AC-xLSTM: an enhanced information flow and adaptive differential modeling framework for chaotic time series prediction
摘要
Chaotic time series are ubiquitous in natural and engineering systems, characterized by high nonlinearity and extreme sensitivity to initial conditions. These traits make long-term forecasting challenging. Existing chaotic time series forecasting methods often struggle with error accumulation and lack robustness in predicting the complex nonlinear dynamics of chaotic systems, resulting in inconsistent and inaccurate predictions. To address these challenges, we propose a novel deep learning framework, AC-xLSTM, with the following key contributions: (1) The attention mechanism is enhanced by replacing the QKV computation with a Multilayer Perceptron, improving the model’s ability to capture the complex temporal dependencies in chaotic time series. (2) A carefully designed mechanism through cross-weighting interactions between the gates, optimizing information flow and ensuring consistency and stability in long-term forecasting. (3) The AC-xLSTM incorporates an adaptive explicit differential modeling approach to effectively capture the nonlinear dynamic characteristics of chaotic systems, enabling precise short-term predictions. Rigorous evaluations on the Rössler, Chen, Lorenz, and Mackey-Glass benchmark chaotic systems demonstrate our model’s superiority. It drastically outperforms the powerful xLSTM baseline, reducing MSE an average of 96.70% across all tested systems. Critically, the model exhibits exceptional noise robustness with 5% added Gaussian noise, its MAE remained as low as 1.34e-3 on the Rössler system, compared to the baseline’s 7.29e-3. This combination of high accuracy and validated resilience establishes AC-xLSTM as a new benchmark for reliable chaotic time series forecasting.