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

TL;DR

FR-Mamba introduces a hybrid neural network combining Fourier Neural Operator and State Space Model to improve physical field reconstruction by effectively capturing both spatial and long-range temporal dependencies.

Contribution

The paper presents a novel hybrid framework that integrates FNO and SSM for enhanced time-series physical field reconstruction, addressing limitations of existing deep learning methods.

Findings

Outperforms existing PFR methods in flow field reconstruction

Achieves high accuracy on long sequence predictions

Effectively captures both spatial and temporal dependencies

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.