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

• URL: http://arxiv.org/abs/2505.18080v1
• Date: Fri, 23 May 2025 16:39:07 GMT
• Title: AFD-STA: Adaptive Filtering Denoising with Spatiotemporal Attention for Chaotic System Prediction
• Authors: Chunlin Gong, Yin Wang, Jingru Li, Hanleran Zhang,
• Abstract summary: AFD-STA Net presents a framework for predicting high-dimensional chaotic systems governed by partial differential equations.<n>The framework shows promising potential for realworld applications requiring simultaneous handling of measurement uncertainties and high-dimensional nonlinear dynamics.
• Score: 4.833734041528231
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Adaptive Relative Pose Estimation Framework with Dual Noise Tuning for Safe Approaching Maneuvers [0.0]
  This work presents a complete pipeline integrating advanced computer vision techniques with adaptive nonlinear filtering.<n>A Convolutional Neural Network (CNN), enhanced with image preprocessing, detects structural markers from chaser imagery.<n>A UKF framework is selected for its ability to handle nonlinear relative dynamics to estimate the full relative pose.
  arXiv  Detail & Related papers  (2025-07-22T04:13:03Z)
• Data-Driven Reconstruction and Characterization of Stochastic Dynamics via Dynamical Mode Decomposition [0.0]
  Noise limits the performance and predictive capabilities of classical and quantum dynamical systems.<n>We introduce a general, data-driven framework based on Dynamical Mode Decomposition (DMD) to analyze system dynamics under noise.<n>This methodology provides a broadly applicable tool for diagnostic, predictive, noise mitigation analyses, and control in complex systems.
  arXiv  Detail & Related papers  (2025-07-08T08:59:06Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• KFD-NeRF: Rethinking Dynamic NeRF with Kalman Filter [49.85369344101118]
  We introduce KFD-NeRF, a novel dynamic neural radiance field integrated with an efficient and high-quality motion reconstruction framework based on Kalman filtering. Our key idea is to model the dynamic radiance field as a dynamic system whose temporally varying states are estimated based on two sources of knowledge: observations and predictions. Our KFD-NeRF demonstrates similar or even superior performance within comparable computational time and state-of-the-art view synthesis performance with thorough training.
  arXiv  Detail & Related papers  (2024-07-18T05:48:24Z)
• Dynamic Importance Learning using Fisher Information Matrix (FIM) for Nonlinear Dynamic Mapping [0.2455468619225742]
  This work presents a methodology for dynamically determining relevance scores in black-box models.<n>The proposed method leverages a gradient-based framework to uncover the importance of variance-driven features.<n>The practical utility of this approach is showcased through its application to an industrial pH neutralization process.
  arXiv  Detail & Related papers  (2024-06-08T08:12:41Z)
• Recurrent Deep Kernel Learning of Dynamical Systems [0.5825410941577593]
  Digital twins require computationally-efficient reduced-order models (ROMs) that can accurately describe complex dynamics of physical assets. We propose a data-driven, non-intrusive deep kernel learning (SVDKL) method to discover low-dimensional latent spaces from data. Results show that our framework is capable of (i) denoising and reconstructing measurements, (ii) learning compact representations of system states, (iii) predicting system evolution in low-dimensional latent spaces, and (iv) modeling uncertainties.
  arXiv  Detail & Related papers  (2024-05-30T07:49:02Z)
• Neural Harmonium: An Interpretable Deep Structure for Nonlinear Dynamic System Identification with Application to Audio Processing [4.599180419117645]
  Interpretability helps us understand a model's ability to generalize and reveal its limitations. We introduce a causal interpretable deep structure for modeling dynamic systems. Our proposed model makes use of the harmonic analysis by modeling the system in a time-frequency domain.
  arXiv  Detail & Related papers  (2023-10-10T21:32:15Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.