A time series prediction method fusing multi-resolution embedding and spectral adaptive filtering

Abstract

The application discloses a non-stationary time series prediction method fusing multi-resolution embedding and spectrum adaptive filtering, and is realized based on an SFAT-Net architecture: step 1, a multi-scale non-stationary time series benchmark data set is constructed and preprocessed and divided; step 2, an SFAT-Net prediction architecture containing SAFB, MRT-PE and ARDA modules is designed; step 3, a model is trained by inputting preprocessed data, a high-performance model is obtained, and a prediction result curve is generated; step 4, the effectiveness and complementarity of each module are verified through an ablation experiment; and step 5, model deployment is realized, and the prediction effect under different tasks and steps can be visualized. The application innovatively designs SAFB and integrates MRT-PE and ARDA, strengthens multi-scale representation and long-range frequency capture, relieves non-stationarity, improves robustness, and greatly optimizes the non-stationary time series prediction performance.

Description

[0001] A time series prediction method integrating multi-resolution embedding and spectral adaptive filtering Technical Field

[0003] This invention relates to the fields of data mining and machine learning technology, and in particular to a time series prediction method that integrates multi-resolution embedding and spectral adaptive filtering. It is applicable to the accurate prediction of multi-scale non-stationary time series in engineering scenarios such as smart grid operation monitoring, traffic flow prediction, meteorological disaster early warning, and power transformer temperature monitoring. Background Technology

[0005] Time series forecasting is a core research area in data mining and machine learning. Its forecasting accuracy directly determines the scientific validity and effectiveness of engineering decisions such as smart grid scheduling, transportation resource allocation, and meteorological disaster prevention and control. Real-world engineering scenarios often exhibit inherent characteristics such as strong non-stationarity, complex long-range time series dependencies, multi-scale frequency fluctuations, and dynamic distribution shifts, posing significant challenges to the design of efficient forecasting models.

[0006] Traditional time series forecasting methods mainly rely on statistical models such as ARIMA, exponential smoothing, and linear regression. These methods fit data patterns based on fixed mathematical assumptions and cannot adapt to the nonlinear fluctuations and high-dimensional coupling characteristics of modern large-scale time series. Their performance degrades significantly when dealing with long-term forecasting tasks and non-stationary data.

[0007] With the development of deep learning technology, data-driven prediction models such as Transformer, CNN, and MLP have emerged one after another, but they still have many technical shortcomings: Transformer-type models (such as iTransformer and PatchTST) capture long-range dependencies through self-attention mechanisms, but suffer from high computational complexity and limited ability to extract multi-scale information in the frequency domain; CNN-type models (such as ModernTCN) rely on local convolution to efficiently extract temporal features, but are difficult to model long-distance global associations; MLP-type models (such as TimeMixer) simplify the network structure to improve computational efficiency, but lack targeted designs for multi-scale feature fusion and non-stationarity adaptation.

[0008] Furthermore, the conventional normalization strategies employed by existing prediction models rely on fixed statistical features at the dataset level, which cannot adapt to the dynamic distribution shifts of time series over time. This leads to instability in the model inference process and further reduces the robustness of the prediction results. Meanwhile, most existing models focus solely on time-domain or frequency-domain modeling, lacking an efficient fusion mechanism for spectral-time features, making it difficult to simultaneously capture both the global trend and local fluctuations of time series.

[0009] Therefore, there is an urgent need for an efficient prediction method that addresses the inherent characteristics of non-stationary time series, solving problems such as insufficient long-range dependency modeling, weak multi-scale feature extraction capability, poor adaptability to distribution shift, and low efficiency of spectral-temporal feature fusion in existing technologies, so as to achieve high-precision, high-robustness, and high-efficiency prediction of non-stationary time series.

[0010] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0012] The purpose of this invention is to provide a time series prediction method that integrates multi-resolution embedding and spectral adaptive filtering, thereby solving the problems of insufficient long-range dependency modeling, weak multi-scale feature extraction capability, poor adaptability to dynamic distribution shift, and low efficiency of spectral-temporal feature fusion in non-stationary time series prediction.

[0013] To achieve the above objectives, this invention provides a non-stationary time series prediction method based on an improved SFAT-Net model, comprising:

[0014] Step 1: Collect raw non-stationary time series data, and complete data preprocessing and dataset partitioning;

[0015] Step 2: Improve the SFAT-Net model by optimizing the ARDA module, upgrading the MRT-PE module, and enhancing the SAFB module;

[0016] Step 3: Train the model to obtain an efficient trained model and output prediction results and performance metrics;

[0017] Step 4: Perform an ablation experiment;

[0018] Step 5: Deploy the method and visualize its predictive application effects in real-world engineering scenarios.

[0019] Preferably, in the above technical solution, the non-stationary time series raw data obtained in step 1 includes time series data with different sampling frequencies, different sequence lengths, and different environmental conditions.

[0020] Preferably, in the above technical solution, the preprocessing in step 1 includes outlier removal, missing value imputation, and sequence sliding window segmentation. The dataset is divided into training set, validation set, and test set according to industry-standard proportions to ensure the integrity, validity, and rationality of the data and training.

[0021] Preferably, in the above technical solution, step 2, improving the SFAT-Net model, includes:

[0022] (1) The ARDA module is optimized and integrated into the input layer of SFAT-Net. This module achieves instance-level reversible normalization by calculating the temporal mean and standard deviation of each channel of each instance, and then introduces channel-level learnable affine transformation to improve feature flexibility. The core calculation process of this module can be expressed as follows:

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[0028] in, Given the input sequence, For batch size, For sequence length, For channel dimension, This is the minimum value for numerical stability. , For channel-level learnable scaling and offset parameters, These are normalized spatial predictions.

[0029] (2) The MRT-PE module in the backbone network of the original SFAT-Net model is upgraded to an improved MRT-PE module. This module first performs non-overlapping patching on the sequence, then achieves multi-resolution decomposition through discrete wavelet transform, and completes linear projection after scale alignment and feature stitching. Its core calculation process can be expressed as follows:

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[0036] in, Where DWT is the patch length and DWT is the discrete wavelet transform. This is a low-frequency approximation component. For high-frequency detail components, , For scale alignment function, Embed dimensions into the model.

[0037] (3) The SAFB module is enhanced in the spectrum-time fusion part of the original SFAT-Net model. This module realizes the conversion from time domain to frequency domain through fast Fourier transform. After static spectrum filtering and input adaptive spectrum modulation, it is restored to time domain features through inverse Fourier transform. Then, the spectrum-time feature fusion is completed by combining the gating mechanism. Its core calculation process can be expressed as:

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[0046] in, For Fast Fourier Transform, For spectral representation, For learnable static spectral filters, For element-wise multiplication, It is the Sigmoid activation function. It is a feedforward network. For channel-level splicing, , For gating layer weights and biases.

[0047] Preferably, in the above technical solution, step 3 trains the model on the training set of the non-stationary time series dataset, using the Adam optimizer to iteratively optimize the model parameters, with the learning rate starting from... Based on the performance of the validation set, a hybrid MAE loss function with joint time-domain and frequency-domain supervision was selected to obtain an efficient prediction model after training using the improved method. The loss function expression is as follows:

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[0049] in For time domain loss, For frequency domain loss, For balance coefficient, The total number of samples, These are the model's predicted values. For the true value, For Fast Fourier Transform.

[0050] Preferably, in the above technical solution, step 3 inputs the preprocessed non-stationary time series test data into the trained model to obtain the model's prediction results, and outputs the true value-predicted value comparison curve, error distribution heatmap, and core performance indicators such as MSE, MAE, MAPE, and RMSE.

[0051] Preferably, in the above technical solution, step 4, conducting ablation experiments on a non-stationary time series dataset, includes combining and training each improved module to obtain the MSE, MAE values ​​and GFLOPs of each model, and comparing the specific results.

[0052] Preferably, in the above technical solution, step 5 exports the model to ONNX format based on the PyTorch framework, deploys it to an edge computing device or cloud server, visualizes the prediction effect of the method in actual engineering scenarios such as smart grids, traffic flow, and meteorological disaster early warning, and applies the method to the decision-making system of actual industrial production and social operation.

[0053] (1) This invention is an improved non-stationary time series prediction method based on the SFAT-Net model. It optimizes the ARDA module, upgrades the MRT-PE module, and enhances the SAFB module on the original SFAT-Net model. The optimized ARDA module effectively mitigates the adverse effects of dynamic distribution shifts through instance-level reversible normalization and symmetric inverse normalization, improving the model's adaptability to non-stationary data and its robustness in inference. The upgraded MRT-PE module, through multi-resolution decomposition using discrete wavelet transform, allows each token to simultaneously encode low-frequency trends and high-frequency details, strengthening the model's multi-scale feature extraction capabilities and enriching the temporal representation dimensions. The enhanced SAFB module, through a combination of frequency-domain static filtering and adaptive modulation, efficiently captures long-range frequency dependencies, improving the efficiency of spectral-temporal feature fusion while suppressing redundant high-frequency noise, comprehensively improving the model's accuracy and robustness in predicting non-stationary time series.

[0054] (2) This invention is a non-stationary time series prediction method based on the SFAT-Net model. When this method is deployed to edge computing devices or cloud servers and applied to real-world engineering automation decision-making, it can collect field data in real time and complete high-precision online prediction. It is suitable for various engineering scenarios such as smart grids, traffic scheduling, and weather warning. The specific effect exceeds the theoretical practical application, providing reliable data support for resource allocation, risk prevention and control and operation monitoring, and improving the operational efficiency of industrial and social systems. Attached Figure Description

[0056] Figure 1 This is a flowchart of a time series prediction method that integrates multi-resolution embedding and spectral adaptive filtering according to the present invention.

[0057] Figure 2 This is a diagram illustrating the overall architecture of non-stationary time series forecasting methods.

[0058] Figure 3 This is a diagram of the enhanced SAFB module (Spectral Adaptive Filtering).

[0059] Figure 4 This is a structural diagram of the upgraded MRT-PE module (wavelet multi-resolution embedding);

[0060] Figure 5 This is the optimized ARDA module structure diagram;

[0061] Figure 6 This is a heatmap of the cointegration attention distribution of non-stationary sequences;

[0062] Figure 7 This is a heatmap of the attention distribution within a non-stationary sequence;

[0063] Figure 8 It is a heatmap of attention distribution within a stationary sequence;

[0064] Figure 9 It is a radar chart comparing the performance of multiple datasets;

[0065] Figure 10 This is a bar chart of the ablation experiment results;

[0066] Figure 11 It is a visualization of the prediction results with a 96-step length;

[0067] Figure 12 This is a visualization of the prediction results with a 336-step timeframe. Detailed Implementation

[0069] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0070] Unless otherwise expressly stated, throughout the specification and claims, the term "comprising" or its variations such as "including" or "comprises" shall be understood to include the stated elements or components without excluding other elements or other components.

[0071] like Figures 1 to 12 As shown, a time series prediction method integrating multi-resolution embedding and spectral adaptive filtering includes the following steps:

[0072] Step 1: Collect raw non-stationary time series data, and complete data preprocessing and dataset partitioning.

[0073] (1) Considering the characteristics of non-stationary time series in actual engineering scenarios, such as multi-scale fluctuations and distribution shifts, the original data collected in this invention includes time series data with different sampling frequencies (minute level, hour level, day level), different sequence lengths (as short as 96 time steps and as long as 720 time steps) and different environmental conditions.

[0074] (2) For the preprocessing of the original data, we invited professionals in the field of data mining to process it using a standardized process: First, outliers were removed by the 3σ criterion and missing values ​​were filled by linear interpolation; then, sliding window segmentation was performed according to a fixed time window to construct input-output sample pairs (the length of the input sequence was set to 96 or 720 depending on the scenario, and the prediction step size covered multiple horizons such as 96, 192, 336, and 720); finally, the dataset was divided into training set, validation set and test set in a ratio of 7:2:1, which were used for model training, hyperparameter tuning and performance verification, respectively, to ensure the integrity, validity and rationality of the data and training.

[0075] Step 2: Improve the SFAT-Net model by optimizing the ARDA module, upgrading the MRT-PE module, and enhancing the SAFB module.

[0076] (1) The ARDA module was optimized and integrated into the input layer of SFAT-Net as the first feature processing module after data preprocessing. This module dynamically adapts to non-stationary distribution shifts through instance-level reversible normalization, and adds a feature stability verification mechanism to further improve the robustness of the model. The core calculation process of the ARDA module follows the original formula in the paper, as follows:

[0077] First, calculate the time-series mean and standard deviation for each channel of each instance:

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[0079] in, Given the input sequence, For batch size, For sequence length, For channel dimension, It is the minimum value for numerical stability (takes a value of 1e-6).

[0080] Normalization based on instance-level statistical features:

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[0082] Introducing channel-level learnable affine transformations enhances feature flexibility:

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[0084] in, , The channel-level learnable scaling and offset parameters are adaptively updated via backpropagation.

[0085] After the prediction is completed, the original scale is restored by symmetric inverse normalization:

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[0088] in, This is a normalized spatial prediction. This is the final predicted value. The design effectively isolates the interference of non-stationary distribution shifts through a symmetrical process of "normalization-modeling-denormalization," while preserving the original statistical characteristics of the data.

[0089] (2) The MRT-PE module in the backbone network of the original SFAT-Net model is upgraded to an improved MRT-PE module, and the scale alignment function after wavelet decomposition is optimized to enhance the representation ability of multi-scale features. The core calculation process of this module follows the original formula in the paper, as follows:

[0090] First, the normalized sequence is divided into non-overlapping patch partitions:

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[0092] in, Patch length (set to 16 or 32 depending on dataset characteristics). This represents the number of patches.

[0093] Perform a J-level discrete wavelet transform (DWT) on each patch to decompose it into low-frequency trend components and high-frequency detail components:

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[0095] in, It is a low-frequency approximation component (capturing global trends). For high-frequency detail components (capturing local fluctuations). Set the decomposition scale (default is 3).

[0096] The wavelet coefficients of different lengths are mapped to a unified dimension using a scaling alignment function:

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[0098] in, , For learnable or deterministic scale alignment operations, ensure that coefficients of different resolutions are projected onto a consistent feature space.

[0099] The aligned multi-scale features are stitched together and linearly projected to generate patch tokens.

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[0103] in, Set the embedding dimension for the model (default is 512). For the final constructed token sequence, ensure that each token simultaneously encodes multi-scale frequency information.

[0104] (3) The SAFB module is enhanced in the spectral-temporal fusion part of the original SFAT-Net model. The initialization strategy and gating fusion mechanism of the static spectral filter are optimized to improve the efficiency of spectral-temporal feature fusion. The core calculation process of this module follows the original formula in the paper, as follows:

[0105] First, perform a Fast Fourier Transform (FFT) on the token sequence to transform it to the frequency domain:

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[0107] in, For Fast Fourier Transform, Spectral representation.

[0108] Enhance low-frequency trends and suppress high-frequency noise using a static spectral filter:

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[0110] in, It is a learnable static spectral filter (initialized with a low-pass prior). This is an element-wise multiplication in the frequency domain.

[0111] Introducing input adaptive spectral modulation to dynamically adapt to different sequence characteristics:

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[0114] in, It is a lightweight mapping function. It is the Sigmoid activation function. For dynamic spectral response weights.

[0115] The frequency domain features are restored to time domain features using the inverse Fourier transform (IFFT), and residuals are then refined.

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[0118] in, This is a real part extraction operation. It is a feedforward network with residual connections.

[0119] Fusing spectral and temporal features through a gating mechanism:

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[0122] in, For output to the time-domain backbone network, For channel-level splicing, , For the gate layer weights and biases, To achieve adaptive balance of spectral-temporal features through weight fusion.

[0123] Step 3: Train the model to obtain an efficient training model and output prediction results and performance metrics.

[0124] During training, the improved SFAT-Net model is iteratively trained using the preprocessed training set. The model employs the Adam optimizer specified in the paper for parameter optimization, and the learning rate is calculated from the candidate set. The loss function is adaptively selected based on the performance of the validation set; the loss function is entirely the time-domain-frequency-domain joint supervised hybrid MAE loss function proposed in the paper, and its expression is as follows:

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[0126] Among them, the time-domain average absolute error loss is:

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[0128] Frequency domain mean absolute error loss:

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[0130] Balance coefficient (range of values) (determined through cross-validation of the validation set). The total number of samples, These are the model's predicted values. For the true value, For Fast Fourier Transform.

[0131] Early stopping (with a patience value of 10) is used during training to prevent overfitting. Training stops when the validation set loss shows no decrease for 10 consecutive epochs, and the optimal model is saved. Preprocessed test set data is input into the trained model, and the output includes a true-to-predicted value comparison curve, an error distribution heatmap, and core performance metrics such as MSE, MAE, MAPE, and RMSE, visually demonstrating the model's prediction performance.

[0132] Step 4: Conduct ablation experiments

[0133] Ablation experiments were conducted on the improved SFAT-Net model to verify the effectiveness of each optimization module and the complementarity between modules. The experimental design fully complied with the paper's standards. The specific procedure is as follows:

[0134] Using the original SFAT-Net model as the baseline, we added the ARDA optimization module (+A), the MRT-PE upgrade module (+M), and the SAFB enhancement module (+S) in sequence to construct 7 module combinations (Base, +A, +M, +S, +A+M, +A+S, +M+S, Full), and trained them uniformly on the ETTh1 dataset (keeping the hyperparameters consistent).

[0135] The experimental metrics used were MSE, MAE (to evaluate prediction accuracy), and GFLOPs (to evaluate computational efficiency) specified in the paper, and the performance data of each model were recorded at different prediction step sizes (96, 192, 336, 720).

[0136] Experimental Results Analysis: Adding the ARDA optimization module alone reduced the MAE of the model by 3%-5% on non-stationary datasets, verifying its advantage in distribution shift adaptation; adding the MRT-PE upgrade module alone reduced the MSE of the model on multi-scale fluctuation datasets by 4%-6%, demonstrating the effectiveness of multi-resolution representation; adding the SAFB enhancement module alone reduced the error of the model on long-range dependent datasets by 5%-7%, proving the advantage of spectral-temporal fusion; the Full model (joint optimization of the three modules) achieved the best performance on all datasets and prediction step sizes, with an average MSE reduction of 8%-12% and GFLOPs remaining at a level comparable to the original model, verifying the complementarity between modules and the effectiveness of the improvement strategy.

[0137] Step 5: Deploy and visualize the predictive application effects of this method in real-world engineering scenarios.

[0138] (1) Based on the PyTorch framework, the trained improved SFAT-Net model is exported to the ONNX format to adapt to the deployment requirements of edge computing devices (such as NVIDIA Jetson Xavier NX) and cloud servers (such as Alibaba Cloud ECS GPU instances). Differentiated deployment schemes are designed for different engineering scenarios: for scenarios with high real-time requirements such as smart grids and traffic scheduling, local deployment on edge devices is adopted, and the inference latency is controlled within 100ms; for large-scale scenarios such as meteorological disaster early warning and photovoltaic power prediction, cloud cluster deployment is adopted to support batch data parallel processing.

[0139] (2) Develop a visualization prediction platform that integrates three major functions: data acquisition, online prediction, and result display. The platform collects real-time field sensor data (such as power grid load, traffic flow, and meteorological monitoring data), and after preprocessing, inputs it into the deployment model to obtain prediction results. The platform visualizes and displays real-time prediction values, historical prediction curves, error statistics charts, and early warning threshold prompts. At the same time, it provides an API interface to connect with the engineering decision-making system and automatically converts the prediction results into practical instructions such as resource scheduling suggestions and risk warning signals.

[0140] (3) The improved SFAT-Net model was tested in four practical scenarios: smart grid operation monitoring, traffic flow scheduling, meteorological disaster early warning, and power transformer temperature monitoring. The total testing time exceeded 3 months. The test results showed that the prediction accuracy of the improved SFAT-Net model was 8%-15% higher than that of the original model, while the inference efficiency remained the same, which can effectively support engineering decision-making.

[0141] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A time series prediction method integrating multi-resolution embedding and spectral adaptive filtering, characterized in that, include: Step 1: Construct a multi-scale non-stationary time series benchmark dataset and complete data preprocessing and partitioning; Step 2: Design the SFAT-Net prediction architecture and build three core modules: the spectral adaptive filtering branch SAFB, the multi-resolution temporal patch embedding module MRT-PE, and the adaptive reversible distribution alignment module ARDA. Step 3: Train the SFAT-Net model by inputting preprocessed time series data to complete the training, obtain a high-performance prediction model, and generate prediction result curves. Step 4: Conduct ablation experiments to verify the effectiveness and complementarity of the SAFB, MRT-PE, and ARDA modules; Step 5: Deploy the method and visualize its prediction performance under different prediction tasks and step sizes.

2. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, The time series data obtained in step 1 has strong non-stationarity, complex long-range time series dependence, multi-scale frequency fluctuations and dynamic distribution shift characteristics, covering typical engineering application scenarios such as power transformer temperature, meteorology, traffic flow, and solar power generation.

3. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, Step 1 performs linear interpolation to fill missing values ​​and 3σ principle to remove outliers in the time series data. The data is then divided into training, validation and test sets in a 7:2:1 ratio along the time dimension to ensure the temporal consistency of the data distribution.

4. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, Step 2, building the SFAT-Net model, includes: (1) Construct an adaptive invertible distribution alignment module (ARDA) for the input sequence. (Where B is the batch size, L is the sequence length, and C is the number of channels), calculate the time-series mean and standard deviation for each channel of each instance: in To prevent extremely small values ​​from division by zero, perform instance-level normalization: Introducing channel-level learnable affine transformations: in Learnable scaling and offset parameters; inverse normalization is performed after prediction: (2) Design a multi-resolution timing patch embedding module (MRT-PE) to divide the input sequence into N non-overlapping patches. ( (where P is the patch length), and perform J-level discrete wavelet transform (DWT) on each patch: in As a low-frequency trend component, For the high-frequency detail components at scale j; map them to a unified dimension using a scale alignment function: After concatenation, a token is embedded using linear projection. Finally, construct the token sequence. ( (for the embedding dimension) (3) Construct a spectral adaptive filtering branch (SAFB) for the input features. Perform frequency domain transformation: in For Fast Fourier Transform (FFT) Spectral representation; after static spectral filtering: in For learnable static low-pass filters; input adaptive spectral modulation: in It is a lightweight mapping function. Use the Sigmoid activation function; inverse transform back to the time domain and refine: With time-domain backbone output Through gating fusion: in For channel-level splicing, These are the gating parameters.

5. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, Step 3 uses the Adam optimizer to optimize model parameters, with the learning rate starting from... The middleware is selected based on validation set performance, and joint supervision is conducted using a hybrid MAE loss function: in For time domain loss, For frequency domain loss, This is the balance coefficient; To predict the total number of samples, For predicted values, For the true value, For Fast Fourier Transform, and ( For batch size, For sequence length, (Number of channels).

6. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, Step 3: Divide the test set timing data according to the input length. After slicing, input the data into the trained model and output the predicted step size. The prediction results are obtained, and a comparison curve between the predicted and actual values ​​and an error distribution histogram are generated.

7. The non-stationary time series prediction method based on SFAT-Net according to claim 1, characterized in that, Step 3 uses TimeBridge as the baseline backbone to construct eight model combinations: "Baseline Model, +MRT-PE, +SAFB, +ARDA, +SAFB+ARDA, +MRT-PE+ARDA, +MRT-PE+SAFB, and Full (three-module integration)". Ablation experiments are conducted on the ETTh1 dataset to compare the MSE and MAE metrics of each combination under different prediction step sizes, verifying the effectiveness and complementarity of the modules. The calculation methods for MSE and MAE are as follows: N is the total number of prediction samples. For predicted values, This is the actual value.

8. In the non-stationary time series prediction method based on SFAT-Net according to claim 1, step 5 exports the model to ONNX format using the PyTorch framework, wherein MAPE and RMSE are calculated as follows: This method can be applied to practical engineering scenarios such as smart grid monitoring and meteorological disaster early warning.

Images