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

TL;DR

This work addresses the problem of predicting high-dimensional spatiotemporal chaotic PDE systems from observational data by leveraging phase-space reconstruction to connect attractors across time. The proposed AFD-STA Net fuses adaptive filtering (Adap-EWMA), parallel spatiotemporal attention, gated fusion, and a six-layer deep projection (DynaFC6) to map observed attractors to delayed attractors, achieving robust short-term predictions even under Gaussian noise. Ablation studies show spatiotemporal attention as the most critical component, and comparisons across KS, Brusselator, and Swift-Hohenberg demonstrate strong performance relative to baselines. The authors acknowledge limitations in long-term attractor evolution and propose future work using optical-flow-inspired mechanisms to capture deformation trends via an optical-flow–spatiotemporal joint attention framework, potentially improving stability under attractor mutations.

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.

Figures (11)

• Figure 1: Demonstrates the overall strcuture.
• Figure 2: Demonstrates the the matrix dimension changes under each module’s processing.
• Figure 3: Spatiotemporal attention architecture
• Figure 4: Fusion module architecture
• Figure 5: DynaFC6 Network architecture

Theorems & Definitions (3)

• Theorem 1
• Definition 1
• Theorem 2