FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model

• URL: http://arxiv.org/abs/2505.16083v1
• Date: Wed, 21 May 2025 23:54:36 GMT
• Title: FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model
• Abstract summary: Physical field reconstruction aims to predict the state distribution of physical quantities based on limited sensor measurements.<n>Existing deep learning methods often fail to capture long-range temporal, time-evolving dependencies.<n>We propose FR-Mamba, a novel flow field reconstruction framework based on state space modeling.
• Score: 9.340916033226604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physical field reconstruction (PFR) aims to predict the state distribution of physical quantities (e.g., velocity, pressure, and temperature) based on limited sensor measurements. It plays a critical role in domains such as fluid dynamics and thermodynamics. However, existing deep learning methods often fail to capture long-range temporal dependencies, resulting in suboptimal performance on time-evolving physical systems. To address this, we propose FR-Mamba, a novel spatiotemporal flow field reconstruction framework based on state space modeling. Specifically, we design a hybrid neural network architecture that combines Fourier Neural Operator (FNO) and State Space Model (SSM) to capture both global spatial features and long-range temporal dependencies. We adopt Mamba, a recently proposed efficient SSM architecture, to model long-range temporal dependencies with linear time complexity. In parallel, the FNO is employed to capture non-local spatial features by leveraging frequency-domain transformations. The spatiotemporal representations extracted by these two components are then fused to reconstruct the full-field distribution of the physical system. Extensive experiments demonstrate that our approach significantly outperforms existing PFR methods in flow field reconstruction tasks, achieving high-accuracy performance on long sequences.

Related papers

• Learning Spatio-Temporal Foundation Models from Pure Synthetic Data [85.23980441738811]
  NeoST is a scalable synthetic-training corpus to real-world bias, a latent-space reasoning architecture that generates and iteratively refines multiple future trajectories, and latent-space objectives that emphasize structural dynamics and enable inference-time correction under distribution shifts.<n>Extensive experiments across diverse real-world benchmarks show that NeoST consistently outperforms existing STFMs in diverse real-worldtemporal systems.
  arXiv  Detail & Related papers  (2026-06-27T02:56:46Z)
• Multi-Rate Mixture of Experts for Accelerating Liquid Neural Network Training [5.248012610915348]
  Liquid Neural Networks (LNNs) address some of these limitations through continuous-time dynamics.<n>We propose a Multi-Rate Mixture-of-Experts (MR-MoE) framework built on top of Liquid Neural Networks.<n>In the proposed architecture, multiple LNN-based experts operate at distinct time scales, enabling the model to explicitly separate fast-changing dynamics from slow-evolving temporal trends.
  arXiv  Detail & Related papers  (2026-06-10T15:43:20Z)
• DSFNet: Learning Dual-Domain Spectral Operators for Multi-Modality Spatio-Temporal Forecasting in Urban Transportation Systems [51.72074484150301]
  We propose the Dual-Domain Spectral Network (DSFNet) to explicitly model the relationships between variables.<n>Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns.<n>Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets.
  arXiv  Detail & Related papers  (2026-06-05T07:33:57Z)
• PIMSM: Physics-Informed Multi-Scale Mamba for Stable Neural Representations under Distribution Shift [16.230225739605316]
  We argue that failure to preserve scientific temporal structure contributes to brittleness under distribution shift.<n>We propose Physics-Informed Multi-Scale Mamba, a state-space architecture that maps spectrum-estimated transition points between frequency regimes.<n>On Human Connectome Project fMRI, PIMSM improves robustness and representation stability under severe temporal-context truncation.
  arXiv  Detail & Related papers  (2026-05-08T04:58:05Z)
• FoSS: Modeling Long Range Dependencies and Multimodal Uncertainty in Trajectory Prediction via Fourier State Space Integration [21.39395366378851]
  We present FoSS, a dual-branch framework that unifies frequency-domain reasoning with linear-time sequence modeling.<n>Experiments on Argoverse 1 and Argoverse 2 benchmarks demonstrate that FoSS achieves state-of-the-art accuracy while reducing computation by 22.5% and parameters by over 40%.
  arXiv  Detail & Related papers  (2026-03-01T21:38:59Z)
• MEMTS: Internalizing Domain Knowledge via Parameterized Memory for Retrieval-Free Domain Adaptation of Time Series Foundation Models [51.506429027626005]
  Memory for Time Series (MEMTS) is a lightweight and plug-and-play method for retrieval-free domain adaptation in time series forecasting.<n>Key component of MEMTS is a Knowledge Persistence Module (KPM), which internalizes domain-specific temporal dynamics.<n>This paradigm shift enables MEMTS to achieve accurate domain adaptation with constant-time inference and near-zero latency.
  arXiv  Detail & Related papers  (2026-02-14T14:00:06Z)
• Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamics [51.85385061275941]
  Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics.<n>Recent generative models have shown promise in accelerating simulations, yet they struggle with long-horizon generation.<n>We present STAR-MD, a scalable diffusion model that generates physically plausible protein trajectories over micro-scale timescales.
  arXiv  Detail & Related papers  (2026-02-02T14:13:28Z)
• FreqFlow: Long-term forecasting using lightweight flow matching [3.5235875824926346]
  We introduce FreqFlow, a novel framework that leverages conditional flow matching in the frequency domain for deterministic MTS forecasting.<n>FreqFlow transforms the forecasting problem into the spectral domain, where it learns to model amplitude and phase shifts.<n>Experiments on real-world traffic speed, volume, and flow datasets demonstrate that FreqFlow achieves state-of-the-art forecasting performance.
  arXiv  Detail & Related papers  (2025-11-20T14:50:13Z)
• Multivariate Long-term Time Series Forecasting with Fourier Neural Filter [55.09326865401653]
  We introduce FNF as the backbone and DBD as architecture to provide excellent learning capabilities and optimal learning pathways for spatial-temporal modeling.<n>We show that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling.
  arXiv  Detail & Related papers  (2025-06-10T18:40:20Z)
• FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systems [51.15230303652732]
  FLEX (F Low EXpert) is a backbone architecture for generative modeling of-temporal physical systems.<n>It reduces the variance of the velocity field in the diffusion model, which helps stabilize training.<n>It achieves accurate predictions for super-resolution and forecasting tasks using as few features as two reverse diffusion steps.
  arXiv  Detail & Related papers  (2025-05-23T00:07:59Z)
• Convolutional Long Short-Term Memory Neural Networks Based Numerical Simulation of Flow Field [3.9561033879611944]
  An improved Convolutional Long Short-Term Memory (Con-vLSTM) Neural Network is proposed as the baseline network.<n> numerical simulations of flow around a circular cylinder were conducted.<n>Results demonstrate that the improved ConvLSTM model can extract more temporal and spatial features.
  arXiv  Detail & Related papers  (2025-05-21T13:54:37Z)
• A Physics-Informed Convolutional Long Short Term Memory Statistical Model for Fluid Thermodynamics Simulations [0.0]
  Direct numerical simulations of fluid thermodynamics are computationally prohibitive.<n>We present a physics-informed architecture for RBC, a canonical example of convective flow.<n>Inference is penalized with respect to the governing partial differential equations to ensure interpretability.
  arXiv  Detail & Related papers  (2025-05-16T06:47:00Z)
• Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator [0.0]
  Microstructural evolution plays a critical role in shaping the physical, optical, and electronic properties of materials.<n>Traditional phase-field modeling accurately simulates these phenomena but is computationally intensive.<n>This study introduces a novel approach utilizing Fourier Neural Operator (FNO) to achieve resolution-invariant modeling.
  arXiv  Detail & Related papers  (2025-03-18T11:19:08Z)
• Cross Space and Time: A Spatio-Temporal Unitized Model for Traffic Flow Forecasting [16.782154479264126]
  Predicting backbone-temporal traffic flow presents challenges due to complex interactions between temporal factors. Existing approaches address these dimensions in isolation, neglecting their critical interdependencies. In this paper, we introduce Sanonymous-Temporal Unitized Unitized Cell (ASTUC), a unified framework designed to capture both spatial and temporal dependencies.
  arXiv  Detail & Related papers  (2024-11-14T07:34:31Z)
• UmambaTSF: A U-shaped Multi-Scale Long-Term Time Series Forecasting Method Using Mamba [7.594115034632109]
  We propose UmambaTSF, a novel long-term time series forecasting framework. It integrates multi-scale feature extraction capabilities of U-shaped encoder-decoder multilayer perceptrons (MLP) with Mamba's long sequence representation. UmambaTSF achieves state-of-the-art performance and excellent generality on widely used benchmark datasets.
  arXiv  Detail & Related papers  (2024-10-15T04:56:43Z)
• SFANet: Spatial-Frequency Attention Network for Weather Forecasting [54.470205739015434]
  Weather forecasting plays a critical role in various sectors, driving decision-making and risk management. Traditional methods often struggle to capture the complex dynamics of meteorological systems. We propose a novel framework designed to address these challenges and enhance the accuracy of weather prediction.
  arXiv  Detail & Related papers  (2024-05-29T08:00:15Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)
• Spatial-Temporal Transformer Networks for Traffic Flow Forecasting [74.76852538940746]
  We propose a novel paradigm of Spatial-Temporal Transformer Networks (STTNs) to improve the accuracy of long-term traffic forecasting. Specifically, we present a new variant of graph neural networks, named spatial transformer, by dynamically modeling directed spatial dependencies. The proposed model enables fast and scalable training over a long range spatial-temporal dependencies.
  arXiv  Detail & Related papers  (2020-01-09T10:21:04Z)

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.