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
• Authors: Jiahuan Long, Wenzhe Zhang, Ning Wang, Tingsong Jiang, Wen Yao,
• 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.

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