## 2 Related Work
### Time-Series Forecasting with Machine Learning  
With the improvement of computing power and the convenience of data acquisition, traditional machine learning models have been introduced into time-series prediction. These models can achieve accurate prediction of time-series data by learning the complex mapping relationship between input features and output targets without explicit modeling [9; 10; 11]. [PERSON] [12] introduced multi-layer perceptron (MLP) into time-series prediction and applied the nonlinear mapping function through the backpropagation algorithm for nonlinear dynamic systems. [PERSON] [13] proposed the Support Vector Regression (SVR) time-series model, which adopted the \(\epsilon\)-insensitive loss function and kernel technique to have a stronger generalization ability for nonlinear data. [PERSON] [14] applied XGBoost to financial market prediction and selected the closing price and trading volume lagging periods as key factors through feature importance analysis, which verified the adaptability of the gradient boosting tree to non-stationary time series. [PERSON] [15] proposed a combined regression framework (CRF), which decomposed multi-step prediction into several independent regression problems and introduced the bagging strategy to reduce variance. [PERSON] [16] proposed a Lazy Learning framework, which dynamically constructs neighbor sub-models through local weighted regression, and realizes stable prediction when the feature dimension is extended to 50 dimensions on UCI multivariate datasets, thus solving the problem of dimension disaster of high-dimensional time series. Recent studies show that linear models are still competitive in high-signal-to-noise-ratio time-series data. [PERSON] [17] used learnable linear layers instead of complex nonlinear transformations and restricted the Frobenius norm of the weight matrix through ridge regression, which achieved the same accuracy as Autoformer with only a few parameters on the ETTh1 dataset. [PERSON] [18] employed a linear transformation approach for time-series forecasting, demonstrating that simple linear models can effectively capture complex temporal patterns. [PERSON] [19] further designed a deep linear network to achieve multi-scale trend decomposition by stacking multiple linear layers, which achieved performance comparable to complex models at low complexity. Meanwhile, researchers have proposed a variety of alternative deep learning architectures. For example, [PERSON] [20] constructed a dual recurrent architecture based on GAN, in which both the generator and the discriminator were designed to capture the dynamic characteristics of time series. [PERSON] [21] employed a Deep Convolutional Generative Adversarial Network (DCGAN) that utilizes multi-channel convolution to extract features from stock data and generate future price series. [PERSON] [22] proposed the Neural Basis Expansion Analysis (N-BEATS) architecture, which focuses on mining the intrinsic interpretable structure of time series. [PERSON] [23] introduced causal convolution, extended convolution, and parallel computing to solve the problem of slow training speed and difficulty in capturing long-term dependence of RNN series in sequence modeling, and improved the performance of sequence prediction tasks. [PERSON] [24] integrated multivariate feature extraction, spatiotemporal decomposition, and LSTM memory units. This approach effectively combines the spatial features extracted by SATCN with the temporal features derived from LSTM, allowing the model to comprehensively account for both spatial and temporal dimensional information. [PERSON] [25], inspired by TCN, proposed a new basic structure for temporal convolution that combines ds-inception and 1D CBAM mechanisms. Machine learning methods break the strict assumptions on data distribution and demonstrate significant capability in complicated scenarios. However, most models tend to focus on the local information of the current time step, which makes it difficult to capture the deep temporal dependencies in the sequence.