5 papers
A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions
Damien Rigutto, Manuel Ratz, Miguel A. Mendez
Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements,…
Learning with Physical Constraints
Miguel A. Mendez, Jan van Den Berghe, Manuel Ratz +2
This chapter provides three tutorial exercises on physics-constrained regression. These are implemented as toy problems that seek to mimic grand challenges in (1) the super-resolut…
Meshless data-driven decompositions with RBF-based inner products
Manuel Ratz, Alessandro Parente, Miguel Alfonso Mendez
Data-driven modal decompositions are useful tools for compressing data or identifying dominant structures. Popular ones like the dynamic mode decomposition (DMD) and the proper ort…
Statistical Methods and Modal Decompositions for Gridded and Scattered Data: Meshless Statistics and Meshless Data Driven Modal Analysis
Miguel A. Mendez, Manuel Ratz, Damien Rigutto
Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image vel…
A meshless and binless approach to compute statistics in 3D Ensemble PTV
Manuel Ratz, Miguel A. Mendez
We propose a method to obtain superresolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). The method is ''meshless'' because it doe…