State space model: a magical tool for state prediction in Nonlinear systems

Nonlinear prediction has extensive applications across various industries. Most current deep learning methods rely on large parameter scales to forcefully memorize nonlinear features, which requires high-performance hardware and generally yields average results. Recently proposed state space models offer advantages such as smaller parameter scales and faster training and inference speeds but have not yet been applied to nonlinear prediction tasks. To address the aforementioned limitations, we integrated the existing inference and prediction architecture with a state space model to complete the given nonlinear prediction task, proposing the Integrated State Prediction Model. This method innovatively incorporates the Mamba-S6 state space model to make long-term accurate predictions based on the contextual features of nonlinear sequences. Compared to traditional approaches, it effectively enhances training speed while maintaining efficiency in both training and inference processes. State space models demonstrate exceptional nonlinear prediction performance, maintaining extremely high accuracy with a minimal parameter scale, and effectively capturing the system’s nonlinear features without divergence in long-term prediction tasks. Most current nonlinear prediction methods are unable to effectively handle long-term prediction problems in chaotic models. In contrast, our model has a strong ability to extract nonlinear features and demonstrates excellent long- and short-term prediction performance on the selected chaotic models. The test results show that the prediction performance of our model does not degrade as the prediction horizon increases, providing a significant advantage in handling complex nonlinear state prediction tasks.