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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…
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,…
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…