AFD-STA: Adaptive Filtering Denoising with Spatiotemporal Attention for Chaotic System Prediction

TL;DR

AFD-STA Net is a neural framework that combines adaptive filtering and spatiotemporal attention to improve prediction accuracy of high-dimensional chaotic systems governed by PDEs, demonstrating robustness and noise tolerance.

Contribution

The paper introduces a novel neural architecture integrating adaptive filtering with spatiotemporal attention for enhanced chaotic system prediction.

Findings

Effective in maintaining accuracy under chaotic regimes

Demonstrates noise robustness through adaptive filtering

Component analysis confirms importance of attention mechanisms

Abstract

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.