用自适应滤波与时空注意力预测高维混沌系统，抗噪能力强。
AFD-STA: Adaptive Filtering Denoising with Spatiotemporal Attention for Chaotic System Prediction
- 自适应指数平滑+位置感知衰减系数，稳定重构吸引子。
- 时空注意力捕捉跨时序与空间依赖，提升动态建模精度。
- 适合处理含测量噪声的高维非线性系统预测任务。
本文提出AFD-STA Net，一种融合自适应滤波与时空动态学习的神经框架，用于预测由偏微分方程控制的高维混沌系统。该架构包含：1）具有位置感知衰减系数的自适应指数平滑模块，实现鲁棒吸引子重构；2）并行注意力机制，捕捉跨时序与空间依赖；3）多尺度特征的动态门控融合；4）具备维度扩展能力的深层投影网络。在非线性偏微分方程系统上的数值实验表明，该模型在平滑与强混沌状态下均保持高预测精度，并通过自适应滤波展现出良好噪声容忍度。组件消融实验确认各模块关键贡献，尤其凸显时空注意力在学习复杂动力学交互中的核心作用。该框架在需同时处理测量不确定性与高维非线性动态的实际应用中具有广阔前景。
原文摘要 · Abstract (English)
This paper presents AFD-STA Net, a neural framework integrating adaptive filtering and spatiotemporal dynamics learning for predicting high-dimensional chaotic systems governed by partial differential equations. The architecture combines: 1) An adaptive exponential smoothing module with position-aware decay coefficients for robust attractor reconstruction, 2) Parallel attention mechanisms capturing cross-temporal and spatial dependencies, 3) Dynamic gated fusion of multiscale features, and 4) Deep projection networks with dimension-scaling capabilities. Numerical experiments on nonlinear PDE systems demonstrate the model's effectiveness in maintaining prediction accuracy under both smooth and strongly chaotic regimes while exhibiting noise tolerance through adaptive filtering. Component ablation studies confirm critical contributions from each module, particularly highlighting the essential role of spatiotemporal attention in learning complex dynamical interactions. The framework shows promising potential for real-world applications requiring simultaneous handling of measurement uncertainties and high-dimensional nonlinear dynamics.
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