Spatial adaptive multivariate time sequence prediction method fused with conditional random field
By integrating the conditional random field module in the spatiotemporal graph neural network, the dynamic evolution process of topological relationships between variables is explicitly modeled, and the problem that the spatiotemporal graph neural network cannot effectively capture the space-time dependence without physical topological structure or insufficient expression ability is solved, and effective capture and prediction of dynamic space-time dependence of multiple timings is achieved.
Patent Information
- Application Number
- CN202411821268.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-04-04
AI Technical Summary
The existing spatiotemporal graph neural networks cannot effectively capture spatiotemporal dependence in the absence of physical topology or insufficient expression capabilities, and most methods only consider static spatiotemporal dependence and cannot effectively deal with the dynamic spatial dependence problem of multiple timings.
The spatially adaptive multivariate timing prediction method of fusion conditional random fields is adopted to automatically learn the optimal topological structure through graph structure learning, and the conditional random field module is used to explicitly model the dynamic evolution process of topological relationships among variables to capture dynamic spatial dependence.
Effectively capture the dynamic spatiotemporal dependence of multiple time series, improving the accuracy and robustness of multi-time sequence prediction, especially in scenarios where physical topology or insufficient expression capabilities are lacking.
Smart Images
Figure CN119760308A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of time series prediction, and in particular to a spatially adaptive multivariate time series prediction method that integrates conditional random fields. Background Art
[0002] There are three main methods for multivariate time series prediction. First, traditional statistical methods include autoregressive integrated moving average (ARIMA) and seasonal decomposition model (SARIMA). These methods use historical data of time series to build models in the time dimension, assuming that there is a linear relationship between data points. Then, machine learning methods introduce higher flexibility to multivariate time series prediction. Algorithms such as support vector machine (SVM) and random forest (RF) can learn nonlinear features to improve prediction accuracy. Machine learning methods capture complex patterns from historical data through feature extraction and model training. Finally, deep learning methods have gradually become the mainstream of multivariate time series prediction in recent years. Recurrent neural networks (RNNs) represented by long short-term memory networks (LSTMs) and gated recurrent units (GRUs), time-domain convolutional networks (TCNs), and Transformers can effectively process the time dependency of sequence data and capture long-term and short-term dynamic features.
[0003] In order to simultaneously capture the dependencies of multivariate time series in the time and space dimensions, time series learning methods such as RNN, TCN, and Transformer are combined with graph neural networks (GNNs) specifically used to process graph structured data. The proposed Spatio-Temporal Graph Neural Network (STGNN) is currently an advanced method for multivariate time series prediction.
[0004] The main drawback of traditional statistical methods such as ARIMA and SARIMA is that they make linear assumptions about data and are difficult to handle complex nonlinear relationships. In addition, these methods have high requirements for the selection and setting of model parameters, which may lead to insufficient model fitting. Machine learning methods such as SVM and random forest, although they have stronger nonlinear modeling capabilities and can better learn dynamic change patterns in data, cannot handle high-dimensional data. At the same time, the performance of these methods is heavily dependent on feature engineering, which requires artificially constructing features based on expert experience. They usually require more training samples to ensure the generalization ability of the model and lack direct modeling of time dependency. Deep learning methods such as GRU and Transformer, although they perform well in capturing the dynamic characteristics of time series and have strong nonlinear learning capabilities, their training process requires a large amount of high-quality data and computing resources, and the model interpretability is poor. In addition, deep learning models are prone to overfitting problems in small sample conditions.
[0005] The deep spatiotemporal prediction model built based on the spatiotemporal graph neural network (STGNN) still has two problems when capturing complex dynamic spatiotemporal dependencies: the first is the problem of missing topological structure, that is, there is no physical topological structure for graph learning in some application scenarios; the second is the problem of dynamic spatial dependency, that is, the spatial dependency between variables changes over time. Summary of the invention
[0006] In response to the above technical problems, the present invention provides a spatially adaptive multivariate time series prediction method integrating conditional random fields.
[0007] The present invention is implemented by adopting the following technical scheme: a spatial adaptive multivariate time series prediction method based on a fused conditional random field, based on a spatial adaptive multivariate time series prediction model based on a fused conditional random field, explicitly models the dynamic evolution process of the topological relationship between variables over time, and captures dynamic spatial dependencies, specifically comprising the following steps:
[0008] Step S1: According to the graph structure learning, a topological structure A for performing graph convolution operation is obtained;
[0009] Step S2: Using the conditional modeling and global information processing capabilities of the conditional random field, a CRF conditional random field module is constructed based on the linear chain conditional random field model to capture dynamic spatial dependencies;
[0010] Step S3: Set the loss function, and deploy the spatial adaptive multivariate time series prediction model trained on the training data set to the actual production environment to predict the future situation of the multivariate time series.
[0011] Specifically, the spatially adaptive multivariate time series prediction model performs end-to-end optimization learning in a data-driven manner, and records the observation sequence of N system variables in the same system in the past T time steps as:
[0012]
[0013] in, is the observed value of N system variables at time step t;
[0014] Multivariate time series prediction is defined as predicting the sequence X of the next τ time steps based on the historical sequence observed in the past T time steps. T+1:T+τ , formally described as:
[0015]
[0016] Among them, f represents the prediction model, Θ represents all the parameters that need to be learned in the model, Represents the predicted value.
[0017] Specifically, the overall calculation of the spatial adaptive multivariate time series prediction model includes:
[0018] A=gl(E;Θ g );
[0019] r t =σ(x t ||B t-1 ]* A W r +b r );
[0020] u t =σ([x t ||B t-1 ]* A W u +b u );
[0021]
[0022]
[0023] B t =crf(h t ,A;Θ c );
[0024] Among them, A represents the adjacency matrix corresponding to the spatial topology graph obtained by the graph structure learning function gl(), and the parameter of graph structure learning is Θ g ;* A represents the graph convolution operation, r t and u t Respectively represent the reset gate and update gate in the GRU network, W r , W u and is the weight parameter that needs to be learned in the GRU unit, b r , b u and is the bias parameter that needs to be learned in the GRU network, and the parameters that need to be learned in the graph convolution and the parameters that need to be learned in the GRU network are represented as Θ st ; crf() function is used to embed static spacetime into h t Convert to B t , contains the evolution information of the topological structure of the current time step, thereby obtaining dynamic spatiotemporal embedding; the parameters that need to be learned by the CRF conditional random field module are expressed as Θ c ; || represents the feature vector concatenation operation, ⊙ represents the Hadamard product operation, and the activation function
[0025] Specifically, the calculation of the topological structure A in step S1 specifically includes the following steps:
[0026] Step S11: Assign learnable parameters to N variables, denoted as an embedding dictionary Feature vectors corresponding to N variables; for any two variables e i ∈ E and e j ∈ E, calculate the association strength s ij :
[0027]
[0028]
[0029] where m is a hyperparameter, representing m different semantic relationships; are weight parameters and bias parameters to be learned;
[0030] Step S12: Set a hyperparameter k. When the association strength is less than k, it is considered that there is no spatial association between two variables. That is, in the adjacency matrix A, when s ij ≥ k, A ij = s ij , when s ij < k, A ij = 0;
[0031] Step S13: After calculating the graph structure A, for the input feature x t at the current time step, capture spatial dependencies through the graph convolution operation * A . The calculation formula is:
[0032] * A (x t ) = (I N + softmax(A))x t W ＊ + b ＊ ;
[0033] where I N represents the identity matrix, softmax() is the activation function, W ＊ and b ＊ are weight and bias parameters to be learned.
[0034] Specifically, the steps for the CRF conditional random field module in step S2 to capture dynamic spatial dependencies are as follows:
[0035] Regard the target as N random variables, as the condition, and need to model the conditional probability p(B t |h t ), and maximize the conditional probability argmaxp(B t|h t ) to obtain dynamic spatiotemporal embedding;
[0036] The conditional random field that should be constructed is defined as:
[0037]
[0038] Among them, Z() represents the normalization factor and E() represents the energy function.
[0039] Specifically, the energy function includes a unary potential energy function ψ u () and the binary potential energy function ψ p (), the one-dimensional potential energy function ψ u () is defined as:
[0040]
[0041] The binary potential energy function ψ p () is defined as:
[0042]
[0043] Among them, τ ij Indicates the degree of disconnection between node i and its neighbor node j at the current time step, σ ip Indicates the degree of newly created connection between node i and its non-neighbor node p at the current time step;
[0044] Finally, the energy function in the conditional random field model is defined as:
[0045]
[0046] in, They represent the set of neighbor nodes and the set of non-neighbor nodes of node i respectively. α, β and γ are hyperparameters, which serve as balancing factors to adjust the importance of each part in the energy function. Their value range is [0,1], and α+β+γ=1.
[0047] Specifically, the solution to maximize the conditional probability is to define an approximate distribution Q(B t ) to replace the conditional probability distribution, and use the mean field theory to derive the optimal approximate distribution, including:
[0048] The approximate distribution Q(B t ) is considered as the product of N independent marginal distributions According to the mean field theory, the optimal approximation is solved by minimizing the KL divergence between the approximate distribution and the conditional probability distribution, which is described as:
[0049] min KL(Q(B t )||p(B t|h t ));
[0050] Best approximate distribution Substitute the energy function to obtain the marginal distribution for:
[0051]
[0052] By calculation And with the help of coordinate gradient descent optimization algorithm, the dynamic spatiotemporal embedding of node i is obtained The update formula is:
[0053]
[0054] Among them, the initial value
[0055] Specifically, it also includes:
[0056] Use two fully connected neural networks to update the disconnection degree τ in the formula ij and the degree of new connection σ ip Inferring, the calculation formula is:
[0057]
[0058] Will and The corresponding adjacency relations are respectively and It means that for all N nodes, the calculation formula of disconnection and new connection degree is expressed in matrix form as follows:
[0059]
[0060] For N variables in the system, the dynamic spatiotemporal embedding B at time step t t The calculation formula is:
[0061] B t =αh t -βτh t +γσh t ;
[0062] Get the hidden state h of the model output at the last time step of the historical sequence T Finally, a linear transformation layer is used to transform h T Map the output to the specified dimension to get the prediction result for the next τ time steps.
[0063] Specifically, the loss function in step S3 adopts the mean absolute error MAE loss, which is set as:
[0064]
[0065] where Θ = {Θ g ,Θ c ,Θ st} are all the parameters that need to be learned.
[0066] The beneficial effect of the present invention is that the existing spatiotemporal graph neural network cannot effectively capture spatiotemporal dependencies when the physical topological structure is missing or the expression ability is insufficient. To address this problem, the present invention designs an adaptive graph structure learning method to automatically learn the optimal topological structure from historical data sets. The single time series prediction method cannot capture the spatial dependencies of multivariate time series. Although the existing spatiotemporal graph neural network can model time and space dependencies at the same time, most methods only consider static spatiotemporal dependencies. To address the dynamic spatial dependency problem of multivariate time series, the present invention proposes a pluggable module based on conditional random fields for effectively modeling dynamic spatial associations, thereby obtaining a dynamic spatiotemporal embedding representation of multivariate time series for prediction. BRIEF DESCRIPTION OF THE DRAWINGS
[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.
[0068] Figure 1 This is a schematic diagram of the overall framework of the model in the embodiment of the present invention;
[0069] Figure 2 A schematic diagram of a GRU network unit with graph convolution in one embodiment of the present invention;
[0070] Figure 3 A schematic diagram of a map structure learning process in one embodiment of the present invention;
[0071] Figure 4 Schematic diagram of the CRF module calculation process in one embodiment of the present invention. DETAILED DESCRIPTION
[0072] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.
[0073] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.
[0074] The following is combined with Figures 1 to 4 , some embodiments of the present invention are described in detail. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.
[0075] The present invention proposes a spatial adaptive multivariate time series prediction method based on a fused conditional random field. Based on the spatial adaptive multivariate time series prediction model based on a fused conditional random field, the dynamic evolution process of the topological relationship between variables over time is explicitly modeled to capture dynamic spatial dependencies. Specifically, the method includes the following steps:
[0076] Step S1: According to the graph structure learning, a topological structure A for performing graph convolution operation is obtained;
[0077] Step S2: Using the conditional modeling and global information processing capabilities of the conditional random field, a CRF conditional random field module is constructed based on the linear chain conditional random field model to capture dynamic spatial dependencies;
[0078] Step S3: Set the loss function, and deploy the spatial adaptive multivariate time series prediction model trained on the training data set to the actual production environment to predict the future situation of the multivariate time series.
[0079] In one embodiment, the present invention considers capturing the dynamic spatiotemporal dependencies of multivariate time series, and proposes a spatially adaptive multivariate time series prediction model that integrates conditional random fields to achieve accurate prediction of the future development trend of multivariate time series. On the basis of the existing standard spatiotemporal graph neural network (STGNN), in order to solve the problem that the physical topological structure is missing or the expression ability is insufficient in some application fields, and it is difficult to effectively characterize the complex spatial associations between variables, this embodiment constructs a multi-semantic spatial structure adaptive learning module for automatically learning spatial relationships from training data; in order to solve the problem of dynamic spatial dependency, this embodiment utilizes the conditional modeling and global information processing capabilities of conditional random fields, and constructs a CRF conditional random field module (hereinafter collectively referred to as CRF module) based on the linear chain conditional random field model, which is used to explicitly model the dynamic evolution process of the topological relationship between variables over time, thereby capturing dynamic spatial dependencies. The multivariate time series prediction model proposed by the present invention can be optimized and learned end-to-end in a data-driven manner.
[0080] In this embodiment, the observation sequence of N system variables in the same system in the past T time steps is recorded as in is the observed value of N system variables at time step t. The multivariate time series prediction problem can be defined as predicting the sequence X of the next τ time steps based on the historical sequence observed in the past T time steps. T+1:T+τ , formally described as:
[0081]
[0082] Where f represents the prediction model, Θ represents all the parameters that need to be learned in the model, Represents the predicted value.
[0083] In this embodiment, the overall framework of the model is described as follows:
[0084] The overall framework of the model in this embodiment is as follows Figure 1 As shown, at the tth time step, the overall calculation process of the model is described as follows:
[0085] A=gl(E;Θ g )
[0086] r t =σ(x t ||B t-1 ]* A W r +b r )
[0087] u t =σ([x t ||B t-1 ]* A W u +b u )
[0088]
[0089]
[0090] B t =crf(h t ,A;Θ c )
[0091] Among them, A represents the adjacency matrix corresponding to the spatial topology graph obtained by the graph structure learning function gl(), and the parameter of graph structure learning is Θ g ;* A represents the graph convolution operation, r t and u t Respectively represent the reset gate and update gate in GRU, such as Figure 2 As shown, W r , W u , is the weight parameter that needs to be learned in the GRU unit, b r , bu , is the bias parameter to be learned in the GRU unit, and the parameters to be learned in the graph convolution and the parameters to be learned in the GRU are represented as Θ st ; crf() function is used to embed static spacetime into h t Convert to B t , contains the evolution information of the topological structure of the current time step, thereby obtaining dynamic spatiotemporal embedding. The parameters that the CRF module needs to learn are expressed as Θ c || represents the feature vector concatenation operation, ⊙ represents the Hadamard product operation, and the activation function
[0092] Graph structure learning (such as Figure 3 As shown), CRF module (as Figure 4 As shown in the figure), and the specific settings of model training are as follows.
[0093] Graph structure learning: The purpose of graph structure learning is to obtain the topological structure A for graph convolution operations. This embodiment first assigns learnable parameters to N variables, represented as an embedding dictionary The eigenvectors corresponding to N variables. For any two variables e i ∈E,e j ∈E, the correlation strength s between variables is calculated by the following formula ij :
[0094]
[0095]
[0096] Where m is a hyperparameter, representing m different semantic relationships. are the weight parameters and bias parameters that need to be learned. Considering that the coefficients of graph structures in most real applications are non-negative, the present invention sets a hyperparameter κ. When the correlation strength is less than κ, it is considered that there is no spatial correlation between the two variables, that is, in the adjacency matrix A, when s ij When ≥ k, A ij =s ij , when s ij <κ, A ij =0.
[0097] After the graph structure A is calculated, for the input feature x of the current time step t , through graph convolution operation* A The calculation formula to capture spatial dependence is:
[0098] * A (x t )=(I N +softmax(A))xt W ＊ +b ＊
[0099] Among them I N represents the identity matrix, softmax() is the activation function, W ＊ and b ＊ are the weights and bias parameters that need to be learned. In the present invention, the graph convolution operation is used to replace the matrix multiplication operation in the GRU network update gate and reset gate.
[0100] In this embodiment, the conditional random field module: the hidden state h obtained by the GRU unit at each time step t The static spatiotemporal dependency between multivariate sequences is captured. In order to capture the dynamic spatial dependency, the present invention designs a CRF module based on the conditional random field model to embed the static spatiotemporal dependency into h t Transform to dynamic spatiotemporal embedding B t The specific calculation process is described as follows:
[0101] The target Considered as N random variables, As a condition, we need to calculate the conditional probability p(B t |h t ) model, maximizing the conditional probability argmaxp(B t |h t ) to obtain dynamic spatiotemporal embedding, and the corresponding conditional random field is:
[0102]
[0103] Where Z() represents the normalization factor, and E() represents the energy function. How to define a suitable energy function and maximize the conditional probability solution are two problems that need to be solved. The solutions proposed by the present invention will be described in turn below.
[0104] In this embodiment, the energy function is defined as follows:
[0105] In the conditional random field model, the energy function usually consists of two parts: the unary potential energy function ψ u () and the binary potential energy function ψ p (), the former is used to measure the confidence of a single node annotation, and the latter is used to measure the correlation between the annotations of two nodes, thereby modeling the global dependency.
[0106] In the present invention, the designed one-dimensional potential energy function is as follows:
[0107]
[0108] Minimizing this function can make the distance between the target spatiotemporal embedding and the original static spatiotemporal embedding as small as possible and keep them similar, thereby retaining the learned static spatiotemporal dependencies to the greatest extent and avoiding model forgetting.
[0109] In the present invention, the designed binary potential energy function is as follows:
[0110]
[0111] Among them, τ ij Indicates the degree of disconnection between node i and its neighbor node j at the current time step, σ ip Represents the degree of newly established connection between node i and its non-neighbor node p at the current time step. Minimizing this binary potential energy function enables the target spatiotemporal embedding to characterize the changing process of the connection relationship between nodes, thereby capturing dynamic spatial dependencies.
[0112] After defining the one-dimensional potential energy function and the two-dimensional potential energy function, we can get the energy function in the conditional random field model:
[0113]
[0114] in They represent the neighbor node set and non-neighbor node set of node i respectively. α, β, and γ are hyperparameters, which serve as balancing factors to adjust the importance of each part in the energy function. Their value range is [0,1], and α+β+γ=1.
[0115] In this embodiment, the conditional probability is solved as follows:
[0116] In the conditional random field model, since the normalization factor is difficult to solve, it leads to the direct maximization of the conditional probability argmaxp(B t |h t ) to solve the target spatiotemporal embedding B t Very difficult. The current effective solution to this problem is to define an approximate distribution Q(B t ) to replace the conditional probability distribution, and then use the mean field theory to find the optimal approximate distribution. Specifically, the approximate distribution Q(B t ) is considered as the product of N independent marginal distributions According to the mean field theory, the optimal approximation can be solved by minimizing the KL divergence between the approximate distribution and the conditional probability distribution, which is formally described as:
[0117] min KL(Q(B t )||p(B t |h t ))
[0118] Best approximate distribution Substituting the energy function into the equation, we can get the marginal distribution for:
[0119]
[0120] By calculation Can get The calculation formula is:
[0121]
[0122] With the help of the coordinate gradient descent optimization algorithm, the dynamic spatiotemporal embedding of node i can be further obtained The update formula is:
[0123]
[0124] The initial value
[0125] For the disconnection degree τ in the update formula ij and the degree of new connection σ ip , the present invention uses two fully connected neural networks to perform inference respectively, and the calculation formula is:
[0126]
[0127]
[0128] Will and The corresponding adjacency relations are respectively and Indicates that, for all N nodes, the calculation formula for the degree of disconnection and new connection is expressed in matrix form as:
[0129]
[0130] All parameters Θ that need to be learned in the CRF module c = {W τ ,W σ ,b τ ,b σ For N variables in the system, the dynamic spatiotemporal embedding B at time step t t The calculation formula is:
[0131] B t =αh t -βτh t +γσh t
[0132] In this embodiment, the hidden state h output by the model at the last time step of the historical sequence is obtained. TAfter that, a linear transformation layer is used to transform h T Map the output to the specified dimension to get the prediction result for the next τ time steps.
[0133] In this embodiment, the model training setting specifically includes: the loss function adopts the mean absolute error MAE loss, and the calculation formula is:
[0134]
[0135] where Θ = {Θ g ,Θ c ,Θ st} are all the parameters that need to be learned. The optimizer uses the currently popular Adam optimizer, the learning rate is set to 0.0003, the maximum number of iterations is set to 200, the early-stop technology can be used to end the training early, and the number of waiting times is set to 10. The number of hidden layer neurons of all neural networks is set to 64. The dimension of the embedding dictionary E is set to D = 10, the multi-semantic relationship during graph structure learning is set to m = 5, the threshold τ = 0.35, and the balance factor in the energy function is set to α = 0.60, β = 0.20, γ = 0.20. The model trained on the training data set can be deployed in the actual production environment to predict the future situation of multivariate time series.
[0136] The overall framework of the spatial structure adaptive deep spatiotemporal prediction model that integrates conditional random fields proposed in the present invention can be optimized and learned end-to-end in a data-driven manner.
[0137] The proposed adaptive graph structure learning method enables the model to automatically learn the semantically rich associations between variables from the data.
[0138] The proposed CRF module based on conditional random fields is used to capture dynamic spatial dependencies and can be used as a pluggable module in any spatiotemporal graph neural network.
[0139] For the aforementioned embodiments, for the sake of simplicity, they are all described as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the order of the actions described, because according to the present application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily required by the present application.
[0140] The above embodiments describe the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the changes and modifications made by those skilled in the art shall be within the scope of protection of the appended claims of the present invention without departing from the spirit and scope of the present invention.
Claims
1. A spatially adaptive multivariate time series prediction method integrating conditional random fields, characterized in that: Based on the spatial adaptive multivariate time series prediction model fused with conditional random fields, the dynamic evolution process of the topological relationship between variables over time is explicitly modeled to capture dynamic spatial dependencies. Specifically, the following steps are included: Step S1: According to the graph structure learning, a topological structure A for performing graph convolution operation is obtained; Step S2: Using the conditional modeling and global information processing capabilities of the conditional random field, a CRF conditional random field module is constructed based on the linear chain conditional random field model to capture dynamic spatial dependencies; Step S3: Set the loss function, and deploy the spatial adaptive multivariate time series prediction model trained on the training data set to the actual production environment to predict the future situation of the multivariate time series.
2. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 1, characterized in that: The spatial adaptive multivariate time series prediction model performs end-to-end optimization learning in a data-driven manner, and records the observation sequence of N system variables in the same system in the past T time steps as: in, is the observed value of N system variables at time step t; Multivariate time series prediction is defined as predicting the sequence X of the next τ time steps based on the historical sequence observed in the past T time steps. T+1:T+τ , formally described as: Among them, f represents the prediction model, Θ represents all the parameters that need to be learned in the model, Represents the predicted value.
3. The spatially adaptive multivariate time series prediction method of fusion conditional random fields according to claim 2, characterized in that: The overall calculation of the spatial adaptive multivariate time series prediction model includes: A=gl(E;Θ g ): r t =σ(x t ||B t-1 ]★ A W r +b r ); you t =σ([x t ||B t-1 ]★ A W u +b u ); B t =crf(h t ,A;Θ c ); Among them, A represents the adjacency matrix corresponding to the spatial topology graph obtained by the graph structure learning function gl(), and the parameter of graph structure learning is Θ g ;★ A represents the graph convolution operation, r t and u t Respectively represent the reset gate and update gate in the GRU network, W r , W u and is the weight parameter that needs to be learned in the GRU unit, b r , b u and is the bias parameter that needs to be learned in the GRU network, and the parameters that need to be learned in the graph convolution and the parameters that need to be learned in the GRU network are represented as Θ st ; crf() function is used to embed static spacetime into h t Convert to B t , contains the evolution information of the topological structure of the current time step, thereby obtaining dynamic spatiotemporal embedding; the parameters that need to be learned by the CRF conditional random field module are expressed as Θ c ; || represents the feature vector concatenation operation, ⊙ represents the Hadamard product operation, and the activation function 4. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 3, characterized in that: The calculation of the topological structure A in step S1 specifically includes the following steps: Step S11: Assign learnable parameters to N variables, represented as an embedding dictionary The eigenvector corresponding to N variables; for any two variables e i ∈E and e j ∈E, calculate the correlation strength s between variables ij : Among them, m is a hyperparameter, representing m different semantic relationships; are the weight parameters and bias parameters that need to be learned; Step S12: Set a hyperparameter k. When the association strength is less than k, it is considered that there is no spatial association between two variables. That is, in the adjacency matrix A, when s ij ≥k, A ij = s ij , and when s ij <k, A ij = 0; Step S13: After the graph structure A is calculated, the input feature x of the current time step t , through graph convolution operation★ A Capturing spatial dependency, the calculation formula is: ★ A (x t )=(I N +softmax(A))x t W ★ +b ★ ; Among them, I N represents the identity matrix, softmax() is the activation function, W ★ and b ★ are the weights and bias parameters that need to be learned.
5. The spatially adaptive multivariate time series prediction method of fusion conditional random fields according to claim 4, characterized in that: The CRF conditional random field module in step S2 captures dynamic spatial dependencies and specifically includes the following steps: The target Considered as N random variables, As a condition, we need to calculate the conditional probability p(B t |h t ) model, maximizing the conditional probability argmax p(B t |h t ) to obtain dynamic spatiotemporal embedding; The conditional random field that should be constructed is defined as: Among them, Z() represents the normalization factor and E() represents the energy function.
6. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 5, characterized in that: The energy function includes a one-dimensional potential energy function ψ u () and the binary potential energy function ψ p (), the one-dimensional potential energy function ψ u () is defined as: The binary potential energy function ψ p () is defined as: Among them, τ ij Indicates the degree of disconnection between node i and its neighbor node j at the current time step, σ ip Indicates the degree of newly created connection between node i and its non-neighbor node p at the current time step; Finally, the energy function in the conditional random field model is defined as: in, They represent the set of neighbor nodes and the set of non-neighbor nodes of node i respectively. Δ, β and γ are hyperparameters, which serve as balancing factors to adjust the importance of each part in the energy function. Their value range is [0,1], and α+β+γ=1.
7. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 6, characterized in that: The solution to maximize the conditional probability is to define an approximate distribution Q(B t ) to replace the conditional probability distribution, and use the mean field theory to derive the optimal approximate distribution, including: The approximate distribution Q(B t ) is considered as the product of N independent marginal distributions According to the mean field theory, the optimal approximation is solved by minimizing the KL divergence between the approximate distribution and the conditional probability distribution, which is described as: min KL(Q(B t )||p(B t |h t )); Best approximate distribution Substitute the energy function to obtain the marginal distribution for: By calculation And with the help of coordinate gradient descent optimization algorithm, the dynamic spatiotemporal embedding of node i is obtained The update formula is: Among them, the initial value 8. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 7, characterized in that: Also includes: Use two fully connected neural networks to update the disconnection degree τ in the formula ij and the degree of new connection σ ip Inferring, the calculation formula is: Will and The corresponding adjacency relations are respectively and It means that for all N nodes, the calculation formula of disconnection and new connection degree is expressed in matrix form as follows: For N variables in the system, the dynamic spatiotemporal embedding B at time step t t The calculation formula is: B t =ah t -bth t +gσh t ; Get the hidden state h of the model output at the last time step of the historical sequence T Finally, a linear transformation layer is used to transform h T Map the output to the specified dimension to get the prediction result for the next τ time steps.
9. The spatially adaptive multivariate time series prediction method of fused conditional random fields according to claim 8, characterized in that: The loss function of step S3 adopts the mean absolute error MAE loss, which is set as: where Θ = {Θ g ,Θ c ,Θ st } are all the parameters that need to be learned.