Data-Driven Physical Inquiry: Discovering Relevant Dimensionless Numbers With Physics-Constrained Machine Learning*

Machine learning offers enormously popular methods for interrogating data. However, researchers in the physical sciences remain skeptical of these techniques, as they often produce inscrutable, black-box results. In this work, we present a case study of data-driven physical inquiry -- leveraging machine learning techniques to explore complex data sets, but anchored by physical principles.

As an illustration, we investigate the particle-laden flow conditions that lead to turbulence augmentation or attenuation, inspired by the work of Tanaka and Eaton (2008). We leverage a modern ridge function formulation of the Buckingham Pi Theorem that enables tight coupling with classification algorithms, transforming black-box prediction into an interpretable form.