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

TL;DR

FR-Mamba tackles the challenge of reconstructing time-series physical fields from sparse sensor data by integrating a selective state-space model for long-range temporal dependencies with Fourier Neural Operators for global spatial encoding. The dual-branch FNO-Mamba architecture enables efficient long-sequence modeling and robust spatiotemporal fusion, with a gating mechanism and a 2D Fourier refinement for spatial coherence. Across a cylinder-flow dataset, FR-Mamba outperforms a broad set of baselines in MAE and Max-AE, maintaining accuracy over long sequences and across regions with sharp dynamics. The approach broadens the applicability of state-space models in fluid dynamics and offers a scalable framework for real-time reconstruction of dynamic physical fields.

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.

Figures (9)

• Figure 1: The framework of our FR-Mamba.
• Figure 2: The overview of temporal feature extraction branch.
• Figure 3: The overall calculation process of SSM.
• Figure 4: The overview of spatial feature extraction branch.
• Figure 5: The feature fusion of our FR-Mamba.