Irregular multivariate time series prediction method based on spatio-temporal graph convolutional neural network

Abstract

The application provides a non-regular multivariate time series prediction method based on a space-time graph convolutional neural network, which comprises the following steps: mapping non-regular observation into structured patch features through a learnable continuous-time encoder; enhancing the robustness to space-time drift by extracting amplitude spectrum to suppress phase drift; constructing a decoupled dynamic-static graph learning mechanism to model evolution time series dependence and stable spatial topology respectively; adopting a dynamic-static graph convolutional layer to perform information propagation and hierarchical aggregation; and realizing prediction at any future time point by using a continuous-time decoder. The application can effectively decouple complex space-time dependence, explicitly alleviate the space-time drift problem caused by non-uniform sampling and baseline offset, and significantly improve the prediction accuracy and robustness of the model on non-regular multivariate time series data.

Description

Technical Field

[0001] This invention relates to the field of time series prediction technology, and in particular to an irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural networks. Background Technology

[0002] Irregular multivariate time series data are widely found in fields such as medical monitoring, industrial sensing, and meteorological recording. Their characteristics include uneven sampling intervals, high data missing rates, and asynchronous multivariate sampling. Traditional time series forecasting methods (such as recurrent neural networks and Transformers) typically assume uniform data sampling, making them difficult to apply directly to IMTS (Instantaneous Time Series Forecasting). Existing methods, such as Neural ODEs, can handle continuous-time dynamics, but their computational complexity is high; while attention-based methods improve parallel efficiency, they still struggle to effectively model the spatiotemporal drift problem.

[0003] Spatiotemporal drift manifests as temporal misalignment and baseline drift, causing traditional temporal similarity metrics to fail and consequently affecting the model's ability to capture intrinsic temporal dependencies. Existing graph neural network methods typically couple static spatial topology with dynamic temporal dependencies within the same graph, resulting in entangled spatiotemporal features and making it difficult to model complex spatiotemporal interactions.

[0004] Therefore, there is a need to propose a multivariate time series prediction method that can explicitly decouple spatiotemporal dependencies, effectively suppress spatiotemporal drift, and is applicable to irregular sampling. Summary of the Invention

[0005] In view of the above situation, the main objective of this invention is to propose an irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural networks to solve the above-mentioned technical problems.

[0006] This invention proposes an irregular multivariate time series prediction method based on a spatiotemporal graph convolutional neural network, the method comprising the following steps:

[0007] Step 1: Map the irregular observation set to a structured representation using a learnable continuous-time embedding function, and perform local irregularity aggregation to obtain a patch-level feature tensor;

[0008] Step 2: Extract the amplitude spectrum of the patch-level feature tensor and calculate the similarity to obtain the spectral similarity matrix;

[0009] Step 3: Construct decoupled dynamic graph learning mechanism and static graph learning mechanism, respectively model the temporal dependency relationship and stable spatial topological relationship in the evolution patch-level feature tensor and spectral similarity matrix, so as to obtain dynamic adjacency matrix and static adjacency matrix;

[0010] Step 4: Use a multi-layer dynamic-static graph convolutional network to propagate spatiotemporal information between the dynamic adjacency matrix and the static adjacency matrix, and adopt a hierarchical aggregation strategy to gradually reduce the temporal resolution in order to obtain the spatiotemporal features of deep encoding.

[0011] Step 5: For any given future query time point, use a learnable continuous temporal embedding function to map it into a temporal embedding, and fuse it with the deep encoded spatiotemporal features. Then, map it through a multilayer perceptron to obtain the time series prediction result.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] This invention effectively suppresses spatiotemporal drift caused by irregular sampling by extracting amplitude spectra, thereby improving the robustness of the model under baseline shift and temporal misalignment. Based on this, a decoupled dynamic-static graph learning mechanism is used to accurately model the evolution of temporal dependencies and the stability of spatial topology, respectively. The overall method achieves leading prediction performance on multiple irregular multivariate time series datasets.

[0014] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by means of embodiments of the invention. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the steps of an irregular multivariate time series prediction method based on a spatiotemporal graph convolutional neural network proposed in this invention.

[0016] Figure 2 This is a diagram illustrating the overall structure of an irregular multivariate time series prediction method based on a spatiotemporal graph convolutional neural network proposed in this invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to illustrate some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0019] Please see Figure 1This embodiment provides an irregular multivariate time series prediction method based on a spatiotemporal graph convolutional neural network, the method comprising the following steps:

[0020] Step 1: Use a learnable continuous-time embedding function to map the irregular observation set into a structured representation and perform local irregularity aggregation to obtain a patch-level feature tensor.

[0021] In step 1, the irregular observation set is mapped to a structured representation using a learnable continuous-time embedding function, and local irregularities are aggregated to obtain a patch-level feature tensor. This includes the following sub-steps:

[0022] A learnable continuous-time embedding function is used to map timestamps in an irregular observation set to obtain a time embedding. The irregular observation set includes timestamps, variable numbers, and observed values, and the following relationship exists in the mapping process:

[0023] ;

[0024] in, Indicates time embedding, Represents a timestamp. Indicates the index of the feature dimension, and ; Indicates the first feature dimension ( The corresponding learnable frequency parameters, Indicates the first feature dimension ( The corresponding learnable phase parameters, Represents the total feature dimension. Represents the sine function. This represents the learnable frequency parameter. This represents the learnable phase parameter;

[0025] Learnable embedding vectors are assigned to the variable numbers in the irregular observation set to obtain variable embeddings; the observed values ​​are mapped to numerical embeddings through a learnable linear transformation.

[0026] The initial hidden state is obtained by adding the temporal embedding, variable embedding, and numerical embedding. The following relationship exists in the corresponding process:

[0027] ;

[0028] in, This represents the initial hidden state. Indicates variable embedding, Indicates numerical embedding;

[0029] Based on the initial hidden state, the time axis is divided into The algorithm generates non-overlapping patches and employs a local aggregation layer based on relational graph attention to aggregate the non-uniformly distributed observation points within each patch to the central reference time point of the corresponding patch, thereby obtaining the patch-level feature tensor.

[0030] It should be noted that the initial hidden state This constitutes the set of hidden states corresponding to all observation points.

[0031] Step 2: Extract the amplitude spectrum of the patch-level feature tensor and calculate the similarity to obtain the spectral similarity matrix.

[0032] In step 2, the amplitude spectrum of the patch-level feature tensor is extracted and the similarity is calculated to obtain the spectral similarity matrix. This includes the following sub-steps:

[0033] The last dimension of the patch-level feature tensor is used as the patch feature vector, and a real-number fast Fourier transform is applied to convert it to the frequency domain to obtain the frequency domain complex features obtained through the real-number fast Fourier transform. The following relationship exists in the corresponding process:

[0034] ;

[0035] in, This represents the complex frequency domain characteristics obtained through the real-number fast Fourier transform. This indicates that the data has undergone a real-number Fast Fourier Transform. Represents the feature vector of the patch;

[0036] The amplitude spectrum is calculated based on the complex features in the frequency domain obtained by the real number fast Fourier transform, and then normalized to obtain the normalized amplitude spectrum. The following relationship exists in the corresponding process:

[0037] ;

[0038] in, This represents the normalized amplitude spectrum. This indicates that the data has been normalized.

[0039] The cosine similarity between each patch is calculated based on the normalized amplitude spectrum to obtain the spectral similarity matrix.

[0040] It should be noted that the amplitude spectrum is invariant to linear phase changes caused by time misalignment, thus effectively capturing waveform structural similarity and suppressing the influence of spatiotemporal drift.

[0041] Step 3: Construct decoupled dynamic graph learning mechanism and static graph learning mechanism, respectively model the temporal dependency relationship and stable spatial topological relationship in the evolution patch-level feature tensor and spectral similarity matrix, so as to obtain dynamic adjacency matrix and static adjacency matrix.

[0042] In step 3, a decoupled dynamic graph learning mechanism and a static graph learning mechanism are constructed to model the temporal dependencies and stable spatial topological relationships in the evolutionary patch-level feature tensor and the spectral similarity matrix, respectively, to obtain the dynamic adjacency matrix and the static adjacency matrix. This specifically includes the following sub-steps:

[0043] The explicit numerical correlation of patch-level feature tensors is calculated using a temporal self-attention mechanism to obtain a temporal correlation view. The following relationship exists in the corresponding process:

[0044] ;

[0045] in, Represents a time-related view. This indicates that the data has been processed using the Softmax function. Represents the patch-level feature tensor. and Both represent learnable projection matrices. Indicates matrix transpose. Indicates the dimension of the key vector;

[0046] A feedforward network with residual connections is used to extract the latent semantic context of patch-level feature tensors, and the implicit dependencies of the latent semantic context are calculated to obtain the semantic base view. The following relationship exists in the corresponding process:

[0047] ;

[0048] in, Represents the semantic base view, The latent semantic context representing the patch-level feature tensor. and Both represent learnable linear projection matrices;

[0049] By adaptively fusing the time-related view, semantic base view, and spectral similarity matrix using learnable gating parameters, a dynamic adjacency matrix is ​​obtained. The following relationship exists in the corresponding process:

[0050] ;

[0051] in, Represents a dynamic adjacency matrix. This indicates that the data has been processed using the ReLU function. This represents the learnable gating parameters. Represents the spectral similarity matrix;

[0052] A learnable node embedding matrix is ​​initialized, and the similarity between embeddings is calculated. Then, layer normalization is performed to obtain a static adjacency matrix. The following relationship exists in the corresponding process:

[0053] ;

[0054] in, Represents the static adjacency matrix. This indicates that the process has undergone layer normalization. Represents the learnable node embedding matrix;

[0055] A graph regularization loss function is constructed based on the static adjacency matrix to ensure the sparsity and smoothness of the graph. The following relationship exists in the corresponding process:

[0056] ;

[0057] in, This represents the graph regularization loss function. Indicates the total number of variables. Represents the th element in the static adjacency matrix Line number Column elements, This indicates taking the 2-norm. Indicates the first Learnable node embedding vectors of variables, Indicates the first Learnable node embedding vectors of variables, This represents a hyperparameter that controls the strength of the sparsity penalty. This represents the Frobenius Norm of the matrix.

[0058] Step 4: Use a multi-layer dynamic-static graph convolutional network to propagate spatiotemporal information between the dynamic adjacency matrix and the static adjacency matrix, and adopt a hierarchical aggregation strategy to gradually reduce the temporal resolution in order to obtain the spatiotemporal features of deep encoding.

[0059] In step 4, a multi-layer dynamic-static graph convolutional network is used to propagate spatiotemporal information between the dynamic adjacency matrix and the static adjacency matrix, and a hierarchical aggregation strategy is adopted to gradually reduce the temporal resolution in order to obtain the deep-encoded spatiotemporal features. Specifically, this includes the following sub-steps:

[0060] Construct a dynamic-static graph convolutional network with K layers; utilize the dynamic adjacency matrix to perform time-division operations. Information diffusion is performed to obtain intermediate features after diffusion along the time dimension. The following relationship exists in the corresponding process:

[0061] ;

[0062] in, This represents the intermediate features after diffusion over time. This refers to a multilayer perceptron used for fusing multi-order temporal features. Represents the dynamic adjacency matrix Power, used to simulate Information diffusion in the temporal neighborhood; Represents the input features of a dynamic-static graph convolutional network;

[0063] The intermediate features after time-diffusion are reshaped and then diffused along the static adjacency matrix to obtain the features after spatial-diffusion. The following relationship exists in the corresponding process:

[0064] ;

[0065] in, This represents the features resulting from the diffusion of spatial dimensions. This refers to a multilayer perceptron used for fusing multi-level spatial features. Represents the static adjacency matrix Power, used to simulate Information diffusion within the spatial neighborhood;

[0066] The features after spatial dimension diffusion are subjected to linear transformation and nonlinear activation, and residual connections are made with the input features of the dynamic-static graph convolutional network to obtain the deep encoded spatiotemporal features. The following relationship exists in the corresponding process:

[0067] ;

[0068] in, This represents the spatiotemporal characteristics of deep coding.

[0069] Step 5: For any given future query time point, use a learnable continuous temporal embedding function to map it to a temporal embedding, and fuse it with the deep encoded spatiotemporal features. Then, map it through a multilayer perceptron to obtain the time series prediction result; and optimize the model end-to-end by minimizing the composite loss function.

[0070] In step 5, for any given future query time point, a learnable continuous temporal embedding function is used to map it to a temporal embedding, which is then fused with the deep-encoded spatiotemporal features and mapped through a multilayer perceptron to obtain the time-series prediction result. The model is then optimized end-to-end by minimizing the composite loss function, specifically including the following sub-steps:

[0071] A learnable continuous-time embedding function is used to generate a time embedding for each future query time point;

[0072] The deep-encoded spatiotemporal features are broadcast along the time dimension to a number that aligns with the number of query time points, and then concatenated with the corresponding query time embeddings to obtain the concatenated features.

[0073] The concatenated features are mapped back to the original observation space through a multilayer perceptron to obtain the time-series prediction results of all variables at each query time point;

[0074] The mean squared error between the time series prediction results and the actual values ​​is calculated, and the mean squared error is weighted and summed with the graph regularization loss to obtain the total loss. The following relationship exists in the corresponding process:

[0075] ;

[0076] in, Indicates the total loss. This represents the mean squared error between the predicted and actual values. This represents the hyperparameter used to balance the weights of prediction error loss and graph regularization loss;

[0077] All learnable parameters in the model are optimized end-to-end using the backpropagation algorithm.

[0078] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0079] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0080] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0081] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A non-regular multivariate time series prediction method based on spatiotemporal graph convolutional neural networks, characterized in that, The method includes the following steps: Step 1: Map the irregular observation set to a structured representation using a learnable continuous-time embedding function, and perform local irregularity aggregation to obtain a patch-level feature tensor. This includes the following sub-steps: A learnable continuous-time embedding function is used to map timestamps in an irregular observation set to obtain a time embedding; the irregular observation set includes timestamps, variable numbers, and observation values. Learnable embedding vectors are assigned to the variable numbers in the irregular observation set to obtain the variable embeddings; The observed values ​​are mapped to numerical embeddings through a learnable linear transformation; The initial hidden state is obtained by combining the temporal embedding, variable embedding, and numerical embedding. The timeline is divided based on the initial hidden state. The system uses non-overlapping patches and employs a local aggregation layer based on relational graph attention to aggregate the non-uniformly distributed observation points within each patch to the central reference time point of the corresponding patch, in order to obtain the patch-level feature tensor. Step 2: Extract the amplitude spectrum of the patch-level feature tensor and calculate the similarity to obtain the spectral similarity matrix; Step 3: Construct decoupled dynamic graph learning mechanism and static graph learning mechanism, respectively model the temporal dependency relationship and stable spatial topological relationship in the evolution patch-level feature tensor and spectral similarity matrix, so as to obtain dynamic adjacency matrix and static adjacency matrix; Step 4: Use a multi-layer dynamic-static graph convolutional network to propagate spatiotemporal information between the dynamic adjacency matrix and the static adjacency matrix, and adopt a hierarchical aggregation strategy to gradually reduce the temporal resolution in order to obtain the spatiotemporal features of deep encoding. Step 5: For any given future query time point, use a learnable continuous temporal embedding function to map it into a temporal embedding, and then fuse it with the deep-encoded spatiotemporal features and map it through a multilayer perceptron to obtain the time series prediction result.

2. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 1, characterized in that, In the step of mapping timestamps in an irregular observation set using a learnable continuous-time embedding function to obtain the time embedding, the following relationship exists: ； in, Indicates time embedding, Represents a timestamp. Index representing the feature dimension This represents the learnable frequency parameter corresponding to the first feature dimension. This represents the learnable phase parameter corresponding to the first feature dimension. Represents the total feature dimension. Represents the sine function. This represents the learnable frequency parameter. This represents the learnable phase parameter; In the step of adding time embedding, variable embedding, and numerical embedding to obtain the initial hidden state, the following relationship exists: ； in, This represents the initial hidden state. Indicates variable embedding, This indicates numerical embedding.

3. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 2, characterized in that, In step 2, the amplitude spectrum of the patch-level feature tensor is extracted and the similarity is calculated to obtain the spectral similarity matrix. This specifically includes the following sub-steps: The last dimension of the patch-level feature tensor is used as the patch feature vector, and a real fast Fourier transform is applied to transform it to the frequency domain to obtain the frequency domain complex features obtained by the real fast Fourier transform. The amplitude spectrum is calculated based on the complex features in the frequency domain obtained by the real number fast Fourier transform, and then normalized to obtain the normalized amplitude spectrum. The cosine similarity between each patch is calculated based on the normalized amplitude spectrum to obtain the spectral similarity matrix.

4. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 3, characterized in that, In the step of taking the last dimension of the patch-level feature tensor as the patch feature vector and applying the real-number fast Fourier transform to convert it to the frequency domain to obtain the frequency domain complex features obtained by the real-number fast Fourier transform, the following relationship exists: ； in, This represents the complex frequency domain characteristics obtained through the real-number fast Fourier transform. This indicates that the data has undergone a real-number Fast Fourier Transform. Represents the feature vector of the patch; In the steps of calculating the amplitude spectrum based on the complex features in the frequency domain obtained by the real number fast Fourier transform, and then normalizing it to obtain the normalized amplitude spectrum, the following relationship exists: ； in, This represents the normalized amplitude spectrum. This indicates that the data has been normalized.

5. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 4, characterized in that, In step 3, a decoupled dynamic graph learning mechanism and a static graph learning mechanism are constructed to model the temporal dependencies and stable spatial topological relationships in the evolutionary patch-level feature tensor and the spectral similarity matrix, respectively, to obtain the dynamic adjacency matrix and the static adjacency matrix. Specifically, this includes the following sub-steps: The explicit numerical correlation of patch-level feature tensors is calculated using a temporal self-attention mechanism to obtain a temporal correlation view; A feedforward network with residual connections is used to extract the latent semantic context of patch-level feature tensors, and the implicit dependencies of the latent semantic context are computed to obtain a semantic base view. Learnable gating parameters are used to adaptively fuse time-related views, semantic base views, and spectral similarity matrices to obtain a dynamic adjacency matrix; Initialize a learnable node embedding matrix and calculate the similarity between embeddings, then perform layer normalization to obtain a static adjacency matrix; A graph regularization loss function is constructed based on the static adjacency matrix to ensure the sparsity and smoothness of the graph.

6. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 5, characterized in that, In the step of calculating the explicit numerical correlation of patch-level feature tensors using a temporal self-attention mechanism to obtain a temporal correlation view, the following relationship exists: ； in, Represents a time-related view. This indicates that the data has been processed using the Softmax function. Represents the patch-level feature tensor. and Both represent learnable projection matrices. Indicates matrix transpose. Indicates the dimension of the key vector; In the steps of extracting the latent semantic context of patch-level feature tensors using a feedforward network containing residual connections, and computing the implicit dependencies of the latent semantic context to obtain the semantic base view, the following relationship exists: ； in, Represents the semantic base view, The latent semantic context representing the patch-level feature tensor. and Both represent learnable linear projection matrices; In the step of adaptively fusing the time-related view, the semantic base view, and the spectral similarity matrix using learnable gating parameters to obtain the dynamic adjacency matrix, the following relationship exists: ； in, Represents a dynamic adjacency matrix. This indicates that the data has been processed using the ReLU function. This represents the learnable gating parameters. Represents the spectral similarity matrix; In the steps of initializing a learnable node embedding matrix, calculating the similarity between embeddings, and then performing layer normalization to obtain the static adjacency matrix, the following relationship exists: ； in, Represents the static adjacency matrix. This indicates that the process has undergone layer normalization. Represents the learnable node embedding matrix; In the step of constructing a graph regularization loss function based on a static adjacency matrix to ensure the sparsity and smoothness of the graph, the following relationship exists: ； in, This represents the graph regularization loss function. Indicates the total number of variables. Represents the th element in the static adjacency matrix Line number Column elements, This indicates taking the 2-norm. Indicates the first Learnable node embedding vectors of variables, Indicates the first Learnable node embedding vectors of variables, This represents a hyperparameter that controls the strength of the sparsity penalty. denoted as the Frobenius norm of the matrix.

7. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 6, characterized in that, In step 4, a multi-layer dynamic-static graph convolutional network is used to propagate spatiotemporal information between the dynamic adjacency matrix and the static adjacency matrix, and a hierarchical aggregation strategy is adopted to gradually reduce the temporal resolution in order to obtain the deep-encoded spatiotemporal features. Specifically, this includes the following sub-steps: Construct a dynamic-static graph convolutional network with K layers; utilize the dynamic adjacency matrix to perform time-division operations. Information diffusion is performed to obtain intermediate features after diffusion in the time dimension; The intermediate features after diffusion in the time dimension are reshaped and then diffused along the static adjacency matrix to obtain the features after diffusion in the spatial dimension. The features after spatial dimension diffusion are subjected to linear transformation and nonlinear activation, and residual connections are made with the input features of the dynamic-static graph convolutional network to obtain the deep-encoded spatiotemporal features.

8. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 7, characterized in that, We construct a dynamic-static graph convolutional network with K layers; and utilize the dynamic adjacency matrix to perform time-dimensional operations. In the step of information diffusion to obtain intermediate features after diffusion along the time dimension, the following relationship exists: ； in, This represents the intermediate features after diffusion over time. This refers to a multilayer perceptron used for fusing multi-order temporal features. Represents the dynamic adjacency matrix Power of 1 Represents the input features of a dynamic-static graph convolutional network; In the step of reshaping the intermediate features after time-diffusion and then diffusing them along the static adjacency matrix to obtain the features after spatial-diffusion, the following relationship exists: ； in, This represents the features resulting from the diffusion of spatial dimensions. This refers to a multilayer perceptron used for fusing multi-level spatial features. Represents the static adjacency matrix Power of; In the steps of performing linear transformations and nonlinear activations on the features after spatial dimension diffusion, and then performing residual connections with the input features of a dynamic-static graph convolutional network to obtain the deep-encoded spatiotemporal features, the following relationship exists: ； in, This represents the spatiotemporal characteristics of deep coding.

9. The irregular multivariate time series prediction method based on spatiotemporal graph convolutional neural network according to claim 8, characterized in that, In step 5, for any given future query time point, a learnable continuous temporal embedding function is used to map it to a temporal embedding, which is then fused with deep-encoded spatiotemporal features and mapped through a multilayer perceptron to obtain the temporal prediction result. This specifically includes the following sub-steps: A learnable continuous-time embedding function is used to generate a time embedding for each future query time point; The deep-encoded spatiotemporal features are broadcast along the time dimension to a number that aligns with the number of query time points, and then concatenated with the corresponding query time embeddings to obtain the concatenated features. The concatenated features are mapped back to the original observation space through a multilayer perceptron to obtain the time-series prediction results of all variables at each query time point.

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