Time sequence prediction model based on double-domain multiple variables

Abstract

The invention provides a time sequence prediction model based on double domains and multiple variables, and the model simultaneously extracts a long-short time dependency relationship, an inter-variable dependency relationship and an intra-variable dependency relationship in a time domain and a frequency domain, so that the precision of time sequence prediction and the generalization ability of the model are improved. The model is composed of a time sequence input module, a decomposition embedding module, a trend prediction module, a remainder prediction module and a fusion output module. Firstly, mutual conversion of a time domain and a frequency domain is realized through DFT (Discrete Fourier Transform), secondly, a trend component and a remainder component are respectively predicted by adopting a double-branch structure, and finally, two prediction results are added to obtain a final prediction result of a multivariable long-time sequence. According to the invention, the average prediction precision of the model is improved; in the design of the model, the principle of modular design is followed, and a convolution architecture is adopted, so that the calculation complexity is effectively reduced, and the expandability and efficiency of the model are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of time prediction, and particularly relates to a time series prediction model based on a double-domain multivariate. BACKGROUND

[0002] Time series prediction is a process of predicting future data based on historical data. Through the analysis of historical data, the inherent law can be revealed, so as to predict the trend of future data. This method is widely used in various fields, including computer science, meteorology, medicine, etc. Time series prediction can be divided into two categories according to the dimension of data: univariate time series prediction and multivariate time series prediction. Univariate time series prediction mainly depends on the change of a variable over time, focusing on the analysis of the time correlation of the variable. The purpose is to predict the future value through the trend and periodic pattern in the historical data. Multivariate time series prediction extends on the basis of univariate, considering the interaction between multiple related variables and their relationship with time. Compared with univariate prediction, multivariate prediction not only focuses on the time dependence of a single variable, but also understands the interactive influence between variables. For example, in energy consumption prediction, temperature, humidity, wind speed and other variables will all have an impact on power demand, so they must be considered together. Multivariate long time series prediction is more challenging than univariate prediction, because it needs to handle the dynamic relationship between multiple variables at the same time. By introducing multiple dimensions of data, the model can more comprehensively capture the complex variable dependence relationship, thereby improving the accuracy of prediction.

[0003] Time prediction problems have been extensively studied by many scholars, and various prediction algorithms have been proposed based on different techniques. Mainly divided into prediction algorithms based on statistical learning, prediction algorithms based on deep learning and prediction algorithms based on generative models, in recent years, there have been many achievements in related work. In multivariate time series prediction, how to understand and model the relationship between variables is one of the key factors to improve prediction accuracy. Crossformer adopts a two-stage attention mechanism that processes cross-time and cross-dimension stages sequentially, breaking away from pure time attention. It divides each dimension's time series into patches, embeds them into 2D vectors, and performs attention. UniTST points out that cross-time and cross-dimension attention methods cannot directly and explicitly learn complex inter-variable and intra-variable dependencies. It proposes a unified attention mechanism by flattening patch tokens, integrating a scheduling module to reduce memory complexity and improve model feasibility. FFDA-GNN combines graph neural networks with spatial attention mechanisms to enhance the ability to capture dependencies between multiple variables; it uses parallel multi-layer dilated convolutions and channel attention mechanisms to extract multi-channel features from time series data, making full use of multi-channel information in time series data to improve prediction performance. iTtransformer innovatively reverses the time and variable dimensions in the standard Transformer model, learns the correlation between variables, and improves the model's understanding of the relationship between multiple variables, achieving good results.

[0004] Time series decomposition is a common method widely used in processing complex time series data. It helps to analyze and understand the internal structure of data by splitting the original time series into multiple independent components, usually including trend component, periodic component and random component. Through this decomposition method, periodic fluctuations, long-term trends and random noise in the data can be more clearly identified, providing a basis for more accurate prediction and model building. Especially when dealing with multi-dimensional or multivariate time series data, the decomposition method can effectively reduce the complexity of the data and reveal the deep patterns hidden in the data.

[0005] TimesNet introduces TimesBlock, which embeds 1D time series into 2D tensors for analysis to effectively capture multi-periodicity. FTMixer takes advantage of the observation that time domain is effective in capturing local dependencies while frequency domain is good at learning global dependencies. It applies convolution in the frequency domain to capture global dependencies. At the same time, it uses the discrete cosine transform (DCT) which is simpler to calculate than the discrete Fourier transform (DFT) to transform multi-scale patches, and then applies convolution to capture local dependencies. WITRAN captures long-term and short-term repeating patterns by implementing information transmission in a double-particle flow, proposing a new paradigm. The horizontal and vertical gated selection unit (HVGSU) using bidirectional gated selection unit (GSC) is used to simulate global and local correlations. CycleNet enhances time series prediction by modeling periodic patterns, introducing residual cycle prediction (RCF) technology that uses learnable cyclic periods to model inherent periodic patterns in sequences and predicts the remaining residual components of the modeled cycles. Fredformer identifies the frequency bias problem in time series data, where learning tends to disproportionately focus on low or high frequencies. It solves this problem by normalizing frequencies to eliminate bias. However, traditional time series decomposition enhancement methods usually only analyze from the statistical and time domain perspectives, ignoring the effective use of frequency domain information. This approach results in insufficient utilization of information and fails to fully exploit the potential rules in time series. SUMMARY

[0006] Therefore, the present application aims to overcome the above-mentioned problems in the prior art, and proposes a time series prediction model based on dual-domain multivariate.

[0007] To achieve the above-mentioned purposes, the technical scheme of the present application is as follows:

[0008] A time series prediction model based on dual-domain multivariate, comprising a time series input module, a decomposition embedding module, a trend prediction module, a residual prediction module, and a fusion output module; the time series input module uses RevIN to preprocess time series data;

[0009] The decomposition embedding module is used to extract the dependency relationship of variables, independently embed variables in the sequence, retain the variable dimension in the original sequence, and then use Fourier transform to divide the initial time series into trend items and periodic items;

[0010] The trend prediction module captures the feature representation in the strengthened time series through the fusion of spatial attention and channel attention mechanisms;

[0011] The residual prediction module is independent of embedded features and variables, uses DWConv to independently learn the time dependence of each variable time series, adopts a large kernel to expand the receptive field, assigns adaptive weights to each variable through a variable attention mechanism, and uses group convolution to capture intra-variable and inter-variable dependencies;

[0012] The fusion output module fuses the time domain features and frequency domain features extracted by the two branches, maps through Head, and finally obtains the prediction output after the inverse normalization processing of RevIN.

[0013] The prediction model realizes the mutual conversion between time domain and frequency domain through Fourier transform, adopts a double-branch structure, respectively predicts the trend component and the residual component, and finally adds the two prediction results to obtain the final prediction result of the multivariate time series.

[0014] Further, the time series input module eliminates the adverse effects of data distribution offset on model performance by introducing RevIN normalization operation, and the specific implementation process includes: assuming that the input multivariate time series data is represented as where M represents the number of variables of the multivariate time series, L x represents the length of the time series, and the mean and standard deviation of the input data are calculated as follows:

[0015]

[0016] The mean and standard deviation calculated by the above formula are used to standardize the input data x t to obtain standardized data as shown in the following formula:

[0017]

[0018] where γ, β ∈ R M are learnable affine parameter vectors, and the data distribution offset is eliminated after normalization processing.

[0019] Further, the decomposition embedding module is implemented as follows:

[0020] Given the multivariate time series input The input is reshaped to X in ∈ R M ×1×T The channel dimension is introduced so that each variable can be processed independently.

[0021] The convolution layer has a kernel size of P and a step size of S, which divides the sequence into several patches Convolution maps a single input channel to D output channels to obtain an embedding tensor X emb ∈ R M×D×Nwhere N denotes the number of patches;

[0022] The input time series is decomposed into two branches by Fourier transform, one for periodic term and the other for trend term, and then fused in the final output stage.

[0023] Further, the trend prediction module implements the process as follows:

[0024] Given a feature In order to effectively obtain more comprehensive global information representation in space, the trend variable convolution module uses global average pooling and global maximum pooling at the same time, respectively obtaining and As shown in the following formula:

[0025]

[0026] Two global vectors are obtained by a Conv-ReLU-Conv, respectively and Summing them up, the channel attention weight representation is obtained through a gating mechanism As shown in the following formula:

[0027]

[0028] The weight representation M n is multiplied by the input feature F to obtain the result F', and then the same calculation is performed in the channel direction to obtain and The maximum and average features in the channel are aggregated by mapping and splicing in the second dimension, and the spatial attention weight representation is generated through a gating mechanism The weight representation M n is multiplied by the input feature F' to obtain the final prediction result.

[0029] Further, the residual prediction module is composed of L stacked blocks, each block containing DWConv and RVGC. DWConv is responsible for learning the long and short time dependencies of each univariate time series independently, and applies a convolution kernel on each input feature. RVGC consists of channel attention and grouped convolution. Channel attention explicitly models the mutual dependence between channels, adaptively learns the importance of each channel through the network, and gives each channel a different weight coefficient, strengthens important features, and suppresses unimportant features. Then, the group convolution is used to capture the interaction between variables in adjacent time windows, and the variable time window pairs are organized into shared kernel groups for processing.

[0030] Further, the mean square error (MSE) and the mean absolute error (MAE) are used as performance indicators to evaluate the accuracy of the model prediction.

[0031] Compared with the prior art, the time series prediction model based on the dual-domain multivariate has the following advantages:

[0032] The average prediction accuracy of the model is improved compared with the prior art, and the overall performance is improved. In the design of the model, the principle of modular design is followed, and the convolution architecture is adopted, thereby effectively reducing the computational complexity and improving the scalability and efficiency of the model BRIEF DESCRIPTION OF DRAWINGS

[0033] The accompanying drawings, which form a part of the present application, are intended to provide further understanding of the present application and are incorporated herein for explanation by way of the exemplary embodiments of the present application. The present application is explained by way of illustration with reference to the accompanying drawings in which:

[0034] Figure 1 A prediction module framework of the present application is shown in the figure;

[0035] Figure 2 A trend variable group convolution (TVGC) module of the present application is shown in the figure. DETAILED DESCRIPTION

[0037] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0038] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0039] In multivariate time series prediction, we consider a multivariate time series X∈R M×T , where M represents the number of variables and T represents the length of the time series. Each element corresponds to the value of the mth variable at time step t. The sequence X m ∈R T represents the complete time series of the mth variable. Given a time interval Δt, the subsequence represents the observation data of all M variables between time steps t0 and t0+Δt.

[0040] Our goal is to build a prediction model ∮ that can use the observation data in the past period to predict the future time series value. Specifically, given a historical time window where H represents the length of the window, the model ∮ predicts the future time step data based on the information of the window, denoted as where S represents the length of the prediction window, and this process can be expressed by the following function relationship:

[0041] The model captures the time-dependent relationship in the historical sequence through learning, and realizes accurate prediction of the future sequence.

[0042] The overall structure of the time series prediction model based on the dual-domain multivariate proposed in the application is shown in the figure Figure 1 The model is composed of a time series input module, a decomposition embedding module, a trend prediction module, and a residual prediction module, and finally fuses and outputs.

[0043] (1) Time series input module: RevIN is used to preprocess time series data to reduce the influence of data distribution deviation, improve the stability and prediction accuracy of the model.

[0044] (2) Decomposition embedding module: To extract the dependency of variables, the sequence is independently embedded with variables, and the variable dimension in the original sequence is retained. Then, the initial time series is divided into trend items and periodic items using Fourier transform. According to the different characteristics of time series components, different prediction methods are used.

[0045] (3) Trend prediction module: This module captures the feature representation in the time series through the fusion of spatial attention and channel attention mechanism.

[0046] (4) Residual prediction module: Based on the embedded features and variable independence, DWConv is used to independently learn the time dependence of each variable time series and use large kernels to expand the receptive field, improve the temporal modeling ability, and capture the short-term and long-term dependencies in the time dimension. Through the variable attention mechanism, each variable is assigned an adaptive weight to dynamically respond to the change of variable importance. Group convolution is used to capture the dependency between variables. This combination method enhances the model's ability to learn complex relationships in multivariate time series data.

[0047] (5) Fusion output: After feature fusion of the time domain features and frequency domain features extracted by the two branches, through Head mapping, the final prediction output is obtained after the inverse normalization processing of RevIN.

[0048] Time series data usually changes in mean and variance over time. This change leads to inconsistency between the training set and the test set, i.e. data distribution deviation. This deviation can seriously affect the generalization ability and prediction accuracy of the model. In order to solve this problem, RevIN normalization operation is introduced in the time series input module to eliminate the adverse effects of data distribution deviation on model performance.

[0049] Specifically, assume that the input multivariate time series data is represented as where M represents the number of variables of the multivariate time series, Lx denotes the length of the time series. The RevIN module adopted by the present application includes symmetric normalization and reverse normalization operations, and the calculation of the mean and standard deviation of the input data is shown in formula (1) and formula (2):

[0050]

[0051] The mean and standard deviation calculated by formula (1) and formula (2) are used to normalize the input data x t to obtain standardized data as shown in formula (3):

[0052]

[0053] In formula (3), γ, β ∈ R M is a learnable affine parameter vector, and ∈ is a very small positive number to prevent division by zero and improve numerical stability. After normalization, the data distribution deviation is eliminated and the robustness of the model is improved. RevIN normalizes and reverses the operation, so that the model remains consistent during training and testing, thereby effectively improving the performance of the time series prediction model. Therefore, the present application performs reverse normalization processing in the fusion output module.

[0054] Assume that the time series data before reverse normalization is The output after reverse normalization is as shown in formula (4):

[0055]

[0056] The previous embedding method treats the entire multivariate time series as a single sample with M features, ignoring the potential relationship between variables. This variable mixed embedding method will block and embed the entire multivariate time series as a whole, which to some extent causes the information between different variables to be mixed, the variable dimension information to be lost, and the independent learning ability of the model for each variable feature to be affected. We regard each univariate time series in the multivariate time series as an individual sample with 1 feature, and independently embed it, while maintaining the integrity of the variable dimension, paying more attention to the independence between variables and feature expression, and improving the feature capture ability of the model for each variable. Specifically, given a multivariate time series input The input is reshaped to X through a non-squeezing operation in ∈ R M×1×T The channel dimension is introduced so that each variable can be processed independently. Then, the convolutional layer kernel size is P, and the step is S, which divides the sequence into several patches The convolution maps a single input channel to D output channels, thereby obtaining an embedding tensor X emb ∈ R M×D×Nwhere N denotes the number of patches. By processing each variable independently, the variable dimension information is effectively preserved, avoiding the loss of variable features in traditional hybrid embedding, and improving the expressiveness and predictive ability of multivariate time series models.

[0057] After that, we decompose the input time series into periodic and trend components by Fourier transform, and process them separately. In the final output stage, we fuse the two components and output them.

[0058] First, the model removes the top K dominant components in the frequency domain of each input, X t The input is multivariate, and each dimension can have different frequency patterns. Therefore, we process each input X t independently based on the channel using discrete Fourier transform DFT(·) and inverse DFT(·) as shown in equation (5):

[0059]

[0060] DFT(·) transforms the input into complex Fourier components, then uses the Amp(·) function to calculate the amplitude of each frequency, and TopK(·) selects the top K frequency set with the largest amplitude. FLT(·) is an operation that filters out K t frequencies from Z t Then, we use IDFT(·) to restore the top K components to the time domain trend component and get the residual component by removing from X t as shown in equation (6):

[0061]

[0062] Here, DFT(·) and IDFT(·) can be implemented using Fast Fourier Transform (FFT) with a computational complexity of O(LlogL). The complexity of TopK and FLT operations is O(L+K). It is important to note that all these operations are gpu-friendly and can be fully parallelized. By converting the time series from the time domain to the frequency domain using discrete Fourier transform, filtering the data, and then reconstructing the corresponding time series components using inverse Fourier transform, we can express complex time series using simple components, reducing the complexity of the initial sequence and the difficulty of the model prediction.

[0063] Since is a high-frequency trend component containing only the top K frequency information, we mainly focus on the variable dependence relationship of the trend component. In the trend component, how to extract features between variables and within variables, we designed a trend variable group convolution (TVGC) module as shown in Figure 2As shown, by learning local interactions within a time window, it can flexibly adapt to the dynamic relationship between variables over time. Through in-depth analysis of local dependencies in time series, this module captures key variable dependencies, thereby optimizing the model's understanding of complex data patterns.

[0064] Specifically, the global average pool is used to retain the attention between variables, and the global max pool is used to capture the attention information within variables. The inter-variable attention and intra-variable attention are fused, and the input features are first passed through a channel attention module to obtain channel weight representation, and then the importance of each channel of the input features is adjusted. The updated features are passed through a spatial attention module to obtain spatial weight representation, which corresponds to adjusting the importance of each feature after updating.

[0065] Given a feature In order to effectively obtain more comprehensive global information representation in space, the trend variable convolution module uses global average pooling and global maximum pooling at the same time, respectively obtaining and As shown in equation (7):

[0066]

[0067] Then, the two global vectors are passed through a Conv-ReLU-Conv to obtain and Next, the sum of the two is obtained, and the channel attention weight representation is obtained through a gating mechanism (implemented by a sigmoid function) As shown in equation (8):

[0068]

[0069] The weight representation M n is multiplied by the input feature F to obtain the result F'. After that, the same calculation is performed in the channel direction to obtain and In the second dimension, the maximum and average features on the channel are aggregated by concatenation mapping. Then, a gating mechanism is used to generate a spatial attention weight representation The weight representation M n is multiplied by the input feature F' to obtain the final prediction result.

[0070] Specifically, the residual prediction branch is composed of L stacked blocks, each block containing DWConv and RVGC.

[0071] DWConv is responsible for learning the long-short time dependencies of each univariate time series independently. DWConv applies convolution kernels on each input feature separately, allowing it to learn unique temporal patterns and dynamic changes for each feature. This approach effectively captures the time series information of individual features while reducing computational complexity and improving model efficiency. By modeling each feature independently, DWConv can more flexibly adapt to different dynamic characteristics in multivariate time series, further improving the model's prediction ability and generalization ability.

[0072] The RVGC module consists of two parts: channel attention and grouped convolution. Channel attention explicitly models the interdependence between channels by adaptively learning the importance of each channel and assigning different weight coefficients to each channel, thereby strengthening important features and suppressing non-important features. Then, group convolution is used to capture the interaction between variables in adjacent time windows. The variable time window pairs are organized into shared kernel groups for efficient processing. By sharing kernels between these groups, the model can adapt to evolving dependencies. This ensures that the model automatically adjusts and captures the mutual influence between different time steps when processing long time series data, effectively dealing with evolving dependencies. This efficient feature learning mechanism is particularly suitable for processing complex time series data with long time spans, improving the model's prediction ability and generalization performance.

[0073] The effectiveness of the model is demonstrated through experiments as follows.

[0074] The performance of FCMNet is evaluated on six widely used multivariate time series datasets.

[0075] ETT: The ETT (Electric Transformer Temperature) dataset contains transformer oil temperature data, including four subsets ETTm1, ETTm2, ETTh1, and ETTh2, each representing different time granularities and history spans.

[0076] Weather: The Weather dataset includes meteorological variables such as temperature, humidity, wind speed, and pressure collected from multiple weather stations.

[0077] Exchange: The Exchange dataset records the daily exchange rates of the world's eight major currencies.

[0078] Table 1 provides a detailed overview of each dataset, including the number of time steps and sampling frequency.

[0079] Table 1

[0080]

[0081] For evaluation, the present application uses mean squared error (MSE) and mean absolute error (MAE) as performance indicators, where lower values reflect better prediction accuracy. MSE refers to the mean of the sum of the squares of the differences between the predicted values and the true values, as shown in equation (9), and MAE refers to the mean of the sum of the absolute values of the differences between the predicted values and the true values, as shown in equation (10). For the i-th instance, the calculation of MSE(i) and MAE(i) is as follows:

[0082]

[0083] The experimental environment configuration of the present application is shown in Table 2.

[0084] Table 2

[0085]

[0086]

[0087] When performing hyperparameter setting, the present application uses the Adam optimizer and selects MSE as the loss function. The learning rate ranges from 0.0001 to 0.0002, which is adjusted for each dataset. According to the size of the dataset, the batch size is set to 32, 128, 256 or 512, the dropout is set to 0.3, the embedding parameter P is 8, and S is 4. The model is composed of 1 to 3 blocks L, and the training is run to 100 epochs, using the EarlyStopping mechanism. If the validation loss stagnates for 20 epochs, the early stopping will be triggered to prevent model overfitting and improve its generalization ability.

[0088] To verify the performance of the model of the present application in multivariate time series prediction, the model of the present application is compared with popular time series prediction models. These comparison models include MTS-mixers, ConvTimeNet, PatchTST, iTransformer, DLinear, and TimesNet. Table 3 is the prediction result evaluation index of all models on six datasets using MSE and MAE, with the best value indicated in red. As can be seen from Table 3, the MSE and MAE values of the model of the present application are mostly the smallest on all six public datasets, indicating that the prediction accuracy of the model of the present application is generally higher than that of other models.

[0089] Table 3

[0090]

[0091]

[0092] In order to further verify the contribution of each module of the FCMNet model to the overall performance, the present application carries out an ablation experiment. The sequence decomposition structure, the TVGC module and the RVGC module of the FCMNet are replaced respectively, and the experimental results are compared with the complete FCMNet.

[0093] The present application decomposes into two branches of periodic terms and trend terms by Fourier transform, and uses Moving Average (MA) to replace the decomposed sequence. In Table 4, MA is the model replaced by MA, and DFT is the overall model using Fourier transform decomposition. Using MSE and MAE as evaluation indexes, it can be seen from the table that after introducing the DFT decomposition operation, the average MSE and MAE are reduced by 2.4% and 2.4% respectively. This shows that the model proposed by the present application effectively improves the prediction performance by using Fourier transform decomposition processing on time series.

[0094] Then, ablation experiments are carried out on the two important modules TVGC and RVGC proposed. The two modules are replaced by the basic linear layer, and the environment configuration of the ablation experiment remains unchanged to ensure the integrity of the decomposition and prediction process. Table 5 is the ablation experiment results.

[0095] From the experimental results, when the TVGC and RVGC modules are replaced, the average MSE values increase by 1% and 5.2% respectively, and the average MAE values increase by 0.6% and 3.3% respectively. The performance of the model in prediction is significantly reduced. This shows that the modules proposed by the present application effectively capture the dependence between cross-variables in time series, significantly enhance the ability of the model, and make it an efficient and effective mechanism to identify and utilize the correlation between these variables. By accurately modeling the dynamic interaction between different variables, each module in the model plays a crucial role, and when all modules work together, the prediction accuracy of the model is significantly improved.

[0096] Table 4

[0097]

[0098] Table 5

[0099]

[0100] The present application obtains quantitative results by calculating the relative amplitude change of Fourier components between input and output in the frequency domain, and checks the relative change of trend term and residual term. Specifically, in all benchmarks, the change of trend term is smaller than that of residual term. It is considered that this is the reason why using channel attention is so effective in capturing frequency changes, because its offset is relatively small.

[0101] We analyze the hyperparameter K, and we select K ∈ {4, 8, 12, 24}. We perform a sensitivity analysis on the hyperparameter K that represents the maximum frequency count selection. As the prediction length increases, larger values of K become more significant, leading to a significant performance advantage. This is because the model receives more frequency information from the increased prediction steps. For example, larger values of K can improve the performance of all prediction stages in datasets with higher sampling rates (e.g., ETTm2). This can be because the sample granularity of the dataset (minute-level) is finer than the yearly and hourly sampling, which produces richer frequency signals in ETTm2, improving the model's performance on these datasets.

[0103] The above description is merely preferred embodiments of the present application, but not to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall fall within the scope of protection of the present application.

Claims

1. A time series forecasting model based on two domains and multiple variables, characterized in that: It includes a time series input module, a decomposition and embedding module, a trend prediction module, a residual prediction module, and a fusion output module; The time series input module uses RevIN to preprocess the time series data; The decomposition and embedding module is used to extract the dependencies of variables, perform independent variable embedding on the sequence, retain the variable dimension in the original sequence, and then use Fourier transform to decompose the initial time series into trend and periodic terms. The trend prediction module captures and enhances feature representations in time series by fusing spatial attention and channel attention mechanisms. The remaining prediction module is independent of the embedded features and variables. It uses DWConv to independently learn the time dependence of each variable's time series and adopts a large kernel to expand the receptive field. It assigns adaptive weights to each variable through a variable attention mechanism and uses group convolution to capture the intra- and inter-variable dependencies. The fusion output module fuses the time-domain and frequency-domain features extracted from the two branches, then obtains the prediction output through Head mapping and finally through RevIN inverse normalization. The prediction model achieves mutual conversion between the time domain and the frequency domain through Fourier transform, adopts a dual-branch structure, and predicts the trend component and the residual component separately. Finally, the two prediction results are added together to obtain the final prediction result of the multivariate time series.

2. The time series prediction model based on dual-domain multivariate analysis according to claim 1, characterized in that: The time series input module eliminates the adverse effects of data distribution bias on model performance by introducing RevIN normalization. The specific implementation process includes: Assume the input multivariate time series data is represented as follows Where M represents the number of variables in a multivariate time series, L x The length of the time series is indicated, and the mean and standard deviation of the input data are calculated as follows: Using the mean and standard deviation calculated by the above formula, the input data x t Standardization is performed to obtain standardized data. As shown in the following formula: Where γ, β∈R M It is a learnable affine parameter vector, which is normalized to eliminate data distribution bias.

3. The time series prediction model based on dual-domain multivariate prediction according to claim 1, characterized in that: The decomposition and embedding module is implemented as follows: Given multivariate time series input The input is reshaped into X through a non-squeezing operation. in ∈R M×1×T Introducing a channel dimension allows each variable to be processed independently; The convolutional layer has a kernel size of P and a stride of S, dividing the sequence into several patches. Convolution maps a single input channel to a D output channel, resulting in an embedding tensor X. emb ∈R M×D×N , where N represents the number of patches; The input time series is decomposed into two branches, periodic and trend, through Fourier transform. These are processed separately, and then merged and output in the final output stage.

4. The time series prediction model based on dual-domain multivariate as described in claim 1, characterized in that: The trend prediction module is implemented as follows: Given a feature To effectively obtain a more comprehensive global information representation in space, the trend variable convolution module uses both global average pooling and global max pooling, respectively, to obtain... and As shown in the following formula: Two global vectors are obtained by passing them through a Conv-ReLU-Conv. and Summing the two, a gating mechanism is used to obtain the channel attention weight representation. As shown in the following formula: Let the weight be M n Multiplying the result F by the input feature F yields the result F′, and then the same calculation is performed in the channel direction to obtain the result. and The second dimension is used for concatenation mapping, aggregating the maximum and average features across channels, and a spatial attention weight representation is generated through a gating mechanism. Let the weight be M n Multiply the result by the input feature F′ to obtain the final prediction result.

5. The time series prediction model based on dual-domain multivariate prediction according to claim 1, characterized in that: The remaining prediction module consists of L stacked blocks, each containing two parts: DWConv and RVGC. DWConv is responsible for independently learning the long and short time dependencies of each univariate time series, applying convolutional kernels to each input feature. RVGC consists of two parts: channel attention and group convolution. Channel attention explicitly models the interdependencies between channels, adaptively learning the importance of each channel through the network, and assigning different weight coefficients to each channel to strengthen important features and suppress unimportant features. Then, group convolution is used to capture the interactions between variables in adjacent time windows, and the variable time windows are organized into a shared kernel group for processing.

6. The time series prediction model based on dual-domain multivariate prediction according to claim 1, characterized in that: It also includes using mean squared error (MSE) and mean absolute error (MAE) as performance metrics to evaluate the accuracy of model predictions.

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