Time sequence prediction method and system based on double-domain feature fusion

Abstract

The invention discloses a time prediction method and system based on double-domain feature fusion. The method and system adapt to long and short term time series prediction requirements of multiple scenes such as weather forecast, energy scheduling, traffic flow and financial exchange rate. The method comprises the steps that a multi-field data set is obtained and preprocessed, and instance normalization is carried out; performing double-domain multi-scale characteristic decomposition by adopting down-sampling and discrete wavelet transform to obtain continuous trend and high-frequency mutation details; a local unit is obtained through patch cutting and embedding, local time sequence association is mined through depth separable convolution, cross-patch global interaction is achieved in combination with a multi-layer perceptron, and local-to-global progressive fusion is completed; and constructing bidirectional attention flow enhanced cross-domain and cross-scale collaboration, and combining with standardized data training to obtain a prediction model. According to the invention, the method can improve the depiction capability of non-stable and non-linear complex time sequence data containing abrupt change and multi-period superposition, gives consideration to the adaptability of long and short term prediction, remarkably improves the accuracy of multi-field time sequence prediction, and promotes the application of the prediction technology in multiple scenes.

Description

Technical Field

[0001] This application relates to the field of time series prediction technology in multiple scenarios, and in particular to a time series prediction method and system based on dual-domain feature fusion. Background Technology

[0002] Time series forecasting is a core technology that uses the dynamic patterns and time-step dependencies of historical data to quantitatively infer future data trends. It plays an irreplaceable supporting role in many fields such as weather forecasting, energy dispatching, traffic management, and financial analysis. For example, the meteorological field needs to use multiple indicators such as temperature and humidity to support disaster prevention and mitigation decisions; the energy system needs to rely on power load forecasting to optimize grid dispatching; and the transportation sector needs to use traffic flow forecasting to alleviate road network congestion. These scenarios all place high demands on the accuracy, efficiency, and adaptability of forecasting models to complex data.

[0003] Current research on time series forecasting both domestically and internationally has seen a trend of multiple technical approaches advancing in parallel. However, existing technical systems have not yet fully overcome the core difficulties in long-series forecasting and exhibit significant common limitations: Traditional methods based on statistical models (such as the ARIMA series, STL decomposition, and exponential smoothing models) rely on rigorous mathematical theory, assume data stationarity and linear relationships, offer strong interpretability, and have been widely applied to short-series, low-complexity scenarios such as univariate monthly sales data forecasting. ARIMA uses differencing to stationaryize the series, and STL separates the seasonal, trend, and residual components of the series. However, limited by the assumptions of stationarity and linearity, they cannot adapt to the non-stationary and nonlinear characteristics of long-series data, and struggle to handle cross-variable correlations in multi-channel data, particularly in high-frequency bursts. In complex scenarios with multiple cycles and variations, prediction accuracy drops significantly. Machine learning-based prediction methods (such as Support Vector Machines (SVM), Random Forests, and Gradient Boosting Trees (XGBoost / LightGBM)) can better handle non-stationary and non-linear data through nonlinear mapping or ensemble learning strategies, demonstrating superior performance compared to traditional statistical models in short-to-medium sequence prediction tasks. However, they suffer from limitations such as insufficient ability to capture long-term dependencies in long sequences and the need to manually design cross-channel feature interaction strategies for multi-channel data, restricting their application in high-dimensional long-sequence scenarios. Deep learning-based prediction methods, such as Recurrent Neural Networks (RNNs) and their variants LSTM / GRU, Convolutional Neural Networks (TCNs), and Graph Neural Networks (GCNs), offer various solutions. While the Transformer architecture, at its core, overcomes the limitations of traditional methods, it still has shortcomings in adapting to the complex characteristics of long sequences. Regarding the basic model, LSTM / GRU alleviates the gradient vanishing problem of RNNs through gating mechanisms, but its computational complexity increases exponentially with sequence length, making it difficult to handle sequences longer than 100 steps. TCN expands the receptive field through dilated convolutions but is weak in capturing global trends. GCN requires domain prior knowledge to model spatial relationships, limiting its versatility. In terms of multi-scale feature representation, temporal modeling (TimeMixer, AMD) only focuses on multi-granular features in the temporal domain, ignoring high-frequency abrupt changes in the video domain. Frequency domain modeling (WPMixer, TimesNet) extracts frequency components using wavelets / Fourier transforms, but... Ignoring the continuous dynamics of the time domain leads to the fragmentation of information between the two domains. In terms of local-global fusion and cross-dimensional collaboration, models such as DeformableTST and TimePro struggle to balance local detail representation, global interaction, and progressive fusion. Models such as CrossFormer and PatchTST either neglect cross-channel collaboration or lack cross-channel dependency mining. In summary, existing deep learning-based time series models have not solved the core problems of dual-domain collaborative representation, local-to-global progressive fusion, and multi-scale and channel fusion interaction. Faced with the complex characteristics of long-series non-stationarity, multi-period superposition, and high-frequency mutations, it is difficult to fully mine the inherent laws of data and cannot fully meet the actual needs of various fields for high-precision and high-robust prediction.

[0004] Patent (CN120124686A) discloses a time series prediction method, apparatus, device, and storage medium. Its core solution focuses on multi-variable, multi-scale feature mining, specifically including: acquiring first time series data spanning at least two variables; extracting second time series data at at least two different time scales; and finally outputting predicted data for the second time period through time node feature interaction and variable node feature interaction. This method improves the model's robustness to noise through multi-scale and multi-variable dual interaction, but it has significant drawbacks: First, it does not involve the extraction and fusion of frequency domain features, limiting itself to multi-scale division and interaction within the time domain. This fails to capture key information such as periodic fluctuations in the frequency dimension, resulting in limited prediction accuracy for non-stationary sequences. Second, the feature interaction process does not distinguish between local details and global trends, achieving information fusion only through node-level interaction. This makes it difficult to accurately characterize the correlation between local details and global trends in time series data, easily leading to detail loss in long-series prediction scenarios.

[0005] Patent (CN119622319A) discloses a time series prediction method based on periodic embedding and multi-scale features. Targeting the temperature prediction scenario of electric transformers, it extracts periodic patterns, decomposes non-periodic residuals into high and low frequency components, and combines graph convolutional networks with residual connection optimization to achieve feature fusion. While this method improves prediction stability for specific scenarios through multi-scale decomposition and periodic embedding, it still has shortcomings: Firstly, it does not introduce frequency domain-specific modeling methods; the periodic pattern extraction is based solely on time-domain statistical analysis, failing to accurately characterize the periodic distribution of the frequency dimension. Secondly, global trend capture relies on spatial correlation modeling using graph convolutional networks, lacking a dedicated module for the gradual fusion of local and global time series data. As the sequence length increases, it is prone to the problem of long-range trends becoming disconnected from local details, making it difficult to transfer to long-sequence prediction scenarios such as meteorology and energy.

[0006] Patent (CN120124686A) discloses a time series forecasting method, apparatus, device, and storage medium. Its core solution focuses on multi-variable, multi-scale feature mining, aiming to improve prediction performance by fully utilizing the multi-dimensional correlation information of data. The implementation process of this method includes: collecting and preprocessing first time series data containing at least two related variables to ensure data integrity and consistency; extracting at least two second time series data at different time scales from the first time series data based on preset time scale division rules to achieve multi-dimensional coverage of short-term fluctuations and medium-to-long-term trends; constructing a dedicated feature interaction module to realize feature interaction between time nodes and feature interaction between variable nodes, with the dual interaction mechanism working synergistically to comprehensively mine hidden correlation information under multiple variables and multiple time scales; finally, inputting the fused features into a prediction network to output the predicted data for the target second time period. This method, through its dual interaction design of multi-scale and multi-variable, effectively enhances the model's adaptability to noise in the data and improves the stability of the prediction results.

[0007] Patent (CN119622319A) discloses a time series prediction method based on periodic embedding and multi-scale features, designed for the specific industrial scenario of transformer temperature prediction. The technical process is as follows: The input transformer temperature time series data is preprocessed to remove outliers and redundant information; time series statistical analysis and pattern recognition techniques are used to accurately extract periodic patterns from the preprocessed data, while the non-periodic residuals in the time series are split into high- and low-frequency components using filtering or decomposition algorithms. The high-frequency components capture short-term rapid fluctuations, while the low-frequency components reflect long-term slow trends; to further enhance feature association mining, a graph convolutional network is introduced to transform different feature dimensions or monitoring nodes into nodes in a graph structure, capturing spatial associations and dependencies between features through graph convolution operations; finally, through the synergistic effect of multi-scale decomposition and periodic embedding, combined with the feature enhancement capabilities of graph convolution and residual connections, the stability and reliability of transformer temperature prediction in this specific scenario are significantly improved.

[0008] While the two types of time series prediction methods mentioned above have made some progress in multivariate modeling and multi-scale feature mining, providing effective ideas for improving prediction performance, from the perspective of broader application scenarios and more complex data characteristics, existing deep learning-based time series prediction methods have not yet effectively solved the core technical problems of dual-domain collaborative representation, local-to-global progressive fusion, and cross-channel and cross-scale dual-domain feature fusion. These bottlenecks limit the model to single-domain modeling, making it difficult to accurately capture key information about high-frequency peaks and low-frequency trends in the data. At the same time, they easily cause local details to be separated from global trends, failing to effectively utilize the correlation between different scales and channels. When faced with the non-stationarity, multi-period superposition, and high-frequency abrupt changes of long-sequence data, it is difficult to fully mine the inherent laws of the data and cannot fully meet the actual needs of various fields for high-precision and robust prediction. Summary of the Invention

[0009] The purpose of this application is to provide a time series prediction method and system based on dual-domain feature fusion, which can improve the accuracy of time series prediction in various fields.

[0010] To achieve the above objectives, this application provides the following solution:

[0011] Firstly, this application provides a time series prediction method based on a dual-domain feature fusion mechanism, including:

[0012] Acquire long and short sequence datasets and perform preprocessing to generate regularized multivariate time series;

[0013] The long and short sequence datasets cover target monitoring data in fields such as meteorology, energy, and transportation. For example, temperature, humidity, and wind speed data in the meteorology field; power load data in the energy field; and traffic flow data in the transportation field. They contain multi-dimensional observations from several continuous historical time units. The preprocessing process needs to remove outliers caused by equipment failure or data acquisition errors.

[0014] Normalization is used to eliminate the distributional differences in data over time, ultimately yielding standard multivariate time series data.

[0015] Multi-scale feature decomposition of multivariate time series is performed by using time-domain multi-scale downsampling to obtain multi-time granular feature data;

[0016] Discrete wavelet transform is used to perform multi-level eigendecomposition on multivariable time series to obtain detailed and approximate feature data of multiple components in the time-frequency domain.

[0017] Patch-based segmentation and embedding processing is performed on time-domain multi-granularity feature data and frequency-domain multi-component feature data to obtain local feature units;

[0018] Local detail capture within the patch is performed on the patched feature representation to obtain temporal correlation features within the patch; the local detail extraction adopts a two-layer depthwise separable convolution operation.

[0019] A global trend extraction operation is performed between patches on local detail data. The global trend capture uses a multilayer perceptron mixer to extract global dependencies.

[0020] A dual-domain bidirectional cross-attention mechanism is constructed to enhance the global features of the two domains across domains and scales, resulting in dual-domain collaboratively enhanced features.

[0021] The features at each scale in the two domains are respectively passed through a linear prediction layer to reconstruct the wavelet domain multi-resolution features, and the time domain multi-scale components are averaged and fused.

[0022] This time series forecasting model is used to predict future trends in multiple fields.

[0023] Optionally, normalization can be used to eliminate distributional differences in the data over time, resulting in standard multivariate time series data, specifically including:

[0024] Given a multivariate time series segment X L ={x t-L+1 ,x t-L+2 ,…x t}, where L is the length of the sequence, x t Represents the multivariate observations at time t;

[0025] Calculate the input time series segment X L The mean μ and standard deviation σ of each variable dimension are obtained through the formula... X L Normalized to a distribution with a mean of 0 and a standard deviation of 1, we obtain the standard multivariate time series data X. L1 ;

[0026] Optionally, multi-scale feature decomposition of multivariate time series is performed using time-domain multi-scale downsampling to obtain multi-time-granularity feature data, specifically including:

[0027] Given a standardized multivariate time series segment X L1 ={x′ t-L+1 ,x′ t-L+2 ,…,x′ t}, where L is the length of the sequence, x′ t Represents the multivariate observations at time t;

[0028] Using formula Multi-scale downsampling decomposition is performed on each variable in the time series to obtain multi-granular features in the time domain; where LI-Down(·) represents linear interpolation downsampling operation, and n is the number of time-domain decomposition levels. The sequence after the i-th level decomposition has a length of L / 2. i-1 .

[0029] Optionally, discrete wavelet transform is used to perform multi-level eigenvalue decomposition on the multivariate time series to obtain detailed and approximate feature data of multiple components in the time-frequency domain, specifically including:

[0030] Given a standardized multivariate time series segment X L1 ={x′ t-L+1 ,x′ t-L+2 ,…,x′ t}, where L is the length of the sequence, x′ t Represents the multivariate observations at time t;

[0031] Using formula and Multi-level wavelet decomposition is performed on each variable of the time series to obtain multi-resolution features in the wavelet domain, i.e., [x m (a),x m (d),x m-1 (d),…x 1 (d)]=DWT(X L1 ,ψ,m); where x i (a) represents the approximate coefficients after decomposition in the i-th dimension, i.e., low-frequency features. * indicates a convolution operation. i+1 (d) represents the detail coefficients after the (i+1)th level decomposition, x i+1 (a) represents the approximate coefficients after the (i+1)th level decomposition, m is the wavelet decomposition level, and ψ is the wavelet type.

[0032] Optionally, patching and embedding processing is performed on the time-domain multi-granularity feature data and the frequency-domain multi-component feature data to obtain local feature units, specifically including:

[0033] Given time series segments of each scale component in a dual-domain environment Where L S Let C be the sequence length of the i-th scale component, and C be the number of variables;

[0034] Using formula X p =Patching(X) m )∈R C×N×P Overlap patch cutting is performed on the components at each scale of the two domains, and each variable sequence is cut to obtain Each patch is mapped to a D-dimensional feature space via a linear embedding layer to obtain X. d ∈R C ×N×D Where, Patching(·) represents the patch cutting operation, N is the number of patches, P is the patch length, V is the step size, and L is the number of patches. SThis represents the sequence length at the corresponding scale.

[0035] Optionally, a local detail capture operation is performed on the patched feature representation to obtain temporal correlation features within the patch, specifically including:

[0036] Using formula X″ d =BN(G(DS-Conv(BN(G(DS-Conv(X p The features are treated as residuals using two depthwise separable 1D convolutions, and 2D-Batch normalization and GELU activation are applied multiple times during the process; where BN(·) represents 2D-Batch normalization, G(·) represents the GELU activation function, and DS-Conv(·) refers to depthwise separable convolution.

[0037] Optionally, a global trend extraction operation between patches can be performed on local detail data, specifically including:

[0038] The features mined from local temporal correlations are then subjected to dimensionality permutation and normalization, i.e., X″ d1 =BN(P(X″) d After adjusting the dimensions, a multilayer perceptron mixer combined with residual connections is used to complete cross-patch interaction in the embedded dimension, i.e., X″. d2 =X″ d1 +L2(G(L1(X″ d1 )); where L1: represents layer 1 in the multilayer perceptron mixer, and L2: represents layer 2 in the multilayer perceptron mixer.

[0039] Optionally, a dual-domain bidirectional cross-attention mechanism is constructed to enhance global features across two domains across different domains and scales, and to collaboratively enhance features across both domains. The attention calculation of the dual-domain bidirectional cross-attention mechanism satisfies the following:

[0040] formula and Two intersecting attention flows are calculated separately: one from the wavelet domain to the time domain and the other from the time domain to the wavelet domain. Finally, the fusion weights are output through a gating layer, resulting in the wavelet fusion feature and the time-domain fusion feature. The fusion process can be represented as:

[0041] X” W =g W ·W′ T +(1-g W )·g W and X″ T =g T ·T′ W +(1-g T )·g T ;in, To embed the square root of the feature dimension, Q(W), K(W), and V(W) are the features from the wavelet domain branch as the query, key, and value, respectively, and Q(T), K(T), and V(T) are the features from the time domain branch as the query, key, and value, respectively. W and g T These are the dynamic gate weights in the wavelet domain and the time domain, respectively.

[0042] Optionally, the features at each scale in the two domains are respectively passed through a linear prediction layer to reconstruct the wavelet domain multi-resolution features, and the time domain multi-scale components are averaged and fused.

[0043] The expressions for the wavelet domain prediction layer and reconstruction process are as follows:

[0044]

[0045] in, For X” W The approximate coefficient sequence and the detail coefficient sequence after splitting;

[0046] The expressions for the temporal prediction layer and reconstruction process are as follows:

[0047]

[0048]

[0049] The final prediction result is Y = αY W +(1-α)Y T ∈R C×T ; where α is the learnable weight.

[0050] Secondly, this application provides a time series prediction system based on dual-domain feature fusion, comprising:

[0051] The data acquisition module is configured to acquire long and short series datasets covering fields such as meteorology, energy, and transportation, wherein the datasets contain multi-dimensional observations of several consecutive historical time units;

[0052] The preprocessing module is configured to preprocess the acquired dataset, remove outliers, and eliminate data distribution differences through normalization operations to generate standard multivariate time series.

[0053] The multi-scale decomposition module is configured to perform bi-domain multi-scale feature decomposition on the standard multivariate time series respectively.

[0054] The patch embedding module is configured to perform patching and embedding processing on dual-domain multi-scale feature data to obtain local feature units.

[0055] The local detail capture module is configured to mine temporal correlation features within local feature units through two-layer depthwise separable convolutions;

[0056] The global feature interaction module is configured to use a multilayer perceptron mixer to extract global dependencies between patches, achieving a gradual fusion from local to global.

[0057] The dual-domain collaborative enhancement module is configured to construct a dual-domain bidirectional cross-attention mechanism to enhance the dual-domain global features across domains and scales, generating dual-domain collaborative enhanced features.

[0058] The prediction fusion module is configured to input the features of each scale in the dual domain into the linear prediction layer, reconstruct the wavelet domain multi-resolution features and fuse the time domain multi-scale components, and output the prediction results of the future change trend of multi-domain data.

[0059] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0060] This application provides a time series prediction method and system based on dual-domain multi-scale fusion. It acquires long and short series datasets covering meteorology, energy, transportation, and other fields, preprocesses them to remove outliers caused by equipment failures or data acquisition errors, generating regular multivariate time series. Then, it uses Reversible Instance Normalization (ReVIN) to eliminate distributional differences in data over time, obtaining standard multivariate time series data. Next, it performs multi-scale feature decomposition on the multivariate time series through temporal multi-scale downsampling to extract multi-temporal granular feature data, while simultaneously employing Discrete Wavelet Transform (DWT). WaveletTransform (DWT) performs multi-level feature decomposition on multivariate time series to extract detailed and approximate feature data of multiple components in the time and frequency domains, and then integrates them to obtain a dual-domain, dual-branch, multi-scale basic feature representation of multi-domain time series. Next, the time-domain multi-granularity feature data and the frequency-domain multi-component feature data are patched and embedded to generate local feature units. The temporal correlation features within the patches are captured through a two-layer depthwise separable convolution (DS-Conv) operation. Then, a multi-layer perceptron (MLP) mixer is used to mine global dependencies between patches to extract global trend features, constructing a progressive fusion link from local details to global trends. Furthermore, a dual-domain bidirectional cross-attention mechanism (DB-CrossAtten) is used to enhance the dual-domain global features across domains and scales, resulting in dual-domain collaborative enhancement features. Finally, the features at each scale of the dual domains are input into a linear prediction layer. Feature optimization is completed by reconstructing wavelet domain multi-resolution features and averaging the fusion of time-domain multi-scale components, ultimately training a time series prediction model. This application proposes a dual-domain feature fusion mechanism. Through Downsampling and DWT algorithms, it achieves precise decoupling of dual-domain features. Combining patch-based embedding with local-global fusion and DB-CrossAtten to enhance feature interaction, it constructs a cross-domain, cross-scale, and cross-channel dual-domain feature fusion system. This system can more effectively and comprehensively mine key information such as non-stationary characteristics, multi-period superposition, and high-frequency abrupt changes in multi-domain time series data, improving the ability to capture complex time series patterns while balancing prediction accuracy and computational efficiency. This improves the accuracy of time series predictions in multiple fields such as meteorology, energy, and transportation, achieving the goal of accurately predicting future trends of key indicators in multiple fields. Accurate predictions of meteorological disasters, energy supply and demand, and traffic flow can assist in disaster prevention and mitigation decision-making, energy scheduling optimization, and rational allocation of transportation resources, supporting efficient urban operation, sustainable energy utilization, and improved public service quality. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 A flowchart of the time series prediction method based on dual-domain feature fusion provided in this application;

[0063] Figure 2 The flowchart illustrates the time series prediction method based on dual-domain feature fusion provided in this application. Detailed Implementation

[0064] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0065] This method targets time series data in fields such as meteorology, energy, transportation, and electricity, and adopts a "training-testing-prediction" process to achieve accurate predictions. First, the dataset is divided into training and testing sets in an 8:2 ratio. If in training mode, the training data is loaded and the settings are initialized. After reversible normalization of the training data, approximation coefficients and multi-level detail coefficients are extracted through discrete wavelet transform, and multi-granular features are extracted through time-domain downsampling. Then, the components at each scale are patched, cut, and embedded. The feature interaction is enhanced through progressive fusion from local details to global trends and a dual-domain bidirectional cross-attention mechanism. Finally, the trained optimal model parameters are saved and the test mode is entered. If in prediction mode, the time series data to be predicted is loaded, the future horizon ph (i.e., the prediction time range) is set, the optimal model parameters are loaded, and the prediction results are obtained. After the prediction is completed, the prediction results of all variables within the future horizon ph are output, and the process ends.

[0066] This application proposes a time series prediction method and system based on dual-domain feature fusion. First, standard time series data are obtained by preprocessing and normalizing time series datasets from meteorology, energy, transportation, and power sectors. Second, approximation coefficients, multi-level detail coefficients, and multi-granularity features are extracted from the time series to construct a multi-feature sequence representation based on the time series. Patch-based embedding is performed on each scale component to achieve progressive fusion from local to detailed aspects, and a dual-domain bidirectional cross-attention mechanism is used to enhance feature interaction. Finally, the model is trained to obtain optimal model parameters, thereby achieving prediction of the predicted data. This application solves the problems of fragmented dual-domain information and insufficient local-to-global collaboration in existing time series prediction methods through dual-domain multi-scale fusion and progressive feature interaction. It achieves high-precision prediction of long and short series in multiple fields such as meteorological disaster early warning, energy supply and demand scheduling, and traffic flow control, providing strong support for scientific decision-making and resource optimization in various fields.

[0067] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] In one exemplary embodiment, this application provides a time series prediction method based on dual-domain feature fusion. For example... Figure 1 and Figure 2 As shown, the time series prediction method based on dual-domain feature fusion provided in this application includes the following steps 1 to 10.

[0069] Step 1: Obtain and preprocess the long and short series datasets to obtain a regularized multivariate time series. The long and short series datasets include the values ​​of multidimensional data over several consecutive historical natural days.

[0070] For example, the power load dataset used is the smart meter monitoring data of various distribution substations in a certain province's power grid from March to June of a certain year. Based on the raw data, the hourly active power, reactive power, voltage deviation, and other electricity consumption information of residents in the corresponding date and region can be obtained, thereby constructing a multi-dimensional power load dataset covering residential, industrial, and commercial scenarios.

[0071] Step 2: Normalization is used to eliminate the distributional differences in the data over time, resulting in standard multivariate time series data. The normalization process is as follows:

[0072] Given a multivariate time series segment X L ={x t-L+1 ,x t-L+2 ,…,x t}, calculate the input time series segment X L The mean and standard deviation of each variable dimension, X LNormalized to a distribution with a mean of 0 and a standard deviation of 1, we obtain the standard multivariate time series data X. L1 Normalization can be obtained using formula (1):

[0073]

[0074] Where L is the length of the sequence, x t Let represent the multivariate observation at time t, μ represent the mean of the time series segment across all variables, and σ represent the standard deviation.

[0075] Step 3: Perform multi-scale feature decomposition on the time-domain multivariate time series using linear interpolation downsampling to obtain multi-time-granularity feature data. The linear interpolation downsampling process is as follows:

[0076] Given a standardized multivariate time series segment X(T), the variables of the time series are downsampled and decomposed at multiple scales. The linear interpolation downsampling can be calculated using formula (2):

[0077]

[0078] Where X(T) is the original multivariate sequence, T∈{t-L+1,t-L+2,…,t}, X i (T') is the sequence after downsampling at the i-th layer, with a length of L / 2. i-1 T' is the time index of the new sequence after downsampling at the i-th layer, T0 is the left sampling point (rounded down) adjacent to the mapping position in the original sequence, and T1 is the right sampling point (rounded up) adjacent to the mapping position in the original sequence.

[0079] Finally, the features at each scale {X1(T'), X2(T'), ..., X} are obtained through the above process. i (T')}, with lengths respectively

[0080] Step 4: Perform multi-level eigenvalue decomposition on the multivariate time series using discrete wavelet transform to obtain detailed and approximate feature data of multiple components in the time-frequency domain. The processing procedure of the discrete wavelet transform algorithm is as follows:

[0081] Given a standardized multivariate time series segment X L1 ={x′ t-L+1 ,x′ t-L+2 ,…,x′ t}, where L is the length of the sequence, x′ t Represents the multivariate observations at time t;

[0082] Using the given high-pass and low-pass filters, multi-level wavelet decomposition is performed on each variable of the time series to obtain multi-resolution features in the wavelet domain. The detail coefficients and approximation coefficients of the (i+1)th dimension can be calculated using formulas (3) and (4), respectively:

[0083]

[0084] Where, x i (a) represents the approximate coefficients after decomposition in the i-th dimension, i.e., low-frequency features. * indicates a convolution operation. i+1 (d) represents the detail coefficients after the (i+1)th level decomposition, x i+1 (a) represents the approximate coefficients after the (i+1)th level decomposition, where m is the wavelet decomposition level and ψ is the wavelet type.

[0085] To avoid information redundancy, only the approximation coefficients of the final layer m are retained, while the approximation coefficient sequence from layer 1 to (m-1) is discarded. This yields the approximation coefficients of the m-th level decomposition and the detail coefficients of each level, i.e., {x} m (a),x m (d),x m-1 (d),…x 1 (d)}.

[0086] Step 5: Perform patching and embedding processing on the time-domain multi-granularity feature data and the frequency-domain multi-component feature data to obtain local feature units. The patching and embedding process is as follows:

[0087] Given time series segments of each scale component in a dual-domain environment Overlap patch cutting is performed on each scale component, and each variable sequence is cut to obtain Each patch is mapped to a D-dimensional feature space via a linear embedding layer. Patch cutting and embedding are calculated using formula (5):

[0088]

[0089] Among them, L s Let C be the length of the m-th sequence, C be the number of variables, N be the number of patches after the cut, P be the patch length, and V be the step size. For X m The univariate sequence corresponding to the c-th variable in W emb Let b be the weight matrix of the linear embedding layer, with dimensions D×P. emb The bias vector of the linear embedding layer has dimension D. Let D be the embedding feature of the s-th sequence, the c-th variable, and the k-th patch.

[0090] Ultimately, several embedded local unit features X can be obtained. d ∈RC×N×D .

[0091] Step 6: Perform local detail capture operation on the patched feature representation to obtain the temporal correlation features within the patch. The process of local detail capture operation is as follows:

[0092] First, the patch features are normalized using 2D-Batch, then dimension substitution is performed. Next, two depthwise separable 1D convolutions are used as feature residuals to mine local temporal dependencies along the patch length dimension. This process involves multiple rounds of 2D-Batch normalization and GELU activation. This operation can be obtained using formulas (6), (7), and (8):

[0093] X′ d =P(BN(X) d (6)

[0094] X′ d1 =BN(G(DS-Conv(X) p ))) (7)

[0095] X″ d =BN(G(DS-Conv(X′) d1 ))) (8)

[0096] Where BN(·) represents 2D-Batch normalization, G(·) represents the GELU activation function, and DS-Conv(·) refers to depthwise separable convolution, including depthwise convolution and pointwise convolution.

[0097] Step 7: Use a multilayer perceptron mixer to perform global trend extraction between patches on the local detail data. The global trend extraction process is as follows:

[0098] After mining the local temporal correlation, the features are subjected to dimension permutation and 2D-Batch normalization again. After adjusting the dimensions, cross-feature interaction is completed in the embedding dimension through a multilayer perceptron mixer. First, the embedding dimension is expanded to tf times the original dimension through a linear layer. Then, nonlinearity is introduced through GELU activation to enhance the feature expression. Combined with Dropout to suppress overfitting, the feature is finally compressed back to the original dimension D through a linear layer. At the same time, residual connections are introduced to superimpose the original features with the features processed by the multilayer perceptron, and finally construct a feature representation that combines local details and global context. This operation process can be obtained through formulas (9) and (10):

[0099] X″ d1 =BN(P(X″) d (9)

[0100] X″ d2 =X″ d1+Linear2(G(Linear1(X″ d1 ))) (10)

[0101] Among them, Linear1∶R D×C×N →R D×C×N*tf This represents layer 1, Linear2:R in a multilayer perceptron mixer. D×C×N*tf →R D×C×N This represents layer 2 in the multilayer perceptron mixer.

[0102] Step 8: Construct a dual-domain bidirectional cross-attention mechanism to enhance global features across domains and scales, and to collaboratively enhance features across both domains. The operation process of the attention mechanism of the dual-domain bidirectional cross-attention mechanism is as follows:

[0103] After the patch embedding local-to-global progressive fusion process, the average of each branch in terms of the number of patches is first taken, and then the branches of wavelet domain multi-scale and time domain multi-scale are combined respectively. They can be calculated using formulas (11) and (12):

[0104]

[0105] Where, X″ d2 [:,n,:] represents the subtensor of all variables and all feature dimensions of the nth patch. Summing n from 1 to n and dividing by N achieves information aggregation across the patch dimensions, yielding X. d3 Stack(·) represents stacking features at different scales together, and S represents the number of scales in the wavelet domain or time domain.

[0106] To adapt to the computational dimension of the bidirectional cross-attention mechanism, the features are first reorganized, combining wavelet features and temporal features X″. d3 ∈R C×S×D Transform into X″ d3 ∈R CS×D Then, in the wavelet-to-time domain attention interaction, the recombined wavelet sequence is used as the query, and the time-domain sequence is used as both the key and value, inputting into the cross-attention layer. The wavelet-to-time domain cross-attention can be calculated using formula (13):

[0107]

[0108] in, It is the square root of the embedded feature dimension.

[0109] In the cross-attention interaction from the time domain to the wavelet domain, the reconstructed time domain sequence is used as the query, and the wavelet sequence is used as the key and value for cross-attention calculation. The cross-attention between the time domain and the wavelet domain can be calculated using formula (14):

[0110] T′W =CrossAttn(Q=X″) d3 (T), K = X″ d3 (W), V=X″ d3 (W))

[0111]

[0112] After completing the bidirectional attention interaction, the enhanced features are restored to their original dimensions. The fusion result W′ of the wavelet domain and time domain branches is then used. T ∈R CS×D and T′ W ∈R CS×D Transform back to W″ T ∈R C×S×D and T′ W ∈R C×S×D Finally, the fusion weights output by the gated layer are introduced to obtain the wavelet fusion features and the temporal fusion features. The fusion process can be calculated using formulas (15) and (16):

[0113] X″ W =g W ·W′ T +(1-g W )·g W (15)

[0114] X″ T =g T ·T′ W +(1-g T )·g T (16)

[0115] Among them, g W and g T These are the dynamic gate weights in the wavelet domain and the time domain, respectively.

[0116] Finally, the overall features in the wavelet domain and time domain after bidirectional cross-attention enhancement are decomposed into scale features in each of the two domain branches. The overall feature decomposition in the wavelet domain and time domain is calculated by formulas (17) and (18), respectively:

[0117]

[0118] in, and These are the approximation coefficients and detail coefficients at level s after bidirectional cross-attention enhancement, respectively. Let be the i-th scale sequence after time-domain partitioning. To simplify the notation in subsequent derivations, the partitioned approximate coefficient sequence will be referred to as in the following text. and detail coefficient sequence Unified To refer to.

[0119] Step 9: The features at each scale in the dual domain are respectively passed through the linear prediction layer to reconstruct the wavelet domain multi-resolution features, and the time domain multi-scale components are averaged and fused. Finally, the dual-domain prediction results are fused. The operation process of dual-domain prediction is as follows: the wavelet domain scale components are reconstructed after passing through the prediction layer and calculated by formulas (19) and (20):

[0120]

[0121] Wherein, Linear(·): R C×D →R C×T For a linear prediction layer, T is the prediction length of each branch sequence, Reconstitution(·) is the wavelet reconstruction operation, Intercepting(·) is the method to truncate the reconstructed tensor to T, and Y... W ∈R C×T This represents the final prediction result in the wavelet domain.

[0122] The wavelet domain components at each scale are averaged and fused after passing through the prediction layer, and are calculated using formulas (20) and (21):

[0123]

[0124]

[0125] Wherein, Linear(·): R C×D →R C×T For a linear prediction layer, T represents the prediction length of each branch sequence. Y represents the prediction result at the i-th scale in the time domain, where n is the number of scales in the time domain. T This represents the final prediction result in the time domain.

[0126] Finally, learnable weights are used to combine wavelet domain and time domain prediction results to adjust the dual-branch contribution and complete the entire long sequence prediction process. The prediction result fused from the time domain and time domain is calculated using formula (23):

[0127] Y = αY W +(1-α)Y T (twenty three)

[0128] Where α is the learnable weight.

[0129] Step 10: Use a time series prediction model with dual-domain feature fusion to predict the future trend of changes in multi-domain data.

[0130] For example, given an electricity load dataset, the training data and test data are first divided in an 8:2 ratio. Then, the encoder and decoder are trained using the standardized multi-feature representation of the training data to obtain the optimal model parameters. After that, the optimal model parameters are loaded, and the model performance is evaluated using the standardized multi-feature representation of the test data to determine the time series prediction model with dual-domain feature fusion. Finally, based on the actual needs, the time series prediction model is used to predict the hourly electricity consumption of the target group in future periods.

[0131] In the performance evaluation of the model, since the traditional L2 Loss calculation of the loss function assumes that the time steps are independent, in order to avoid this problem, the mean squared error (MSE) and mean absolute error (MAE) are calculated by combining the time domain loss function and the frequency domain loss function during model training. The time domain loss function and the frequency domain loss function can be calculated by formula (24):

[0132]

[0133] Where N is the total number of test samples, and Y is the true value of each test sample. For each test sample, the predicted value, For the traditional time-domain loss, M is a learnable frequency-domain mask, ⊙ represents pointwise multiplication, and the frequency-domain mask and frequency-domain loss are multiplied element-wise to achieve weighting of different frequency components, and λ is the weight of the time-domain and frequency-domain loss weighting.

[0134] Based on multi-domain prediction datasets, predictions were made using this application and other methods on multiple datasets in the fields of electricity, weather, energy, and exchange rates. The prediction results are compared in Table 1.

[0135] Table 1 Comparison of multi-domain prediction results of this application with other methods.

[0136]

[0137] Based on multi-domain prediction applications, this application preprocesses the acquired multi-domain datasets to obtain corresponding time series, and uses the extracted time series feature information as input into the model for prediction. This improves prediction accuracy while maintaining interpretability. The model predicts the changing trends of various domains in specific future periods, providing power companies with precise load dispatching references, optimizing power generation capacity planning and power resource allocation; providing the energy industry with supply and demand balance analysis to optimize energy storage and dispatch strategies; providing meteorological disaster early warning support to reduce risk losses; and providing financial institutions, enterprises, and investors with accurate exchange rate forecasts to assist in risk management, thus contributing to scientific decision-making, efficient resource allocation, and stable operation across multiple industries. This application proposes the following three innovations in time series prediction: 1 . 1. A dual-domain, multi-scale decomposition mechanism is proposed. Different feature information, such as high-frequency peaks and low-frequency trends, are extracted from time-series data through downsampling and the DWT algorithm, enriching the feature representation of time-series data. 2. A patch-based, local-to-global progressive fusion mechanism is proposed. A depthwise separable convolution and a multilayer perceptron mixer are used to mine temporal correlations within patches and global interactions across patches, achieving coherent feature capture from local details to global trends. 3. A cross-domain bidirectional cross-attention mechanism is proposed. A bidirectional cross-attention flow is designed to mine cross-domain correlations, activate multi-scale cross-channel complementarity, and enhance the capture of key information.

[0138] Compared with existing technologies, this application has the following advantages: 1. Existing technologies rely solely on multi-scale decomposition in a single domain, i.e., pure time domain or pure frequency domain, failing to consider the complementary information of time domain continuity and frequency domain frequency distribution. The time series prediction mechanism proposed in this application explores a dual-domain multi-scale feature decoupling mechanism, focusing on multiple types of model features, such as high-frequency features, low-frequency features, and overall trends at different scales, enriching the model's information utilization capabilities and greatly improving prediction performance. 2. Existing technologies struggle to balance local detail characterization with global correlation efficiency. The patched local-global progressive fusion mechanism proposed in this application divides the sequence into patch local units, progressively fusioning from local details to global trends, fully capturing key local and global information, thereby improving prediction accuracy and outputting more accurate prediction results for the target variable. 3. Existing technologies do not achieve simultaneous cross-scale and cross-channel dual-domain feature fusion. This application utilizes a bidirectional cross-attention mechanism to enhance feature interaction complementarity in the channel and scale dimensions, achieving multi-dimensional feature fusion across domains, scales, and channels, activating the synergistic value of multiple feature information, and enhancing the model's ability to accurately model complex time series patterns.

[0139] In one exemplary embodiment, this application also provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0140] In one exemplary embodiment, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0141] In one exemplary embodiment, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0142] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant laws and regulations.

[0143] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0144] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0145] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0146] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A time series prediction method based on dual-domain feature fusion, characterized in that, include: Acquire long and short sequence datasets and perform preprocessing to generate well-organized multivariate time series; The long and short sequence datasets cover target monitoring data in fields such as meteorology, energy, and transportation, such as temperature, humidity, and wind speed data in the meteorology field, power load data in the energy field, and traffic flow data in the transportation field. They contain multi-dimensional observations of several continuous historical time units. The preprocessing process needs to remove outliers caused by equipment failure or data acquisition errors. Normalization is used to eliminate the distributional differences in data over time, ultimately yielding standard multivariate time series data; Multi-scale feature decomposition of multivariate time series is performed by using time-domain multi-scale downsampling to obtain multi-time granular feature data; Discrete wavelet transform is used to perform multi-level eigendecomposition on multivariable time series to obtain detailed and approximate feature data of multiple components in the time-frequency domain. Patch-based segmentation and embedding processing is performed on time-domain multi-granularity feature data and frequency-domain multi-component feature data to obtain local feature units; Local detail capture within the patch is performed on the patched feature representation to obtain temporal correlation features within the patch; the local detail extraction adopts a two-layer depthwise separable convolution operation. A global trend extraction operation is performed between patches on local detail data. The global trend capture uses a multilayer perceptron mixer to extract global dependencies. A dual-domain bidirectional cross-attention mechanism is constructed to enhance the global features of the two domains across domains and scales, resulting in dual-domain collaboratively enhanced features. The features at each scale in the two domains are respectively passed through a linear prediction layer to reconstruct the wavelet domain multi-resolution features, and the time domain multi-scale components are averaged and fused. A time series prediction model using dual-domain feature fusion is used to predict future trends in multiple domains.

2. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, Normalization is used to eliminate the distributional differences in data over time, resulting in standard multivariate time series data, specifically including: Given a multivariate time series segment X L ={x t-L+1 ,x t-L+2 ,...,x t }, where L is the length of the sequence, x t Represents the multivariate observations at time t; Calculate the input time series segment X L The mean μ and standard deviation σ of each variable dimension are obtained through the formula... X L Normalized to a distribution with a mean of 0 and a standard deviation of 1, we obtain the standard multivariate time series data X. L1 .

3. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, Multi-scale feature decomposition of multivariate time series is performed using time-domain multi-scale downsampling to obtain multi-time-granular feature data, specifically including: Given a standardized multivariate time series segment X L1 ={x′ t-L+1 ,x′ t-L+2 ,…,x′ t }, where L is the length of the sequence, x′ t Represents the multivariate observations at time t; Using formula Multi-scale downsampling decomposition is performed on each variable in the time series to obtain multi-granular features in the time domain; where LI-Down(·) represents linear interpolation downsampling operation, and n is the number of time-domain decomposition levels. The sequence after the i-th level decomposition has a length of L / 2. i-1 .

4. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, Discrete wavelet transform is used to perform multi-level eigenvalue decomposition on multivariate time series data, obtaining detailed and approximate feature data of multiple components in the time-frequency domain, specifically including: Given a multivariate time series segment X L1 ={x t-L+1 ,x t-L+2 ,…x t }, where L is the length of the sequence, x t Represents the multivariate observations at time t; Using formula and Multi-level wavelet decomposition is performed on each variable of the time series to obtain multi-resolution features in the wavelet domain, i.e., [x m (a),x m (d),x m-1 (d),...,x 1 (d)]=DWT(X L1 ,ψ,m); where x i (a) represents the approximate coefficients after decomposition in the i-th dimension, i.e., low-frequency features. * indicates a convolution operation. i+1 (d) represents the detail coefficients after the (i+1)th level decomposition, x i+1 (a) represents the approximate coefficients after the (i+1)th level decomposition, m is the wavelet decomposition level, and ψ is the wavelet type.

5. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, Patching and embedding processes are performed on time-domain multi-granularity feature data and frequency-domain multi-component feature data to obtain local feature units, specifically including: Given time series segments of each scale component in a dual-domain environment Where is the length of the corresponding scale component, and C is the number of variables; Using formula X p =Patching(X) m )∈R C×N×P Overlap patch cutting is performed on the components at each scale of the two domains, and each variable sequence is cut to obtain Each patch is mapped to a D-dimensional feature space via a linear embedding layer to obtain X. d ∈R C×N×D Where, Patching(·) represents the patch cutting operation, N is the number of patches, P is the patch length, and V is the step size.

6. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, The patched feature representation is subjected to local detail capture operations within the patch to obtain temporal correlation features within the patch, specifically including: Using formula X″ d =BN(G(DS-Conv(BN(G(DS-Conv(X p The features are treated as residuals using two depthwise separable 1D convolutions, with multiple passes of 2D-Batch normalization and GELU activation. Here, BN(·) represents 2D-Batch normalization, G(·) represents the GELU activation function, and DS-Conv(·) refers to depthwise separable convolution.

7. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, Perform global trend extraction operations between patches on local detailed data, specifically including: The features mined from local temporal correlations are then subjected to dimensionality permutation and normalization, i.e., X″ d1 =BN(P(X″) d After adjusting the dimensions, a multilayer perceptron mixer combined with residual connections is used to complete cross-patch interaction in the embedded dimension, i.e., X″. d2 =X″ d1 +L2(G(L1(X″ d1 )); where L1: represents layer 1 in the multilayer perceptron mixer, and L2: represents layer 2 in the multilayer perceptron mixer.

8. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, A dual-domain bidirectional cross-attention mechanism is constructed to enhance global features across two domains and scales, and to collaboratively enhance features across both domains. The attention calculation of the dual-domain bidirectional cross-attention mechanism is as follows: formula and Two intersecting attention flows are calculated separately: one from the wavelet domain to the time domain and the other from the time domain to the wavelet domain. Finally, the fusion weights are output through a gating layer, yielding the wavelet fusion feature and the time-domain fusion feature. The fusion process can be represented as: X″ W =g W ·W′ T +(1-g W )·g W and X″ T =g T ·T′ W +(1-g T )·g T ;in, To embed the square root of the feature dimension, Q(W), K(W), and V(W) are the features from the wavelet domain branch as the query, key, and value, respectively, and Q(T), K(T), and V(T) are the features from the time domain branch as the query, key, and value, respectively. w and g T These are the dynamic gate weights in the wavelet domain and the time domain, respectively.

9. The time prediction method based on dual-domain feature fusion according to claim 1, characterized in that, The features at each scale in the two domains are respectively passed through a linear prediction layer to reconstruct the wavelet domain multi-resolution features, and the time domain multi-scale components are averaged and fused. The expressions for the wavelet domain prediction layer and reconstruction process are as follows: in, Let X′ W The approximate coefficient sequence and the detail coefficient sequence after splitting; The expressions for the temporal prediction layer and reconstruction process are as follows: The final prediction result is Y = αY w +(1-α)Y T ∈R C×T ; where α is the learnable weight.

10. A time series prediction system based on dual-domain feature fusion, executing a time series prediction method based on dual-domain feature fusion as described in any one of claims 1-9, comprising: The data acquisition module is configured to acquire long and short series datasets covering fields such as meteorology, energy, and transportation, wherein the datasets contain multi-dimensional observations of several consecutive historical time units; The preprocessing module is configured to preprocess the acquired dataset, remove outliers, and eliminate data distribution differences through normalization operations to generate standard multivariate time series. The multi-scale decomposition module is configured to perform bi-domain multi-scale feature decomposition on the standard multivariate time series respectively. The patch embedding module is configured to perform patching and embedding processing on dual-domain multi-scale feature data to obtain local feature units. The local detail capture module is configured to mine temporal correlation features within local feature units through two-layer depthwise separable convolutions; The global feature interaction module is configured to use a multilayer perceptron mixer to extract global dependencies between patches, achieving a gradual fusion from local to global. The dual-domain collaborative enhancement module is configured to construct a dual-domain bidirectional cross-attention mechanism to enhance the dual-domain global features across domains and scales, generating dual-domain collaborative enhanced features. The prediction fusion module is configured to input the features of each scale in the dual domain into the linear prediction layer, reconstruct the wavelet domain multi-resolution features and fuse the time domain multi-scale components, and output the prediction results of the future change trend of multi-domain data.

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