Aiming at the problems of redundant information accumulation, low computational efficiency, and fuzzy feature allocation in multiscale time-series prediction of traditional deep echo state network (DeepESN), this article proposed an interlayer sparse compression-based DeepESN model (ICS-DESN). The model uses the sparse sampling technology of deep fusion compressive sensing and the hierarchical dynamic feature extraction mechanism of DeepESN, introduces the adaptive compressed sampling module between the layers, and uses the Gaussian observation matrix to reduce the dimension of the high-dimensional state, which effectively inhibits the stacking of redundant information in the deep network, and explicitly allocates the multiscale temporal features. Through theoretical analysis, it is proven that ICS-DESN satisfies the stability condition of the echo state property (ESP) by constraining the weighted spectral radius of the reservoir. In the experiment, we used multiscenario time-series datasets, such as logistic chaotic systems, Lorenz attractors, sunspot data, NASDAQ stock index, ETTh1 dataset, and weather dataset to validate the effectiveness of the model. The results showed that compared with traditional comparison models, ICS-DESN significantly reduced prediction errors mean squared error (MSE) and mean absolute error (MAE), demonstrating higher computational efficiency and robustness. This research provides an efficient theoretical framework for complex time-series modeling and has potential application value in resource-constrained scenarios, such as edge computing.
Wang et al. (Wed,) studied this question.