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Perception of the full state is an essential technology to support themonitoring, analysis, and design of physical systems, one of whose challengesis to recover global field from sparse observations. Well-known for brilliantapproximation ability, deep neural networks have been attractive to data-drivenflow and heat field reconstruction studies. However, limited by networkstructure, existing researches mostly learn the reconstruction mapping infinite-dimensional space and has poor transferability to variable resolution ofoutputs. In this paper, we extend the new paradigm of neural operator andpropose an end-to-end physical field reconstruction method with both excellentperformance and mesh transferability named RecFNO. The proposed method aims tolearn the mapping from sparse observations to flow and heat field ininfinite-dimensional space, contributing to a more powerful nonlinear fittingcapacity and resolution-invariant characteristic. Firstly, according todifferent usage scenarios, we develop three types of embeddings to model thesparse observation inputs: MLP, mask, and Voronoi embedding. The MLP embeddingis propitious to more sparse input, while the others benefit from spatialinformation preservation and perform better with the increase of observationdata. Then, we adopt stacked Fourier layers to reconstruct physical field inFourier space that regularizes the overall recovered field by Fourier modessuperposition. Benefiting from the operator in infinite-dimensional space, theproposed method obtains remarkable accuracy and better resolutiontransferability among meshes. The experiments conducted on fluid mechanics andthermology problems show that the proposed method outperforms existingPOD-based and CNN-based methods in most cases and has the capacity to achievezero-shot super-resolution.

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