Dimensionally consistent learning with Buckingham Pi

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables parameters, Buckingham Pi theorem provides procedure set dimensionless groups that spans solution space, although this not unique. We propose an automated approach using symmetric self-similar structure available data to discover best collapse these lower space according optimal fit. develop three data-driven techniques use as constraint: (1) constrained optimization problem with non-parametric input–output fitting function, (2) deep learning algorithm (BuckiNet) projects input parameter dimension first layer (3) based on sparse identification nonlinear dynamics equations whose coefficients parameterize dynamics. explore accuracy, robustness computational complexity methods show they successfully identify example problems: bead rotating hoop, laminar boundary Rayleigh–Bénard convection. Three machine are developed discovering physically meaningful scaling parameters from data, constraint.