Clustering dimensionless learning for multiple-physical-regime systems

Abstract

The conventional physical analysis has relied on the researchers’ intelligence and physical insights to establish mathematical models and analyze the dependence of physical systems on dominant parameters in different physical regimes. In this work, a novel data-driven method is proposed to identify different physical regimes without a prior knowledge of governing equations and discover the dominant dimensionless parameters. The proposed method consists of two parts: the first is a data division via cluster analysis, which is utilized to identify different physical regimes via grouping data points into clusters with the weights taken from the key features in active subspace method; the second is a data-driven analysis of dominant dimensionless parameters via the active subspace, which is utilized to discover dominant dimensionless parameters by use of clustering and its resultant information (e.g. eigenpairs of clusters). We use three example problems to demonstrate this method: pipe flows, the spread of oil slicks on a calm sea, and the eddy viscosity in turbulent channel flows. The results obtained show that the present method can identify distinct physical regimes, and discover dominant dimensionless parameters, while the data-driven dimensional analysis without clustering cannot be directly used to the physical systems of multiple physical regimes.