RecFNO: A resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator

Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation ability, deep neural networks have been attractive to data-driven heat and flow field reconstruction studies for practical systems. However, limited by network structure, existing researches mostly learn the reconstruction mapping in finite-dimensional space that usually has poor transferability to the variable resolution of outputs. This paper extends the new paradigm of neural operators and proposes an end-to-end physical field reconstruction method with both excellent performance and mesh transferability named RecFNO. The proposed method aims to learn the mapping from sparse observations to flow and heat fields in infinite-dimensional space, contributing to a more powerful nonlinear fitting capacity and resolution -invariant characteristic. According to different usage scenarios, three types of embeddings are first developed to model the sparse observation inputs: MLP, mask, and Voronoi embedding. The MLP embedding is propitious to more sparse input, while the others benefit from spatial information preservation and perform better with the increase of observation data. Then, stacked Fourier layers are adopted to reconstruct physical field in Fourier space that regularizes the overall recovered field by Fourier modes superposition. Benefiting from the operator in infinite-dimensional space, the proposed method obtains remarkable accuracy and better resolution transferability among meshes. The experiments conducted on fluid mechanics and thermology problems show that the proposed method outperforms existing POD-based and CNN-based methods in most cases and has the capacity to achieve zero-shot super-resolution.

Automated summary

The perception of the full state is crucial for monitoring, analyzing, and designing physical systems. This paper introduces a novel end-to-end physical field reconstruction method called RecFNO, which learns the mapping from sparse observations to flow and heat fields in infinite-dimensional space. The proposed method achieves excellent performance and mesh transferability. Experimental results demonstrate its superiority over existing POD-based and CNN-based methods in most cases, and its ability to achieve zero-shot super-resolution.