Multi-element time series prediction method based on prediction domain transformation and double-path fusion

Abstract

This invention discloses a multivariate time series forecasting method based on prediction domain transformation and dual-path fusion. A time series forecasting model, PDT, is proposed. It utilizes data-adaptive prediction domain transformation to project the time series onto the energy-concentrated optimal latent space for prediction. A dual-path architecture is designed to simultaneously achieve efficient extrapolation of dominant linear trends and capture complex nonlinear dynamics. A masked channel dependency strategy and a lightweight linear encoder are used to adaptively fusion and filter inter-variable dependencies and deeply extract intra-channel features, respectively. The proposed time series forecasting model significantly solves the problem of insufficient nonlinear expressive power of traditional linear models and enhances noise resistance and computational efficiency in high-dimensional multivariate scenarios, comprehensively improving the prediction accuracy and robustness of the model in multivariate time series forecasting tasks.

Description

Technical Field

[0001] This invention belongs to the field of time series forecasting and artificial intelligence technology, specifically relating to a multivariate time series forecasting method based on prediction domain transformation and dual-path fusion. Background Technology

[0002] Multivariate time series forecasting has significant applications in energy management, traffic flow control, and economic decision-making. Real-world systems are typically characterized by the co-evolution of multiple coupled variables, making multivariate time series forecasting more challenging than univariate forecasting.

[0003] Existing mainstream methods for multivariate time series forecasting mainly include Transformer-based models and linear layer-based models. While Transformer-based models possess global modeling capabilities, they suffer from high computational complexity and are prone to overfitting. Linear layer-based models (such as DLinear), while efficient, struggle to capture complex nonlinear dynamics. To overcome the bottleneck of time-domain modeling, existing techniques attempt to introduce frequency-domain transforms (such as Fourier transforms or wavelet transforms) to map signals to a sparse representation space. However, these domain transform methods typically use fixed, data-independent basis functions (such as fixed sine waves), failing to adaptively adjust according to the statistical characteristics of specific datasets. This results in suboptimal feature representations and difficulty in maintaining universal high performance across datasets with varying characteristics. Furthermore, when handling inter-variable dependencies, existing channel-independent strategies ignore inter-variable information, while channel-dependent strategies are prone to introducing noise when processing high-dimensional data. Neither is the optimal strategy for fusing inter-variable dependencies.

[0004] To address the shortcomings of existing linear prediction models in nonlinear feature extraction and the lack of data adaptability and difficulty in capturing optimal prediction features in fixed-basis transformation methods, this invention proposes a novel multivariate time series prediction method. Summary of the Invention

[0005] The present invention adopts the following technical solution:

[0006] This invention proposes a multivariate time series prediction method based on predictive domain transformation and dual-path fusion. The method includes a predictive domain transformation (PDT) module, which comprises a predictive domain transformation module, a spectrum-preserving embedding module, a dual-path processing module (DR), and a fusion output module. The method projects time series data onto a predictive optimal latent space with concentrated energy using the predictive domain transformation, performs deep extraction of time series features using a dual-path parallel architecture, and achieves adaptive fusion of dependencies between variables through a masked channel dependency (MCD) strategy. The method includes the following steps:

[0007] Step (1): Obtain a multivariate time series dataset, perform standardization preprocessing on the multivariate time series dataset, and divide it into a training dataset, a validation dataset, and a test dataset;

[0008] Step (2): Based on the training dataset obtained in step (1), construct the data-adaptive prediction domain transformation basis matrix. and linear prediction mapping ;

[0009] Step (3): Based on the training dataset obtained in step (1), perform group reconstruction, dividing the continuous time series into multiple groups of data consisting of historical sequences and predicted sequences. Each time, N groups of data are randomly selected. The historical sequences in each group of data are input into the time series prediction model PDT. First, it undergoes reversible instance normalization processing, and then the prediction domain transformation basis matrix obtained in step (2) is used. Mapped to the prediction domain, and a high-dimensional feature tensor is generated via the spectrum-preserving embedding module;

[0010] Step (4): Input the high-dimensional feature tensors obtained in step (3) into the dual-path processing module respectively; the linear path processing module LR extracts the dominant linear components for trend extrapolation; the encoding path processing module ER uses full-spectrum features to capture nonlinear dynamics and dependencies between variables.

[0011] Step (5): Map the outputs of LR and ER back to the time domain through inverse transformation, perform weighted fusion, and then process them through Temporal MLP and inverse normalization to obtain the generated prediction sequence based on the training dataset.

[0012] Step (6): Calculate the mean squared error (MSE) between the predicted sequence in the training dataset and the generated predicted sequence based on the training dataset obtained in step (5). Perform backpropagation with minimizing the mean squared error (MSE) as the optimization objective, update the network parameters, and train the time series prediction model PDT.

[0013] Step (7): The validation dataset obtained in step (1) is grouped and reconstructed using the same method as in step (3), and input into the time series prediction model PDT trained in step (6) using the same data input method as in step (3) to obtain the generated prediction sequence based on the validation dataset;

[0014] Step (8): Calculate the mean square error (MSE) between the predicted sequence in the validation dataset and the generated predicted sequence based on the validation dataset obtained in step (7);

[0015] Step (9): Repeat steps (2) to (7) until the mean square error (MSE) obtained in step (8) meets the requirements. Then the network parameters are updated and the time series prediction model PDT is trained, and the optimized time series prediction model PDT is obtained.

[0016] Step (10): Input the input sequence given by the prediction task into the optimized time series prediction model PDT obtained in step (9), perform sequence prediction, output the generated prediction sequence, and complete the prediction task.

[0017] Furthermore, in step (2), based on the training dataset obtained in step (1), sample pairs are constructed using a sliding window, and the adaptive prediction domain transformation basis matrix is ​​constructed offline by statistically analyzing the covariance matrix and solving the trace maximization problem. and linear prediction mapping The specific method for constructing the data-adaptive prediction domain transformation basis matrix is ​​as follows:

[0018] Step (2.1): Construct a historical observation window using a sliding window. and future forecast window Calculate the autocovariance matrix at the sample level cumulatively. and cross-covariance matrix And introduce the Ridge regularization term. Calculate the population covariance matrix ;

[0019] Step (2.2): Construct an optimization objective function to minimize the Frobenius norm of the prediction error, under whitening orthogonal constraints. The error minimization problem is then transformed into a trace maximization problem:

[0020]

[0021] in Selecting the first eigenvalues ​​through eigenvalue decomposition The eigenvectors corresponding to the largest eigenvalues , where r is the dimension of the prediction domain space;

[0022] Step (2.3): Calculate the optimal transformation basis matrix and optimal linear prediction mapping , used for model initialization.

[0023] Furthermore, the specific process of prediction domain mapping and spectrum-preserving embedding in step (3) is as follows:

[0024] Step (3.1): Define the learnable transformation matrix ,in This is the optimal transformation basis matrix obtained in step (2.3). To fine-tune the parameters, the normalized input sequence is... Mapping to the prediction domain yields ;

[0025] Step (3.2): Employ spectral-preserving embedding to expand the feature dimension while maintaining the independence of orthogonal components in the prediction domain, generating an embedding tensor. ,in For the number of variables, To predict the dimension of the domain space, For the embedded dimension.

[0026] Furthermore, in step (4), the linear path processing module LR uses a Top-K truncation strategy to extract only the first K principal components of the embedded tensor, and obtains the linear prediction components by direct mapping and extrapolation through the linear layer. It serves as a low-pass filter and a robust trend predictor.

[0027] Furthermore, the encoding path processing module ER in step (4) includes a mask channel dependency policy MCD and a linear encoder LinearEncoder, and its specific steps are as follows:

[0028] Step (4.1): Construct the inter-channel correlation distance matrix: Calculate the weighted Euclidean distance between variables in the prediction domain. To reduce complexity, only the Top-K components are used for computation:

[0029]

[0030] in, For the first The nth variable in the prediction domain The value of each component The weighted values ​​used in the calculation of each component;

[0031] Step (4.2): Generate a binarized mask matrix: convert the distance matrix into a probability matrix. A binary mask matrix is ​​generated using the threshold sigmoid function. Used to filter noise interference from weakly correlated channels:

[0032]

[0033] in, For two variables The probability that there is a correlation between them. For the Sigmoid function, and These are the slope parameter and the threshold parameter, respectively.

[0034] Step (4.3): Constructing Channel-Level Linear Attention: This involves replacing the traditional dot product calculation with a combination of a statically learnable matrix and a dynamic mask for the input features. Processing is performed; first, the value vector is calculated. And generate attention score matrix Finally, channel fusion features are obtained through residual connections and layer normalization. The calculation formula is as follows:

[0035]

[0036]

[0037]

[0038] in, The projection matrix is ​​a value. It is a statically learnable correlation matrix used to capture long-term stable variable dependencies; The dynamic binary mask generated by the MCD strategy in step (4.2), This represents the Hadamard product, used for dynamically filtering irrelevant channel noise. For normalization operators;

[0039] Step (4.4): Construct a spectrum-level feedforward network: Process the features output from step (4.3) The network performs nonlinear transformations along the spectral dimension. It consists of two linear layers and a GELU activation function, acting independently on the spectral features of each channel. The aim is to extract deep nonlinear dynamics. The calculation formula is as follows:

[0040]

[0041] in, and It is a fully connected layer. For GELU activation function, This is the final context feature tensor output by the linear encoder.

[0042] Furthermore, the fusion and output process in step (5) specifically involves: utilizing learnable weights. Output of LR and ER output After weighted summation, the fused features are decoded using a Temporal Multilayer Perceptron (TMP) with the following calculation formula:

[0043]

[0044] Where Denorm is the inverse normalization operation. This is the final prediction result.

[0045] Furthermore, the present invention adopts the following technical solution:

[0046] A non-transitory computer-readable storage medium storing a computer program thereon, characterized in that the computer program, when executed by a processor, implements the above-mentioned multivariate time series prediction method based on prediction domain transformation and dual-path fusion.

[0047] Furthermore, the present invention adopts the following technical solution:

[0048] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the above-described multivariate time series prediction method based on prediction domain transformation and dual-path fusion.

[0049] The beneficial effects of this invention are:

[0050] This invention utilizes a data-adaptive prediction domain transformation and a dual-path architecture to project time series data onto a high-energy-density prediction optimal latent space. It leverages the Linear Path Processing (LR) module for efficient extrapolation to dominate linear trends and the Encoding Path Processing (ER) module to capture complex nonlinear residuals. This effectively solves the problem of fixed-basis transformation's inability to adapt to data characteristics, improving the model's feature representation capability and computational efficiency under different data distributions. Furthermore, by employing the Masked Channel Dependency (MCD) strategy and a lightweight linear attention mechanism, it adaptively fuses strongly correlated variable information and suppresses irrelevant channel noise through dynamically generated masks, achieving accurate modeling of dependencies between variables. This significantly improves the model's prediction accuracy and robustness on high-dimensional multivariate data, breaking through the nonlinear expression bottleneck while maintaining the efficiency of linear models and enhancing prediction performance. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the overall structure of an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of the model structure framework of an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram comparing the spectrum preservation embedding module of this invention with a traditional embedding module;

[0054] Figure 4 This is a structural diagram of the mask channel dependency strategy according to an embodiment of the present invention;

[0055] Figure 5 This is a structural diagram of the LinearEncoder encoder according to an embodiment of the present invention;

[0056] Figure 6 This document compares the prediction performance of the present invention with that of four existing methods on five public datasets: ETTh1, ETTh2, ETTm1, Weather, and ECL. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and specific implementation steps:

[0058] A multivariate time series forecasting method based on prediction domain transformation and dual-path fusion includes the following steps:

[0059] Step (1): Obtain a multivariate time series dataset, preprocess the dataset, and extract 70% of the data as the training dataset and 30% of the data as the validation dataset.

[0060] like Figure 1The diagram illustrates the overall structure of the invention. The data processing and dataset partitioning section, located at the beginning of the structure diagram, is responsible for performing preliminary processing on the raw data to form the data structure required for the prediction model. The time-series prediction model PDT consists of a prediction domain transformation module, a dual-route processing module (DR), and a fusion output module.

[0061] Step (2): Based on the training dataset obtained in step (1), sample pairs are constructed using a sliding window. By statistically analyzing the covariance matrix and solving the trace maximization problem, the adaptive prediction domain transformation basis matrix is ​​calculated and constructed offline. and linear prediction mapping The specific method for constructing the data-adaptive prediction domain transformation basis matrix is ​​as follows:

[0062] Step (2.1): Construct a historical observation window using a sliding window. and future forecast window Calculate the autocovariance matrix at the sample level cumulatively. and cross-covariance matrix And introduce the Ridge regularization term. Calculate the population covariance matrix ;

[0063] Step (2.2): Construct an optimization objective function to minimize the Frobenius norm of the prediction error, under whitening orthogonal constraints. The error minimization problem is then transformed into a trace maximization problem:

[0064]

[0065] in Selecting the first eigenvalues ​​through eigenvalue decomposition The eigenvectors corresponding to the largest eigenvalues , where r is the dimension of the prediction domain space;

[0066] Step (2.3): Calculate the optimal transformation basis matrix and optimal linear prediction mapping , used for model initialization.

[0067] Step (3): Based on the training dataset obtained in step (1), perform group reconstruction, dividing the continuous time series into multiple groups of data consisting of historical sequences and predicted sequences. 32 groups of data are randomly selected each time, and the historical sequences in each group are input into the time series prediction model PDT. The specific structure of the model is as follows: Figure 2 As shown, the input historical time series is first processed by reversible instance normalization, and then the prediction domain transformation basis matrix obtained in step (2) is used. The prediction domain is mapped to the prediction domain, and a high-dimensional feature tensor is generated via the spectrum-preserving embedding module. The specific process of prediction domain mapping and spectrum-preserving embedding is as follows:

[0068] Step (3.1): Define the learnable transformation matrix ,in This is the optimal transformation basis matrix obtained in step (2.3). To fine-tune the parameters, the normalized input sequence is... Mapping to the prediction domain yields ;

[0069] Step (3.2): Employ spectral-preserving embedding to expand the feature dimension while maintaining the independence of orthogonal components in the prediction domain, generating an embedding tensor. ,in For the number of variables, For the embedded dimension.

[0070] Figure 3 The differences between the spectrum-preserving embedding module used in the time-series prediction model PDT and the traditional model embedding module are demonstrated. The spectrum-preserving embedding module proposed in this method can expand the feature dimension of the model while preserving the spectral features, and significantly enhance the feature expression ability of the model.

[0071] Step (4): Input the high-dimensional feature tensors obtained in step (3) into the dual-path processing module respectively; the linear path processing module LR extracts the dominant linear components for trend extrapolation; the coded path processing module ER uses full-spectrum features to capture nonlinear dynamics and inter-variable dependencies.

[0072] The Top-K truncation strategy used by the LR module only truncates the first few bytes of the embedded tensor. Each principal component is directly mapped and extrapolated through a linear layer to obtain linear prediction components. It serves as a low-pass filter and a robust trend predictor.

[0073] The encoding path processing module ER in step (4) includes the mask channel dependency policy MCD and the linear encoder LinearEncoder. The specific steps are as follows:

[0074] Step (4.1): Construct the inter-channel correlation distance matrix: Calculate the weighted Euclidean distance between variables in the prediction domain. To reduce complexity, only the Top-K components are used for computation:

[0075]

[0076] in, For the first The nth variable in the prediction domain The value of each component This is the weighted value used when calculating each component.

[0077] Step (4.2): Generate a binarized mask matrix: convert the distance matrix into a probability matrix. A binary mask matrix is ​​generated using the threshold sigmoid function. Used to filter noise interference from weakly correlated channels:

[0078]

[0079] in, For two variables The probability that there is a correlation between them. For the Sigmoid function, and These are the slope parameter and the threshold parameter, respectively.

[0080] Step (4.3): Constructing Channel-Level Linear Attention: This involves replacing the traditional dot product calculation with a combination of a statically learnable matrix and a dynamic mask for the input features. Processing is performed. First, the value vector is calculated. And generate attention score matrix Finally, channel fusion features are obtained through residual connections and layer normalization. The calculation formula is as follows:

[0081]

[0082]

[0083]

[0084] in, The projection matrix is ​​a value. It is a statically learnable correlation matrix used to capture long-term stable variable dependencies; The dynamic binary mask generated by the MCD strategy in step (4.2), This represents the Hadamard product, used for dynamically filtering irrelevant channel noise. For normalization operators;

[0085] Step (4.4): Construct a spectrum-level feedforward network: Process the features output from step (4.3) The network performs nonlinear transformations along the spectral dimension. It consists of two linear layers and a GELU activation function, acting independently on the spectral features of each channel. The aim is to extract deep nonlinear dynamics. The calculation formula is as follows:

[0086]

[0087] in, and It is a fully connected layer. For GELU activation function, This is the final context feature tensor output by the linear encoder.

[0088] Step (5): Map the outputs of LR and ER back to the time domain through inverse transformation, perform weighted fusion, and then process them through Temporal MLP and inverse normalization to obtain the generated prediction sequence based on the training dataset. The specific process is as follows: using learnable weights Output of LR and ER output After weighted summation, the fused features are decoded using a Temporal Multilayer Perceptron (TMP) with the following calculation formula:

[0089]

[0090] Denorm is the inverse normalization operation. This is the final prediction result.

[0091] Step (6): Calculate the mean squared error (MSE) between the predicted sequence in the training dataset and the generated predicted sequence based on the training dataset obtained in step (5). With minimizing the mean squared error (MSE) as the optimization objective, backpropagate through the Adam optimizer to update the network parameters and train the time series prediction model PDT.

[0092] Step (7): The validation dataset obtained in step (1) is grouped and reconstructed using the same method as in step (3), and input into the time series prediction model PDT trained in step (6) using the same data input method as in step (3) to obtain the generated prediction sequence based on the validation dataset;

[0093] Step (8): Calculate the mean square error (MSE) between the predicted sequence in the validation dataset and the generated predicted sequence based on the validation dataset obtained in step (7);

[0094] Step (9): Repeat steps (2) to (7) until the mean square error (MSE) obtained in step (8) meets the requirements. Then the network parameters are updated and the time series prediction model PDT is trained, and the optimized time series prediction model PDT is obtained.

[0095] Step (10): Input the input sequence given by the prediction task into the optimized time series prediction model PDT obtained in step (9), perform sequence prediction, output the generated prediction sequence, and complete the prediction task.

[0096] Figure 6 This table displays the experimental results of five methods—PDT, TimeMixer, DLinear, iTransformer, and PatchTST—on six datasets: ETTm1, ETTm2, ETTh1, ETTh2, ECL, and Weather, under the same experimental conditions. The metrics used are mean squared error (MSE) and absolute squared error (MAE). The results of the best-performing model under each experimental condition are shown in bold in the table. Figure 6 As can be seen, the proposed time-series prediction model PDT performs optimally on all prediction tasks across all datasets, demonstrating significant performance improvements over other models. Compared to the current best-performing TimeMixer model, the proposed PDT model reduces the mean squared error (MSE) by 3.6%, 2.0%, 7.3%, 6.2%, 12.0%, and 3.1% across the six datasets, respectively. Compared to the widely used baseline model PatchTST, it reduces the MSE by 4.2%, 2.7%, 9.9%, 6.2%, 21.7%, and 8.2% across the six datasets, respectively. These reductions in prediction error demonstrate that the proposed PDT model achieves optimal prediction performance in long-term multivariate time series prediction tasks and represents a significant performance improvement over existing models.

[0097] From the above description of the embodiments, those skilled in the art can clearly understand that the implementation of the present invention can be achieved by means of software plus the necessary hardware platform. Embodiments of the present invention can be implemented using existing processors, or by dedicated processors used for this or other purposes for suitable systems, or by hardwired systems. Embodiments of the present invention also include non-transitory computer-readable storage media, which include machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and is accessible by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hardwired, or wireless, or a combination of hardwired and wireless), that connection is also considered a machine-readable medium.

[0098] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A multivariate time series prediction method based on prediction domain transformation and dual-path fusion, characterized in that, The system includes a temporal prediction model (PDT), which consists of a prediction domain transformation module, a spectrum-preserving embedding module, a dual-path processing module (DR), and a fusion output module. The PDT projects temporal data onto a prediction optimal latent space with concentrated energy using prediction domain transformation, and performs deep extraction of temporal features using a dual-path parallel architecture. It also achieves adaptive fusion of dependencies between variables through a masked channel dependency strategy (MCD). The system includes the following steps: Step (1): Obtain a multivariate time series dataset, perform standardization preprocessing on the multivariate time series dataset, and divide it into a training dataset, a validation dataset, and a test dataset; Step (2): Based on the training dataset obtained in step (1), construct the data-adaptive prediction domain transformation basis matrix. and linear prediction mapping ; Step (3): Based on the training dataset obtained in step (1), perform group reconstruction, dividing the continuous time series into multiple groups of data consisting of historical sequences and predicted sequences. Each time, Z groups of data are randomly selected. The historical sequences in each group of data are input into the time series prediction model PDT. First, it undergoes reversible instance normalization processing, and then the prediction domain transformation basis matrix obtained in step (2) is used. Mapped to the prediction domain, and a high-dimensional feature tensor is generated via the spectrum-preserving embedding module; Step (4): Input the high-dimensional feature tensors obtained in step (3) into the dual-path processing module respectively; the linear path processing module LR extracts the dominant linear components for trend extrapolation; the encoding path processing module ER uses full-spectrum features to capture nonlinear dynamics and dependencies between variables. Step (5): The outputs of the linear path processing module LR and the coding path processing module ER are mapped back to the time domain through inverse transformation and weighted fusion. After passing through the Temporal Multilayer Perceptron (TemporalMLP) and inverse normalization processing, the generated prediction sequence based on the training dataset is output. Step (6): Calculate the mean squared error (MSE) between the predicted sequence in the training dataset and the generated predicted sequence based on the training dataset obtained in step (5). With minimizing the mean squared error (MSE) as the optimization objective, perform backpropagation, update the network parameters, and train the time series prediction model PDT. Step (7): The validation dataset obtained in step (1) is grouped and reconstructed using the same method as in step (3), and input into the time series prediction model PDT trained in step (6) using the same data input method as in step (3) to obtain the generated prediction sequence based on the validation dataset; Step (8): Calculate the mean square error (MSE) between the predicted sequence in the validation dataset and the generated predicted sequence based on the validation dataset obtained in step (7); Step (9): Repeat steps (2) to (7) until the mean square error (MSE) obtained in step (8) meets the requirements. Then the network parameters are updated and the time series prediction model PDT is trained, and the optimized time series prediction model PDT is obtained. Step (10): Input the input sequence given by the prediction task into the optimized time series prediction model PDT obtained in step (9), perform sequence prediction, output the generated prediction sequence, and complete the prediction task.

2. The multivariate time series prediction method based on prediction domain transformation and dual-path fusion according to claim 1, characterized in that, In step (2), based on the training dataset obtained in step (1), sample pairs are constructed using a sliding window, and the adaptive prediction domain transformation basis matrix is ​​constructed offline by statistically analyzing the covariance matrix and solving the trace maximization problem. and linear prediction mapping The specific method for constructing the data-adaptive prediction domain transformation basis matrix is ​​as follows: Step (2.1): Construct a historical observation window using a sliding window. and future forecast window Calculate the autocovariance matrix at the sample level cumulatively. and cross-covariance matrix And introduce the Ridge regularization term. Calculate the population covariance matrix ; Step (2.2): Construct an optimization objective function to minimize the Frobenius norm of the prediction error, under whitening orthogonal constraints. The error minimization problem is then transformed into a trace maximization problem: in Selecting the first eigenvalues ​​through eigenvalue decomposition The eigenvectors corresponding to the largest eigenvalues , where r is the dimension of the prediction domain space; Step (2.3): Calculate the optimal transformation basis matrix and optimal linear prediction mapping , used for model initialization.

3. The multivariate time series prediction method based on prediction domain transformation and dual-path fusion according to claims 1 and 2, characterized in that, The specific process of prediction domain mapping and spectrum-preserving embedding in step (3) is as follows: Step (3.1): Define the learnable transformation matrix ,in This is the optimal transformation basis matrix obtained in step (2.3). To fine-tune the parameters, the normalized input sequence is... Mapping to the prediction domain yields ; Step (3.2): Employ spectral-preserving embedding to expand the feature dimension while maintaining the independence of orthogonal components in the prediction domain, generating an embedding tensor. ,in For the number of variables, For the embedded dimension.

4. The multivariate time series prediction method based on prediction domain transformation and dual-path fusion according to claim 1, characterized in that, In step (4), the linear path processing module LR uses a Top-K truncation strategy, only truncating the first part of the high-dimensional feature tensor. Each principal component is directly mapped and extrapolated through a linear layer to obtain linear prediction components. It serves as a low-pass filter and a robust trend predictor.

5. The multivariate time series prediction method based on prediction domain transformation and dual-path fusion according to claims 1 and 3, characterized in that, The encoding path processing module ER in step (4) includes the mask channel dependency policy MCD and the linear encoder LinearEncoder. The specific steps are as follows: Step (4.1): Construct the inter-channel correlation distance matrix: Calculate the weighted Euclidean distance between variables in the prediction domain. To reduce complexity, only the Top-K components are used for computation: in, For the first The nth variable in the prediction domain The value of each component The weighted values ​​used in the calculation of each component; Step (4.2): Generate a binarized mask matrix: convert the distance matrix into a probability matrix. A binary mask matrix is ​​generated using the threshold sigmoid function. Used to filter noise interference from weakly correlated channels: in, For two variables The probability that there is a correlation between them. For the Sigmoid function, and These are the slope parameter and the threshold parameter, respectively. Step (4.3): Constructing Channel-Level Linear Attention: This involves replacing the traditional dot product calculation with a combination of a statically learnable matrix and a dynamic mask for the input features. Processing is performed; first, the value vector is calculated. And generate attention score matrix Finally, channel fusion features are obtained through residual connections and layer normalization. The calculation formula is as follows: in, The projection matrix is ​​a value. It is a statically learnable correlation matrix used to capture long-term stable variable dependencies; The dynamic binary mask generated by the MCD strategy in step (4.2), This represents the Hadamard product, used for dynamically filtering irrelevant channel noise. For normalization operators; Step (4.4): Construct a spectrum-level feedforward network: Process the features output from step (4.3) The network performs nonlinear transformations along the spectral dimension. It consists of two linear layers and a GELU activation function, acting independently on the spectral features of each channel. The aim is to extract deep nonlinear dynamics. The calculation formula is as follows: in, and It is a fully connected layer. For GELU activation function, This is the final context feature tensor output by the linear encoder.

6. The multivariate time series prediction method based on prediction domain transformation and dual-path fusion according to claim 1, characterized in that, The fusion and output process in step (5) specifically involves: utilizing learnable weights. Output of LR and ER output After weighted summation, the fused features are decoded using a Temporal Multilayer Perceptron (TMP) with the following calculation formula: Here, Denorm is the inverse normalization operation. This is the final prediction result.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the multivariate time series prediction method based on prediction domain transformation and dual-path fusion as described in any one of claims 1 to 6.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the multivariate time series prediction method based on prediction domain transformation and dual-path fusion as described in any one of claims 1 to 6.

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