A chaotic time series prediction method based on multi-scale decomposition
By combining multi-scale adaptive decomposition and bi-branch long short-term memory network optimization, the problems of prediction accuracy and stability of one-dimensional chaotic time series data are solved, and structured prediction result analysis is provided.
Patent Information
- Application Number
- CN202610245256.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-02
- Publication Date
- 2026-07-10
Smart Images
Figure CN122365321A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of artificial intelligence and signal processing technology, and in particular relates to a chaotic time series prediction method based on multi-scale decomposition. Background Technology
[0002] Chaotic time series signals are a type of one-dimensional time series data that has significant value in applications such as random number generation, secure information communication, and broadband signal processing. However, this type of time series data typically exhibits strong nonlinearity and multi-scale dynamic changes, leading to shortcomings in the prediction accuracy and stability of traditional prediction methods and existing deep learning models.
[0003] Such data typically have a finite predictable time window, and their predictive performance is highly sensitive to the embedding time span and feature construction method. Traditional linear modeling methods struggle to effectively characterize their inherent dynamic structure. In recent years, deep learning methods, represented by Long Short-Term Memory (LSTM) networks, have made significant progress in one-dimensional time-series prediction tasks. However, these methods are often considered "black box" models, as their internal decision-making processes lack interpretability, limiting their application in scenarios requiring high reliability and controllability.
[0004] To improve model interpretability, existing techniques attempt to combine signal processing methods such as wavelet analysis with deep learning models. One type of method uses fixed wavelet basis functions (such as the Daubechies 4 wavelet) to pre-decompose the original signal, and then inputs the decomposed subsequences into the prediction network. However, in this type of method, the wavelet basis functions cannot be adaptively optimized for specific prediction tasks, and the decomposition process and the prediction process are independent of each other. It is difficult to maintain a stable mapping relationship between the decomposition results and the original signal while ensuring prediction performance, thus limiting its performance ceiling.
[0005] Another approach attempts to introduce learnable wavelet filters and perform end-to-end joint training with the prediction network. However, in this type of approach, there is often an optimization conflict between the decomposition objective and the prediction objective, the training process is unstable, and the decomposition structure may degenerate when the prediction loss dominates, causing the decomposition results to lose clear structural meaning, thereby weakening interpretability.
[0006] Furthermore, existing research has proposed interpretable LSTM architectures (such as DeLELSTM) for multivariate time series data, which quantify the predictive contributions of each input variable through a two-branch LSTM structure and least squares fitting methods. However, these methods rely on the multivariate input format and cannot be directly applied to one-dimensional time series data scenarios, thus making it difficult to automatically construct component-level features with clear physical or frequency meanings from a single time series.
[0007] Therefore, existing technologies lack a prediction method that, while ensuring prediction accuracy and training stability, enables multi-scale decomposition and collaborative modeling of the prediction process, and provides a structured analysis basis for the prediction results, for one-dimensional time series data. Summary of the Invention
[0008] To overcome the problems in existing technologies, such as the disconnect between fixed multi-scale decomposition and prediction tasks, the tendency of learnable decomposition structures to degrade during end-to-end training, and the difficulty of adapting existing interpretable deep learning methods to one-dimensional time series data, this invention provides a chaotic time series prediction method based on multi-scale decomposition.
[0009] The present invention provides a chaotic time series prediction method based on multi-scale decomposition, comprising the following steps:
[0010] Step 1: Obtain the chaotic time series signal, which is one-dimensional chaotic time series data.
[0011] Step 2: The input one-dimensional chaotic time series data first enters the multi-scale adaptive decomposition module. This module performs i-level decomposition on the input one-dimensional chaotic time series data to obtain K sub-sequence components. At the same time, this module also includes a reconstruction module for reconstructing constraints; where K=i+1.
[0012] Step 3: Upsample the above K subsequence components to the original signal length and concatenate them in the channel dimension to construct a fused feature tensor.
[0013] Step 4: Input the fused feature tensor into a parallel two-branch long short-term memory network.
[0014] The dual-branch long short-term memory network consists of two branches: one branch is a standard LSTM, which embeds the output signal into the globally synthesized hidden state over the time span; the other branch, a tensorized long short-term memory network, outputs a tensorized hidden matrix, with each row corresponding to the hidden state representation of a component.
[0015] Step 5: At each time step, the tensor-quantized hidden matrix is used to fit the integrated hidden state vector by introducing regularized least squares to obtain the prediction alignment weight vector.
[0016] Step 6: The tensor quantization hidden matrix is compressed at the hidden unit dimension to obtain the component-level compressed hidden state representation. Based on the prediction alignment weight vector and the compressed hidden state, a fused hidden state vector is generated.
[0017] Step 7: Input the fused hidden state vector into the lightweight prediction layer and obtain the temporal prediction value through linear mapping.
[0018] Step 8: During training, jointly optimize the prediction loss based on the predicted value and the reconstruction loss based on signal reconstruction to achieve collaborative optimization between the decomposition layer and the prediction layer.
[0019] Furthermore, in step 2, the multi-scale adaptive decomposition module is implemented through convolutional downsampling operations, using a learnable wavelet decomposition filter bank to decompose the one-dimensional time-series signal into K-1 high-frequency components and one lowest-frequency component.
[0020] Furthermore, in step 2, the convolution kernel of the reconstruction module is obtained by adding its corresponding time-flipped form of the decomposition filter coefficients to a learnable residual term initialized to 0:
[0021] (1)
[0022] in, Represents the i-th level reconstruction sequence. For the weights of the i-th decomposition filter, This indicates a time reversal operation. For learnable residuals initialized to zero, It is a scaling factor less than 1.
[0023] Furthermore, the fitting process in step 5 corresponds to solving the following regularized least squares problem:
[0024] (2)
[0025] in, Let the tensor be the hidden matrix. Let be the comprehensive hidden state vector. This is the regularization coefficient.
[0026] Furthermore, step 6 specifically includes:
[0027] By compressing the tensor-quantized hidden matrix along the hidden unit dimension, we obtain a component-level compressed state representation. .
[0028] By aligning the prediction weights With compression state This indicates that fusion is performed to generate an interpretable hidden state vector. : .
[0029] Furthermore, the total loss function of the co-optimization in step 8 for:
[0030] (3)
[0031] in, For the loss based on the predicted output, The reconstruction loss is based on the difference between the input signal and the reconstructed signal. and These are the weighting coefficients.
[0032] Minimize the total loss function using gradient descent. This allows for the simultaneous updating of learnable parameters in the multi-scale adaptive decomposition module, reconstruction module, bi-branch long short-term memory network, and linear layers.
[0033] The beneficial technical effects of this invention compared to the prior art are as follows:
[0034] This invention constructs an intrinsic structured mechanism while maintaining high prediction accuracy through designs such as learnable multi-scale decomposition and weakly constrained reconstruction, bi-branch dynamic fitting, and semi-cooperative optimization, and provides an analyzable intermediate representation basis for the prediction results. Attached Figure Description
[0035] Figure 1 This is an architecture diagram of a chaotic time series prediction method based on multi-scale decomposition according to the present invention.
[0036] Figure 2 This is a flowchart illustrating the multi-scale adaptive decomposition module.
[0037] Figure 3 This is a flowchart for reconstructing the module.
[0038] Figure 4 This is a diagram of a dual-branch long short-term memory network architecture.
[0039] Figure 5 The bar chart shows the prediction performance over different embedding time spans.
[0040] Figure 6 The bar chart shows the influence intensity of the normalized component prediction. Detailed Implementation
[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0042] This invention discloses a chaotic time series prediction method based on multi-scale decomposition. First, the original one-dimensional chaotic time series data is decomposed into learnable multi-scale values to construct pseudo-multivariate inputs with structural meaning. A weakly constrained reconstruction mechanism maintains a stable mapping relationship between the decomposition results and the original signal. Then, the decomposed multi-scale time series features are input into a parallel bi-branch long short-term memory network. One branch learns the global integrated state of the signal embedding over a time span L, while the other branch characterizes the independent time series state representation of each decomposed component. The hidden states output by the two branches at each time step are correlated through a regularized least-squares fitting process to generate a set of prediction alignment weights, representing the alignment relationship between component-level states and the overall predicted state. Based on this, the component features are weighted and converged to form a fused hidden state vector for prediction. Finally, the time series prediction result is output through a lightweight linear layer.
[0043] The process of this invention is as follows Figure 1 As shown, a collaborative optimization strategy is employed during model training. By jointly constraining the prediction loss and reconstruction loss, the model maintains stable structured intermediate representations while ensuring predictive performance. The resulting intermediate weights and states can be used for further predictive behavior analysis during the inference phase. Specifically, this includes:
[0044] Step 1: Obtain the chaotic time series signal, which is one-dimensional chaotic time series data.
[0045] Step 2: The input one-dimensional chaotic time series data first enters the multi-scale adaptive decomposition module. This module performs i-level decomposition on the input one-dimensional chaotic time series data to obtain K sub-sequence components. At the same time, this module also includes a reconstruction module for reconstructing constraints; where K=i+1.
[0046] Step 3: Upsample the above K subsequence components to the original signal length and concatenate them in the channel dimension to construct a fused feature tensor.
[0047] Step 4: Input the fused feature tensor into a parallel two-branch long short-term memory network.
[0048] The dual-branch long short-term memory network consists of two branches: one branch is a standard LSTM, which embeds the output signal into the globally synthesized hidden state over the time span; the other branch, a tensorized long short-term memory network, outputs a tensorized hidden matrix, with each row corresponding to the hidden state representation of a component.
[0049] Step 5: At each time step, the tensor-quantized hidden matrix is used to fit the integrated hidden state vector by introducing regularized least squares to obtain the prediction alignment weight vector.
[0050] Step 6: The tensor quantization hidden matrix is compressed at the hidden unit dimension to obtain the component-level compressed hidden state representation. Based on the prediction alignment weight vector and the compressed hidden state, a fused hidden state vector is generated.
[0051] Step 7: Input the fused hidden state vector into the lightweight prediction layer and obtain the temporal prediction value through linear mapping.
[0052] Step 8: During training, jointly optimize the prediction loss based on the predicted value and the reconstruction loss based on signal reconstruction to achieve collaborative optimization between the decomposition layer and the prediction layer.
[0053] The flowchart of the multi-scale adaptive decomposition module of this invention is as follows: Figure 2 As shown, this module performs an i-th order decomposition on the input one-dimensional chaotic time series data, generating a total of K (K=i+1) subsequence components with different scale characteristics, thereby transforming the original univariate time series into a pseudo-multivariate representation with structural meaning. The decomposition process is implemented based on a learnable filter bank and is adaptively adjusted according to the prediction task during training.
[0054] To ensure that the learnable decomposition process maintains a clear structured foundation, this invention introduces a reconstruction module after the multi-scale decomposition module. This module applies reconstruction constraints to each sub-sequence component obtained from the decomposition, thereby maintaining a stable mapping relationship between the decomposition result and the original signal. The flowchart is shown below. Figure 3 As shown. This module employs a "flip-residual" weakly constrained reconstruction mechanism, where the reconstruction weights are composed of the time flip of the corresponding decomposition filter coefficients and the addition of a learnable residual term, mathematically expressed as:
[0055] (1)
[0056] in, Represents the i-th level reconstruction sequence. For the weights of the i-th decomposition filter, This indicates a time reversal operation. For learnable residuals initialized to zero, It is a scaling factor less than 1.
[0057] This design ensures that the model is strictly invertible at the beginning of training, and during the training process, by reconstructing the loss constraints, the system eventually forms a set of non-orthogonal, weakly constrained reconfigurable filters. This allows the model to maintain the stability of the decomposition structure while preserving its predictive performance, providing a structural basis for subsequent analysis.
[0058] Since the convolutional downsampling operation shortens the sequence length of each component, it is necessary to restore the time length of all components to their original scale to facilitate subsequent temporal modeling based on recurrent neural networks. This invention employs linear interpolation to upsample each component. Finally, the upsampled K decomposition components are concatenated along the channel dimension to form a fused feature tensor. Where B is the batch size and L is the embedding time span.
[0059] At the feature learning and interaction level, this invention addresses the pseudo-multivariate features formed after adaptive decomposition of one-dimensional chaotic time-series data, and fuses the feature tensor. Given a parallel, two-branch long short-term memory network architecture, its network architecture diagram is as follows. Figure 4 As shown. One branch is a standard LSTM, responsible for learning and fusing information from all components embedded over the time span, outputting the globally synthesized hidden state. Where N is the dimension of the hidden state. Another branch is tensor LSTM, which models the independent temporal dynamics of each component by designing independent gating parameters for each decomposition component, outputting a tensor quantized hidden state matrix. , where D is the number of features, and each row corresponds to the hidden state representation of one component.
[0060] The key element of this invention lies in the dynamic weight fitting mechanism, which utilizes a least squares method with L2 regularization at each time step to tensorize the component states of the LSTM. Using this as a basis, fit the comprehensive state of the standard LSTM. The component-level temporal representations obtained from multi-scale decomposition are correlated with the overall temporal representation.
[0061] The current prediction alignment weight vector is obtained by solving the regularized least squares problem. This fitting process corresponds to solving the following regularized least squares problem:
[0062] (2)
[0063] in, This is the regularization coefficient.
[0064] Furthermore, Compressing at its last hidden unit dimension yields a component-level compressed hidden state representation. This allows the high-dimensional hidden state to be mapped to component features in scalar form.
[0065] The weight vector It changes dynamically over time. This is achieved by using a weight vector... With component-level compression hidden state This indicates that fusion is performed to generate a fused hidden state vector. : .
[0066] Will The input is passed to a lightweight linear layer and linearly mapped to obtain the final predicted value. This fused hidden state vector is only used for prediction at the current time step and is not fed back to the recurrent network, but can serve as the basis for subsequent prediction behavior analysis.
[0067] To coordinate the optimization of different parts of the model, this invention employs a collaborative optimization training strategy. This strategy utilizes a weighted total loss function. Optimize:
[0068] (3)
[0069] in, For the loss based on the predicted output, The reconstruction loss is based on the difference between the input signal and the reconstructed signal. and These are the weighting coefficients.
[0070] This strategy allows the model to maintain a structured foundation while prioritizing prediction accuracy as the primary optimization objective, constrained by a reconstruction loss. The total loss function is minimized using gradient descent. This allows for the simultaneous updating of learnable parameters in the multi-scale adaptive decomposition module, reconstruction module, bi-branch long short-term memory network, and linear layers.
[0071] Example:
[0072] The embodiment uses numerical simulation of the chaotic photoelectric oscillator structure and sets the feedback loop delay. This generates chaotic time-series data with an oscillation frequency of approximately 10 GHz. The feedback loop gain was selected in this study. and Experiments were conducted on two sets of chaotic time series datasets with different parameters.
[0073] Figure 5 This is a bar chart illustrating the prediction performance of the present invention under different embedding time spans L. Figure 5 Display different system parameters The impact on prediction error can be used to illustrate the applicability and performance stability of the model under different conditions.
[0074] Based on the intermediate variables generated during network forward propagation, this embodiment constructs an interpretive evaluation index to quantify the role of different decomposition components in the prediction process. Specifically, this is achieved by using the fused hidden state statistics corresponding to each component. Its linear layer weights By performing a linear combination, the component-level aligned prediction influence is obtained. :
[0075] (4)
[0076] By the influence quantity By taking the absolute value over the time dimension and normalizing it, we obtain the relative influence intensity of each decomposition component in the overall prediction. :
[0077] (5)
[0078] In this way, the present invention can achieve high-precision time series prediction while also outputting the contribution information of each decomposition component to the prediction result, thereby improving the transparency of the model prediction process and providing a basis for prediction behavior analysis.
[0079] Figure 6 for A line graph showing the relative influence of each component over the same embedding time span can be used to illustrate the magnitude of the role of each component in the prediction process.
Claims
1. A chaotic time series prediction method based on multi-scale decomposition, characterized in that, Includes the following steps: Step 1: Obtain the chaotic time series signal, which is one-dimensional chaotic time series data; Step 2: The input one-dimensional chaotic time series data first enters the multi-scale adaptive decomposition module. This module performs i-level decomposition on the input one-dimensional chaotic time series data to obtain K sub-sequence components. At the same time, this module also includes a reconstruction module for reconstructing constraints; where K=i+1. Step 3: Upsample the above K subsequence components to the original signal length and concatenate them along the channel dimension to construct a fused feature tensor; Step 4: Input the fused feature tensor into a parallel two-branch long short-term memory network; The dual-branch long short-term memory network consists of two branches: one branch is a standard LSTM, which embeds the output signal into the globally synthesized hidden state over the time span; the other branch, a tensorized long short-term memory network, outputs a tensorized hidden matrix, where each row corresponds to the hidden state representation of one component. Step 5: At each time step, the tensor-quantized hidden matrix is used to fit the integrated hidden state vector by introducing regularized least squares to obtain the prediction alignment weight vector. Step 6: The tensor quantizes the hidden matrix and compresses it at the hidden unit dimension to obtain the component-level compressed hidden state representation. Based on the predicted alignment weight vector and the compressed hidden state, a fused hidden state vector is generated. Step 7: Input the fused hidden state vector into the lightweight prediction layer, and obtain the temporal prediction value through linear mapping; Step 8: During training, jointly optimize the prediction loss based on the predicted value and the reconstruction loss based on signal reconstruction to achieve collaborative optimization between the decomposition layer and the prediction layer.
2. The chaotic time series prediction method based on multi-scale decomposition according to claim 1, characterized in that, In step 2, the multi-scale adaptive decomposition module is implemented through convolutional downsampling operation, using a learnable wavelet decomposition filter bank to decompose the one-dimensional time series signal into K-1 high-frequency components and one lowest-frequency component.
3. The chaotic time series prediction method based on multi-scale decomposition according to claim 1, characterized in that, In step 2, the convolution kernel of the reconstruction module is obtained by adding its corresponding decomposition filter coefficients in a time-flipped form and a learnable residual term initialized to 0. （1） in, Represents the i-th level reconstruction sequence. For the weights of the i-th decomposition filter, This indicates a time reversal operation. For learnable residuals initialized to zero, It is a scaling factor less than 1.
4. The chaotic time series prediction method based on multi-scale decomposition according to claim 1, characterized in that, The fitting process in step 5 corresponds to solving the following regularized least squares problem: （2） in, Let the tensor be the hidden matrix. Let be the comprehensive hidden state vector. is the regularization coefficient.
5. The chaotic time series prediction method based on multi-scale decomposition according to claim 1, characterized in that, Step 6 specifically includes: By compressing the tensor-quantized hidden matrix along the hidden unit dimension, we obtain a component-level compressed state representation. ; By aligning the prediction weights With compression state This indicates that fusion is performed to generate an interpretable hidden state vector. : .
6. The chaotic time series prediction method based on multi-scale decomposition according to claim 1, characterized in that, The total loss function of collaborative optimization in step 8 for: （3） in, For the loss based on the predicted output, The reconstruction loss is based on the difference between the input signal and the reconstructed signal. and These are weighting coefficients; Minimize the total loss function using gradient descent. This allows for the simultaneous updating of learnable parameters of the multi-scale adaptive decomposition module, reconstruction module, bi-branch long short-term memory network, and linear layers.