AFD-STA: Adaptive Filtering Denoising with Spatiotemporal Attention for Chaotic System Prediction
This work addresses the challenge of handling measurement uncertainties and high-dimensional nonlinear dynamics for real-world applications, representing an incremental improvement through hybrid methods.
The paper tackles the problem of predicting high-dimensional chaotic systems governed by partial differential equations by introducing AFD-STA Net, a neural framework that integrates adaptive filtering and spatiotemporal dynamics learning, demonstrating effectiveness in maintaining prediction accuracy under smooth and strongly chaotic regimes with noise tolerance.
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.