the PM corresponding to all monitoring stations in the prediction window. 2.5 Time series.

[0019] As a preferred embodiment of the first aspect, in each prediction branch, the global Koopman operator is a learnable matrix shared among all prediction branches, the local Koopman operator The multi-layer perceptron with learnable parameters is mapped based on the two-dimensional time series data structure of the current prediction branch input, and the global Koopman operator is used to and the local Koopman operator Koopman operator formed by superposition The measurement vector When the evolution is performed, the evolution result is ,in Koopman operator The power of.

[0020] As a preferred embodiment of the first aspect, the PM 2.5 The spatiotemporal prediction model is pre-trained on the training dataset, and the total loss function used in the training is obtained by weighting the reconstruction loss of the decoder, the prediction loss of the history window, and the prediction loss of the prediction window.

[0021] In a second aspect, the present invention provides a global and local Koopman PM 2.5 A prediction system comprising:

[0022] Data preprocessing module is used to obtain the historical PM of each monitoring station in the target area. 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in the form of a matrix;

[0023] A sequence two-dimensional reshaping module is used to transform the one-dimensional time series data structure from the time domain to the frequency domain through fast Fourier transform, select multiple characteristic frequencies based on the amplitude of the frequency component and determine the period length corresponding to each characteristic frequency, so as to reshape each one-dimensional time series in the one-dimensional time series data structure into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure;

[0024] The spatiotemporal prediction module is used to transform all k feature frequencies The corresponding two-dimensional time series data structure input consists of a PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector Evolution, evolution results The input is reconstructed in the decoder with self-attention mechanism to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

[0025] In a third aspect, the present invention provides a computer electronic device, characterized in that it includes a memory and a processor;

[0026] The memory is used to store computer programs;

[0027] The processor is used to implement the global and local Koopman PM as described in any one of the first aspects above when executing the computer program. 2.5 Prediction method.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention proposes a PM that combines global and local Koopman operators. 2.5 Spatiotemporal multi-step prediction method. This method takes PM into account 2.5 Temporal periodicity and spatial correlation of concentration. In terms of time, global and local Koopman networks are used to capture inter-cycle changes, and self-attention mechanisms are used to represent intra-cycle changes. In terms of space, an adaptive graph convolutional network is used to automatically capture PM 2.5 The spatial properties between the concentration monitoring sites. 2.5 The research and application of spatiotemporal prediction are of great significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 PM for global and local Koopman 2.5Schematic diagram of the steps of the prediction method;

[0031] Figure 2 For PM 2.5 Schematic diagram of the structure of the spatiotemporal prediction model;

[0032] Figure 3 This is the internal processing flow chart of the adaptive graph convolutional network;

[0033] Figure 4 PM for global and local Koopman 2.5 Schematic diagram of the module composition of the prediction system;

[0034] Figure 5 Schematic diagram of the structure of a computer electronic device in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0036] like Figure 1 As shown, in a preferred embodiment of the present invention, a global and local Koopman PM is provided. 2.5 The prediction method includes the following steps S1 to S6. The specific implementation of steps S1 to S6 is described in detail below.

[0037] S1. Obtain the historical PM of each monitoring station in the target area 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in matrix form.

[0038] It should be noted that the above historical PM 2.5 Monitoring data is collected by recording the PM 2.5 PM recorded by monitoring stations 2.5 Monitoring data. These raw data need to be preprocessed to meet the subsequent model input requirements. The key to data processing is time series encoding and data completion operations, both of which belong to existing technologies. Time series encoding is to convert historical PM 2.5The monitoring data are arranged in chronological order to form a one-dimensional time series. The PM 2.5 The concentration value is taken as a data point in the time series. The data completion operation needs to complete the missing data points in the original data to keep the entire time series continuous.

[0039] In an embodiment of the present invention, the specific implementation method of the above step S1 is as follows:

[0040] Get the historical PM of each monitoring station in the target area 2.5 After monitoring the data, the historical PM of each monitoring station is 2.5 The monitoring data is encoded in time series format to obtain the PM corresponding to each monitoring station. 2.5 Concentration time series and calculation of PM 2.5 Missing rate of concentration time series data, excluding PM 2.5 The PM concentration time series of the monitoring stations with missing data exceeding the threshold are then interpolated using the linear interpolation method for the remaining monitoring stations. 2.5 The concentration time series is completed, and each monitoring station obtains the time length Continuous PM in the range 2.5 The concentration time series, as the one-dimensional time series above.

[0041] In the present invention, the data missing rate can be defined as: Data missing rate = PM 2.5 Historical PM values ​​missing in the concentration time series (values ​​of nan represent missing values) 2.5 Number of monitoring data / PM 2.5 The historical PM contained in the concentration time series 2.5 The total number of monitoring data × 100%. Some monitoring sites are eliminated based on the judgment condition that the data missing rate of pollutants at the monitoring sites exceeds the threshold. The specific threshold can be optimized according to the actual data situation.

[0042] It should be noted that the above target area refers to the area that needs to be predicted in the present invention, which can be selected according to actual conditions. For example, PM2.5 in China can be obtained. 2.5 Monitoring site data, including site name, site longitude, site latitude, and PM 2.5 Monitor concentration information with a time granularity of hours. Perform various operations on raw data preprocessing, and perform data processing and analysis based on Python scripts or other automated data processing methods.

[0043] S2. By means of a fast Fourier transform (FFT), the one-dimensional time series data structure is transformed from the time domain to the frequency domain, a plurality of characteristic frequencies are selected based on the amplitude of the frequency component and the period length corresponding to each characteristic frequency is determined, so that each one-dimensional time series in the one-dimensional time series data structure is reshaped into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure;

[0044] It should be noted that for each station, the corresponding one-dimensional time series Is one-dimensional, satisfying , but the one-dimensional time series data structure consists of the one-dimensional time series of all N monitoring stations is in matrix form, satisfying . Each one-dimensional time series has a characteristic frequency The corresponding cycle length Reshape the obtained two-dimensional time series It is also in matrix form, satisfying , but the two-dimensional time series of all N monitoring stations Two-dimensional time series data structure composed of It is a 3D tensor, satisfying Therefore, the one-dimensional time series data structure in the present invention is , two-dimensional time series data structure The "one-dimensional" and "two-dimensional" mentioned in the text are actually defined for a single site, not for all sites globally.

[0045] In an embodiment of the present invention, the specific implementation sub-steps of the above step S2 are as follows:

[0046] S21, the one-dimensional time series data structure Perform fast Fourier transform along the time series direction (i.e., the column direction of the matrix) to obtain a The frequency component matrix of the same dimension is obtained, and the amplitude of each frequency component in the transformed frequency component matrix is ​​taken. The average amplitude of all frequency components is calculated along the site direction (that is, the row direction of the matrix, the average is taken within the row), and the average amplitude of each frequency component at all sites is obtained. The average amplitude of all sites is recorded as . Sort the average amplitudes of all frequency components and take the first k frequency components with the largest average amplitudes The corresponding frequency , these selected frequencies can be used as characteristic frequencies , .

[0047] S22, for each characteristic frequency , the length of the one-dimensional time series Divide by the characteristic frequency Get the corresponding period length , so the characteristic frequency Corresponds to Cycle length . The above one-dimensional time series data structure Each one-dimensional time series in Reshape to period length is the number of rows with characteristic frequency A two-dimensional time series with the number of columns Finally, the two-dimensional time series of all N monitoring stations The characteristic frequency The corresponding two-dimensional time series data structure in the form of a three-dimensional tensor .

[0048] The above one-dimensional time series data structure Convert to a two-dimensional time series data structure The process can be realized by the Reshape function, which is expressed as ,in and Respectively The number of rows and columns. After the cycle length The columns and rows represent the lengths of the corresponding cycles. The intra-cycle and inter-cycle changes below. Can be expanded to:

[0049]

[0050] in, The PM of the ith PM at all N monitoring stations 2.5 Monitoring value composition, .

[0051] According to the selected k characteristic frequencies and cycle lengths, each one-dimensional time series data structure You can get k two-dimensional time series data structures , these tensors represent the reshaped outputs of different cycle lengths Different two-dimensional time changes can more comprehensively reflect the changing laws under different periods.

[0052] It should be noted that the above characteristic frequency The number k is an optimizable hyperparameter. In the embodiment of the present invention, the optimal value is 4.

[0053] S3, all k characteristic frequencies Corresponding two-dimensional time series data structure Input PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, And k prediction branches one by one, each Only one prediction branch is input. Each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector Evolution, evolution results The input is reconstructed in the decoder with self-attention mechanism to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

[0054] The above PM 2.5 The structure of the spatiotemporal prediction model is as follows Figure 2 As shown in the figure, it contains k prediction branches with the same structure. Each prediction branch is composed of an adaptive graph convolutional network, an encoder, a Koopman operator evolution module, a decoder, a self-attention mechanism layer, and a weighted fusion layer cascaded in sequence. The basic internal processing flow is as described above. The detailed implementation of each module in each prediction branch is introduced below.

[0055] 1) Adaptive Graph Convolutional Network

[0056] like Figure 3As shown in Figure 1, the adaptive graph convolution network includes an adaptive graph relational network and a graph convolutional network (GCN), whose input is the two-dimensional time series data structure input in the current prediction branch. , and then pass through the adaptive graph relation network and graph convolution network to get the spatial information embedding .

[0057] In an adaptive graph relational network, a two-dimensional time series data structure for the current prediction branch of the input , it needs to be constructed as a graph with N monitoring sites as nodes , the node is characterized by Two-dimensional time series of each monitoring station Composition, and Figure It is also necessary to construct an adjacency matrix to map the connection strength or weight between nodes and reflect the degree of spatial relationship between nodes. In the present invention, the spatial distance between two monitoring sites can be calculated based on the latitude and longitude coordinates of the monitoring sites. , and then the Gaussian kernel function method is used based on the spatial distance between monitoring sites Construct the initial adjacency matrix. If we follow the conventional adjacency matrix construction method, Figure There are There are monitoring sites In order to avoid excessive number of edges, which will lead to redundancy of graph structure, the Gaussian kernel function method used in this invention sets a minimum threshold based on the traditional Gaussian kernel function method. , the weights directly calculated by the traditional Gaussian kernel function method do not exceed the minimum threshold Therefore, the minimum threshold is used Gaussian kernel function method to calculate the adjacency matrix The calculation formula of the weight between node i and node j is as follows:

[0058]

[0059] In the formula, is the distance between all spaces The standard deviation of

[0060] The above threshold Used to adjust the sparsity of the adjacency matrix. When it is close to 0, the mutual proximity between sites is strengthened and the adjacency matrix is ​​denser. When it is close to 1, the adjacency matrix becomes more sparse, which affects the expression of spatial dependencies. Element composition diagram The N×N dimensional adjacency matrix .

[0061] In the adaptive graph relational network, in addition to building the graph In addition, it is also necessary to use the temporal convolutional network (TCN) to input the two-dimensional time series data structure of the current prediction branch Extract the two-dimensional time series of each monitoring station The corresponding high-level representation vector , , and then the high-level representation vectors corresponding to all N monitoring sites Constructing a high-level representation matrix , the high-level representation matrix The conjugate transposed matrix of With the original matrix The product of is output by ReLU activation function and Softmax function in turn to obtain the adaptive adjacency matrix :

[0062]

[0063] In the formula, The spatial interdependence weights between time series can be obtained. and The activation function is used to process the weights. After these processes, the non-negativity of the weights is ensured and normalized, so that the spatial dependencies between different time series are more reasonable. It reflects the connections and dependencies between time series.

[0064] Therefore, in the above adaptive graph relationship network, the adjacency matrix between N monitoring sites is defined , and defines the adaptive adjacency matrix , these two adjacency matrices will be used in the subsequent graph convolutional network GCN to summarize and extract the spatial dependency information of the data, and finally generate a new data structure with spatial information.

[0065] In the graph convolutional network GCN, its input is the graph constructed in the above adaptive graph relation network And the adaptive adjacency matrix . Graph convolutional network (GCN) is a neural network model specially used to process graph structured data. Its specific principle belongs to the existing technology and can be implemented with reference to the existing technology. Traditional GCN is composed of multiple layers of graph convolution layers cascaded together. The core operation of GCN is to perform feature propagation and node update in each layer of graph convolution layer. Feature propagation refers to the transmission of feature information of a node to its neighboring nodes through the adjacency relationship of the graph. Node update refers to the linear transformation and nonlinear activation of the propagated features to update the feature representation of the node. In each layer of graph convolution layer of traditional GCN, the adjacency matrix during feature propagation often uses a standardized adjacency matrix (i.e., a normalized adjacency matrix). The standardized adjacency matrix is ​​usually obtained by adding a self-loop (i.e., the unit matrix I) to the original adjacency matrix A and performing degree matrix normalization.

[0066] In the graph convolution network GCN of the present invention, its basic principle is similar to that of the traditional graph convolution network GCN. Each graph convolution layer performs feature propagation and node update in each graph convolution layer based on the previous graph convolution layer. However, unlike the traditional GCN, the adjacency matrix of the graph convolution network GCN of the present invention during feature propagation is is the normalized adjacency matrix And the above adaptive adjacency matrix The sum of the normalized adjacency matrix From the initial adjacency matrix Add self-loops (i.e., identity matrices ) and then normalize the degree matrix. Therefore, the operation of each graph convolution layer is expressed by the formula:

[0067] )

[0068] Where: Define the adjacency matrix of the graph convolutional network GCN when performing feature propagation , the normalized adjacency matrix , yes The degree matrix of , , Adopting a minimum threshold in adaptive graph relational networks The initial adjacency matrix calculated by the Gaussian kernel function method , is the identity matrix as a self-loop; Indicates The input of the graph convolutional layer, Indicates The output of the graph convolutional layer, Indicates Layer Trainable parameter matrix of the graph convolutional layer.

[0069] If the graph convolutional network GCN of the present invention has L graph convolutional layers, the output of the last graph convolutional layer in the graph convolutional network is As an adaptive graph convolutional network from two-dimensional time series data structure The spatial information extracted from The computation in the entire adaptive graph convolutional network can be expressed as .

[0070] 2) Encoder

[0071] Encoder It is implemented using a multi-layer perceptron, whose input is the spatial information embedding extracted by an adaptive graph convolutional network. , the output is the measurement vector in the Koopman invariant subspace . Encoder The calculation performed in is expressed as .

[0072] 3) Koopman operator evolution module

[0073] Koopma operator measurement vector is infinite-dimensional, but can be solved by a finite-dimensional matrix To approximate the mapping, we can obtain a finite-dimensional Koopman operator invariant subspace. In other words, the Koopman operator is the propulsion measurement vector The optimal matrix of evolution. In order to simulate the cycle length Based on the dynamic evolution law in the Koopman space, the present invention uses global and local Koopman networks in the Koopman invariant subspace to capture the periodic information change characteristics in the row direction of the two-dimensional tensor. Used to learn shared information between data, local Koopman operator Used to capture local dynamic information within the data.

[0074] Koopman Operator in Koopman Invariant Subspace By the learnable global Koopman operator and learnable local Koopman operators In an embodiment of the present invention, the global Koopman operator is a preset learnable matrix, and is shared among all prediction branches and is used to learn common trends and behaviors between samples. The local Koopman operator The parameter-learnable multilayer perceptron is mapped based on the two-dimensional time series data structure of the current prediction branch input, so it is not shared among all prediction branches. It is obtained by mapping the input data in each prediction branch, which can capture unique local dynamic features and learn the local information features of the data. It is used to calculate the local Koopman operator The multi-layer perceptron also participates in PM 2.5 Training of spatiotemporal prediction models.

[0075] Therefore, in the Koopman operator evolution module, the Koopman operator is used The measurement vector The process of evolving and obtaining the evolution result can be expressed as ,in Koopman operator The power of Represents the Koopman operator of Power.

[0076] 4) Decoder

[0077] Decoder It is also implemented using a multilayer perceptron, whose input is the evolution result under the Koopman invariant subspace The output is the PM corresponding to all monitoring stations in the prediction window. 2.5 Time Series Decoder The calculation performed in is also expressed by the formula .

[0078] 5) Self-attention mechanism layer

[0079] The self-attention mechanism can capture the dependency between any two elements, and this dependency is not limited by the distance between the elements. Therefore, the present invention also uses the self-attention mechanism after the decoder to model the dynamic information changes between cycles in the column direction and capture the intrinsic correlation of time series data, so as to better understand and predict the changing trend of time series data. The processing in can be expressed as , where h is the length of the prediction window, represents the PM corresponding to all monitoring stations in the prediction window 2.5 Time series.

[0080] 6) Weighted Fusion Layer

[0081] Finally, the output of the self-attention mechanism layer in all k prediction branches is All inputs are weighted fusion layer for weighted fusion to get PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series prediction results, the calculation process of the prediction results is expressed as:

[0082]

[0083] The above fusion weight As an optimizable parameter, in the embodiment of the present invention, Activation function of CNN to learn fusion weights , used to control the weighted summation process.

[0084] Finally, it should be noted that S1 to S3 above describe PM 2.5 The calculation process of the spatiotemporal prediction model during inference, but the PM 2.5 Before the spatiotemporal prediction model is actually applied, it needs to be trained on the training data set in advance, and the total loss function used in the training is obtained by weighting the reconstruction loss of the decoder, the prediction loss of the history window, and the prediction loss of the prediction window. The total loss function can be expressed by the formula:

[0085] .

[0086] Above is the reconstruction loss of the decoder, so that the decoder The time series can be reconstructed from the measurement function, calculated as:

[0087]

[0088] In the formula, express The input value at the time, Indicates the length of the historical window at the current moment when the prediction is performed.

[0089] Above is the prediction loss of the historical window, making the global and local Koopman networks the most suitable propagation matrices within the historical window, and the calculation formula is:

[0090]

[0091]

[0092]

[0093] In the formula, Indicates frequency, Indicates The frequency division The input value at the time.

[0094] Above is the prediction loss of the prediction window, which is the final evaluation indicator for measuring the accuracy of the model. The calculation formula is:

[0095]

[0096] In the formula, represents the prediction window length, and Respectively The actual value and predicted value at the moment.

[0097] It should be noted that the time length of the above one-dimensional time series is is the size of the historical window required for subsequent model predictions, rather than the PM recorded at each monitoring station. 2.5 The total length of the monitoring data. Time length It is an optimizable hyperparameter and can be adjusted according to actual conditions. In practical applications, all PM 2.5 The most recent historical window is extracted from the monitoring data as the model input to predict the PM at future moments. 2.5 During the model training dataset construction phase, all PM records at each monitoring station can be 2.5 The monitoring data is processed into a one-dimensional continuous time series, and then the time series is divided into a series of time window, and randomly sample all time windows to construct the input of the training sample. After each sampled time window, data is extracted according to the predicted window size as the ground truth of the training sample. In order to ensure the progress of network training, the data set can be divided according to a preset ratio. For example, the total data set can be divided into a training set, a validation set, and a test set according to the ratio. The process of optimizing network parameters based on the total loss function belongs to the prior art, and the corresponding optimizer can be called to update the parameters.

[0098] It can be understood that the global and local Koopman PM described in S1~S3 above 2.5 The prediction method can actually be implemented through a computer program.

[0099] Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a global and local Koopman PM provided in the above embodiment. 2.5 Prediction method corresponds to a global and local Koopman PM 2.5 Prediction systems, such as Figure 4 As shown, it includes:

[0100] Data preprocessing module is used to obtain the historical PM of each monitoring station in the target area. 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in the form of a matrix;

[0101] A sequence two-dimensional reshaping module is used to transform the one-dimensional time series data structure from the time domain to the frequency domain through a fast Fourier transform (FFT), select multiple characteristic frequencies based on the amplitude of the frequency component and determine the period length corresponding to each characteristic frequency, so as to reshape each one-dimensional time series in the one-dimensional time series data structure into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure;

[0102] The spatiotemporal prediction module is used to transform all k feature frequencies The corresponding two-dimensional time series data structure input consists of a PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector Evolution, evolution results The input is reconstructed in the decoder with self-attention mechanism to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

[0103] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a global and local Koopman PM provided in the above embodiment. 2.5 A computer program product corresponding to the prediction method includes a computer program / instruction, which, when executed by a processor, can implement the global and local Koopman PM as described in the above embodiment. 2.5 Prediction method.

[0104] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a global and local Koopman PM provided in the above embodiment. 2.5 A computer electronic device corresponding to the prediction method, such as Figure 5 As shown, it includes a memory and a processor;

[0105] The memory is used to store computer programs;

[0106] The processor is used to implement the global and local Koopman PM in the above embodiment when executing the computer program. 2.5 Prediction method.

[0107] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention.

[0108] Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a global and local Koopman PM provided in the above embodiment. 2.5 A computer-readable storage medium corresponding to the prediction method, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the global and local Koopman PM in the above embodiment can be implemented. 2.5 Prediction method.

[0109] It is understandable that the above storage medium may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage. The storage medium may also be a U disk, a mobile hard disk, a magnetic disk or an optical disk, etc., which can store program codes.

[0110] It is understandable that the above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0111] It should also be noted that those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the system described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here. In the various embodiments provided in this application, the division of steps or modules in the system and method is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules or steps can be combined or integrated together, and a module or step can also be split.

[0112] In order to facilitate understanding of the technical effects of the present invention, the present invention further describes the global and local Koopman PMs described in S1 to S3 in the above embodiments. 2.5 The prediction method is applied to specific examples to demonstrate its effect.

[0113] Example

[0114] Below is the PM of Beijing, Tianjin and Hebei Province in the Beijing-Tianjin-Hebei region. 2.5 Monitoring data was used as the research object, and the hourly ground pollutant monitoring data from January 1, 2019 to December 31, 2021 was selected as the research object. Based on this data set, the global and local Koopman PM 2.5 The prediction method (hereinafter referred to as the present method) is used to perform PM 2.5The specific steps of spatiotemporal prediction are as described above and will not be repeated here. The following mainly shows its technical details and effects.

[0115] In this embodiment, in the data processing link corresponding to S1, the hourly PM data of national monitoring stations from January 2019 to December 2021 are first collected. 2.5 Concentration data, the data comes from the China National Environmental Monitoring Center (CNEMC, http: / / www.cnemc.cn / ). In the Beijing-Tianjin-Hebei region, data from 234 monitoring stations were extracted. To ensure the availability and accuracy of the data, the following preprocessing steps were performed on the data: 1) Delete monitoring stations that were suspended before December 31, 2021; 2) Delete monitoring stations with no data for 12 consecutive hours a day; 3) Delete monitoring stations with less than 28 days of monthly data coverage. After these processing, the missing data ratio was determined to be 1.74%. Then, the mean input method was used to fill in the 12 consecutive hours of PM 2.5 Missing data, this method is simple and effective, does not rely on any potential variables, and is suitable for processing a small amount of randomly distributed missing data. After data processing, 76 monitoring stations were finally selected as research objects, and the total length of the data sequence of each station was 25913 hours. 2.5 The data is split in chronological order with a ratio of 3:1:1: the first 60% (15548 hours) is used for the training set, the next 20% (5183 hours) is used for the validation set, and the last 20% (5183 hours) is used for the test set. The model is uniformly set to have a 24-hour input history step and a 12-hour prediction step. 2.5 Concentration data to predict PM in the next 12 hours 2.5 concentration.

[0116] Based on the data set obtained by the above processing, a two-dimensional time series data structure corresponding to the k characteristic frequencies of each data sample in the training set, validation set and test set is constructed with reference to the above step S2. In this embodiment, the value of k is 4. In addition, with reference to the above step S3, a PM consisting of k prediction branches is constructed. 2.5 The spatiotemporal prediction model is iteratively trained using the training set and the validation set until the model converges. 2.5 The prediction performance of the spatiotemporal prediction model was verified on the test set, and the mean absolute error MAE, root mean square error RMSE, Pearson correlation coefficient r, and fit index IA were selected as error evaluation indicators.

[0117] In addition, in order to verify the superiority of the method of the present invention (denoted as GLKN), several other spatiotemporal missing data completion methods in the prior art are used for comparison. The specific details of each method are as follows:

[0118] LSTM: LSTM is a deep learning method that is specifically designed to capture and process long-term temporal dependencies. By introducing memory cells, input gates, output gates, and forget gates, LSTM can dynamically manage the storage and update of information, thereby effectively avoiding the gradient vanishing problem that occurs in traditional RNNs when processing long sequence data. However, since the model cannot model spatial relationships, it is only applicable to single site time series prediction.

[0119] MLP: MLP is a feedforward neural network structure that consists of an input layer, multiple hidden layers, and an output layer. Each layer contains several neurons, and the neurons between adjacent layers are connected by weights, and nonlinear mapping is introduced through activation functions to enhance the network's expressiveness. However, since the MLP network mainly relies on fully connected layers, it is difficult to process PMs with spatial or spatiotemporal dependencies. 2.5 There are certain limitations when it comes to concentration data.

[0120] GCN: GCN is a deep learning model that processes graph-structured data. Its core idea is to aggregate feature information between nodes through graph convolution, thereby capturing the spatial dependencies between nodes. Each node in the graph represents a data point, and the edges between nodes represent the relationship between these data points. 2.5 During the forecast, GCN updates the characteristics of each station by aggregating data from surrounding monitoring stations, thereby better understanding the air quality patterns between different regions.

[0121] GC-LSTM: GC-LSTM is a spatiotemporal prediction model that combines the GCN network with the LSTM network. By combining these two network structures, PM can be better captured. 2.5 The GC-LSTM model takes into account the spatial and temporal dependencies in the concentration data, which makes it advantageous in applications that require processing both spatial and temporal information. 2.5 The spatiotemporal correlation of concentration data has high prediction accuracy.

[0122] STGCN: STGCN is a spatiotemporal prediction model that combines temporal convolution and spatial convolution. The model can effectively identify periodic patterns and trends in time series and capture PM by utilizing the GCN network. 2.5 Spatial dependence of concentrations between monitoring sites. 2.5 This combination enables the STGCN model to capture both PM 2.5 Local and global information on concentration, thus providing more accurate predictions

[0123] Finally, PM of different algorithms 2.5 The spatial and temporal prediction performances are shown in Table 1.

[0124] Table 1 Accuracy evaluation indicators of each model

[0125]

[0126] The comparison results of this embodiment show that the prediction model of the GLKN model of the present invention based on the global and local Koopman operators has a significant improvement in prediction accuracy compared with LSTM. Taking the first step prediction as an example, compared with the LSTM with the worst prediction accuracy, the RMSE of the GLKN model in the prediction of 1, 8 and 72 time steps is reduced by 41.8%, 50.6% and 51.5% respectively. Compared with the second best STGCN model, the IA, MAE, RMSE and r of the GLKN model are reduced by 27.8%, 30.9%, 29.6% and 1.6% on average.

[0127] The above-described embodiments are only some preferred implementations of the present invention, but are not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A Global and Local Koopman PM 2.5 The prediction method is characterized in that include: S1. Obtain the historical PM of each monitoring station in the target area 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in the form of a matrix; S2. By means of fast Fourier transform, the one-dimensional time series data structure is transformed from the time domain to the frequency domain, a plurality of characteristic frequencies are selected based on the amplitude of the frequency component and the period length corresponding to each characteristic frequency is determined, so that each one-dimensional time series in the one-dimensional time series data structure is reshaped into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure; S3, all k characteristic frequencies The corresponding two-dimensional time series data structure input consists of a PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector The evolution is performed, and the evolution result is input into the decoder with self-attention mechanism for reconstruction to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

2. Global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that In S1, the historical PM of each monitoring station in the target area is obtained. 2.5 After monitoring the data, the historical PM of each monitoring station is 2.5 The monitoring data is encoded in time series format to obtain the PM corresponding to each monitoring station. 2.5 Concentration time series and calculation of PM 2.5 Missing rate of concentration time series data, excluding PM 2.5 The PM concentration time series of the monitoring stations with missing data exceeding the threshold are then interpolated using the linear interpolation method for the remaining monitoring stations. 2.5 The concentration time series is completed, and each monitoring station obtains the time length Continuous PM in the range 2.5 The concentration time series, as the one-dimensional time series.

3. Global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that The specific implementation steps of S2 are: S21, perform fast Fourier transform on the one-dimensional time series data structure along the time series direction, take the amplitude of each frequency component obtained by the transformation, calculate the average value of the amplitudes of all frequency components along the station direction, and obtain the average amplitude of each frequency component at all stations; sort the average amplitudes of all frequency components, and take the frequencies corresponding to the k frequency components with the largest average amplitudes as the characteristic frequencies ; S22, for each characteristic frequency , the length of the one-dimensional time series Divide by the characteristic frequency Get the corresponding period length , reshape each one-dimensional time series in the one-dimensional time series data structure into a period length is the number of rows with characteristic frequency is a two-dimensional time series with the number of columns; finally, the two-dimensional time series of all N monitoring stations constitute the characteristic frequency The corresponding two-dimensional time series data structure in the form of a three-dimensional tensor.

4. Global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that The PM 2.5 In each prediction branch of the spatiotemporal prediction model, the adaptive graph convolution network includes an adaptive graph relation network and a graph convolution network; In the adaptive graph relationship network, for the two-dimensional time series data structure of the input current prediction branch, it is constructed into a graph with monitoring sites as nodes, and based on the spatial distance between the monitoring sites With minimum threshold The Gaussian kernel function method is used to construct the initial adjacency matrix, and the weights directly calculated by the Gaussian kernel function method do not exceed the minimum threshold At the same time, the high-level representation vector corresponding to the two-dimensional time series of each monitoring station is extracted from the two-dimensional time series data structure of the current prediction branch using the temporal convolutional network, and then the high-level representation matrix is ​​formed by the high-level representation vectors corresponding to all monitoring stations. The product of the conjugate transposed matrix of the high-level representation matrix and the original matrix is ​​successively output through the ReLU activation function and the Softmax function to obtain the adaptive adjacency matrix. The input of the graph convolution network is the graph constructed in the adaptive graph relational network and the adaptive adjacency matrix. The graph convolution network is composed of multiple layers of graph convolution layers cascaded together, and each layer of graph convolution layer performs feature propagation and node update on the basis of the previous layer of graph convolution layer. The adjacency matrix during feature propagation is the sum of the standardized adjacency matrix and the adaptive adjacency matrix. The standardized adjacency matrix is ​​obtained by adding the self-loop to the initial adjacency matrix and performing degree matrix normalization. The output of the last layer of graph convolution layer in the graph convolution network is used as the spatial information embedded in the adaptive graph convolution network extracted from the two-dimensional time series data structure. .

5. Global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that The encoder is implemented using a multi-layer perceptron, whose input is the spatial information embedded in the adaptive graph convolutional network. , the output is the measurement vector in the Koopman invariant subspace .

6. Global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that The decoder is implemented using a multi-layer perceptron, whose input is the evolution result under the Koopman invariant subspace, and whose output is the PM corresponding to all monitoring stations in the prediction window. 2.5 Time series.

7. The global and local Koopman's PM as claimed in claim 1 2.5 The prediction method is characterized in that In each prediction branch, the global Koopman operator is a learnable matrix shared among all prediction branches, the local Koopman operator The multi-layer perceptron with learnable parameters is mapped based on the two-dimensional time series data structure of the current prediction branch input, and the global Koopman operator is used to and the local Koopman operator Koopman operator formed by superposition The measurement vector When the evolution is performed, the evolution result is ,in Koopman operator The power of.

8. A Global and Local Koopman PM 2.5 The prediction system is characterized in that include: Data preprocessing module is used to obtain the historical PM of each monitoring station in the target area. 2.5 Monitoring data, and through time series encoding and data completion to form a length of The one-dimensional time series of N monitoring stations is a one-dimensional time series data structure in the form of a matrix; A sequence two-dimensional reshaping module is used to transform the one-dimensional time series data structure from the time domain to the frequency domain through fast Fourier transform, select multiple characteristic frequencies based on the amplitude of the frequency component and determine the period length corresponding to each characteristic frequency, so as to reshape each one-dimensional time series in the one-dimensional time series data structure into a two-dimensional time series according to each period length, so that the one-dimensional time series data structure is converted into a two-dimensional time series data structure in the form of a three-dimensional tensor, and each characteristic frequency obtains a corresponding two-dimensional time series data structure; The spatiotemporal prediction module is used to transform all k feature frequencies The corresponding two-dimensional time series data structure input consists of a PM consisting of k prediction branches 2.5 In the spatiotemporal prediction model, each prediction branch has a characteristic frequency The corresponding two-dimensional time series data structure is taken as input, and the spatial information is first extracted and embedded through an adaptive graph convolutional network. The adaptive graph convolutional network further integrates the adaptive adjacency matrix generated by the temporal convolutional network on the basis of the standardized adjacency matrix constructed according to the spatial distance of the sites, and then the encoder embeds the extracted spatial information into Mapping to the Koopman invariant subspace forms the measurement vector , in the Koopman invariant subspace, by the learnable global Koopman operator and learnable local Koopman operators Superposition forms the Koopman operator , and using the Koopman operator The measurement vector The evolution is performed, and the evolution result is input into the decoder with self-attention mechanism for reconstruction to obtain the PM corresponding to all monitoring sites in the prediction window. 2.5 The time series is used as the output of the current prediction branch; finally, the outputs of all prediction branches are weighted and fused to obtain PM 2.5 The final output of the spatiotemporal prediction model is the PM of all monitoring stations. 2.5 Time series forecasting results.

9. A computer electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is used to implement the global and local Koopman PM as claimed in any one of claims 1 to 7 when executing the computer program. 2.5 Prediction method.

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