🤖 AI Summary
Physical field reconstruction (PFR) faces significant challenges in modeling long-range spatiotemporal dependencies under sparse sensor configurations, particularly for high-fidelity, full spatiotemporal reconstruction of time-varying flow fields (e.g., velocity, pressure, temperature). To address this, we propose FNO-Mamba—a novel hybrid architecture that synergistically integrates Fourier Neural Operators (FNOs) for efficient global spatial frequency-domain feature extraction with the Mamba state-space model for scalable, long-horizon temporal dependency modeling. This design overcomes classical trade-offs between computational complexity and reconstruction accuracy in temporal modeling, achieving linear-time inference complexity while preserving high-fidelity reconstruction. Evaluated on multi-scale flow field reconstruction tasks, FNO-Mamba consistently outperforms existing state-of-the-art methods, reducing average prediction error over long sequences by 21.6%. The framework establishes a new, efficient, and scalable paradigm for data-driven physical modeling.
📝 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.