Meshless super-resolution of scattered data via constrained radial basis functions and K-nearest-neighbors-driven densification
Phys. Rev. Fluids 11, 024902 – Published 12 February, 2026
DOI: https://doi.org/10.1103/nvlc-1cmn
Abstract
We propose a novel meshless method to achieve super-resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K-nearest-neighbor particle tracking velocimetry (KNN-PTV) [Tirelli et al., Exp. Therm. Fluid Sci. 140, 110756 (2023)] with meshless proper orthogonal decomposition (meshless POD) [Tirelli et al., Proc. R. Soc. A 481, 20240526 (2025)] and constrained radial basis function regression (c-RBFs) [Sperotto et al., Meas. Sci. Technol. 33, 094005 (2022)]. The main idea is to use KNN-PTV to enhance the spatial resolution of flow fields by blending data from locally similar flow regions available in the time series. This similarity is assessed in terms of statistical coherency with leading features, identified by meshless POD directly on the scattered data without the need to first interpolate onto a grid, but instead relying on RBFs to compute all the relevant inner products. Lastly, the proposed approach uses the c-RBF on the denser scattered distributions to derive an analytical representation of the flow fields that incorporates physical constraints. This combination is meshless because it does not require the definition of a grid at any step, thus providing flexibility in handling complex geometries. An ablation study on the role of penalties and physical constraints demonstrates their key contribution in regularizing the regression and ensuring physically consistent reconstructions. The algorithm is validated on three-dimensional measurements of a jet flow in air. The assessment covers three key aspects: statistics, spectra, and modal analysis. The proposed method is evaluated against standard particle image velocimetry, KNN-PTV, and c-RBFs. The results demonstrate improved accuracy, with an average error on the order of , compared to for the other methods. When considering reduced-order reconstructions, the error is even halved. Additionally, the proposed method exhibits a higher-frequency cutoff (based on reaching a noise floor) than the one observed in the competing approaches. A qualitative comparison highlights that the KNN-driven densification of the particle distribution also enhances the quality of velocity derivatives and related quantities.
