Physics-Driven PTV Interpolation Through Learned Regularization

Abstract

This paper deals with spatial interpolation of instantaneous Particle Tracking Velocimetry (PTV) data. Such a task can be handled using generic signal processing tools like B-splines, radial basis functions (RBF) or Kriging. We deal with non time-resolved PTV as gathered by dual frame particle image velocimetry (PIV) systems followed by dual frame PTV algorithms. In such a dual frame context, Physics-based interpolation techniques typically rely on enforcement of divergence free constraints on the interpolated field. The aim of this communication is to explore the wider field of Physics-based PTV interpolators based on learning a deep neural network. These interpolators are learned on a database of flow examples that may be generated by high resolution PIV or DNS. We propose an instance of such a Physics-based PTV interpolator based on the machine learning concept of unrolled optimization. This concept is extended in order to deal with random measurement location, characteristic of PTV data. We also show how to use this concept to perform pressure estimation from PTV data, along with velocity interpolation. The concept is illustrated on a 2D laminar flow, DNS data is used to train and benchmark the proposed method against RBF interpolation. The proposed method is shown to be much more robust than RBF interpolation against low density seeding and noise.