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

arXiv: https://arxiv.org/abs/2505.18080 · HTML: https://mlsanity.com/paper/2505.18080/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 4 of 4)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)

## Built on by (most cited first, 1 of 1)

- [OptFormer: Optical Flow-Guided Attention and Phase Space Reconstruction for SST Forecasting](https://mlsanity.com/paper/2601.06078/) (2025)

## Abstract (arXiv)

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.