Parametric super-resolution of turbulent channel flows from spatially sparse data using a transformer-based neural operator

We propose a transformer-based neural operator as a novel parametric arbitrary-scale super-resolution technique for reconstructing three-dimensional (3D) turbulence fields with direct numerical simulation (DNS) resolution from spatially sparse data. This technique consists of three components: a convolutional neural network-based encoder extracting low-resolution flow features as regular-grid contexts, an interpolation-based conditioning module embedding the contexts onto a set of sparsely distributed points, and a Galerkin-type attention decoder mapping the selected point coordinates to their corresponding flow quantity values. Thanks to the neural operator architecture, the super-resolution technique learns a parameter-dependent mesh-invariant mapping from arbitrary points over continuous domains to their corresponding flow values. The model performance was assessed on DNS data of a 3D turbulent channel flow at two Reynolds numbers (Reτ=130 and 350). At the two upsampling factors (×4 and ×8), the proposed models, trained with a few sparse samples, consistently outperform their convolutional neural network-based counterparts, trained using full high-resolution fields. For variable upsampling factors, our model naturally generalizes across scales, reproducing 3D high-resolution flow fields from a range of coarseness levels. Conversely, its convolutional neural network-based counterpart fails this task as it uses fixed-grid image-to-image mappings. In terms of computational efficiency, utilizing sparse data significantly reduces training time while achieving better accuracy when compared to training on full-field high-resolution data. Notably, our model allows for querying arbitrary points or regions, avoiding the need to generate and store entire high-resolution fields, making it feasible for super-resolution tasks where large-scale, full-resolution turbulence fields cannot fit into graphics processing unit memory.