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Physical systems are characterized by inherent symmetries, one of which is encapsulated in theunits of their parameters and system states. These symmetries enable a lossless order-reduction, e.g.,via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machinelearning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/ornumerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantlyenhance the interpretability and generalizability of ML-discovered secondary laws. Ournumerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysisenables both deep neural networks and sparse regression to reproduce old results, e.g., Stokes law fora sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction.Our results suggest the need to incorporate other physics-based symmetries and invariancesinto ML-based techniques for equation discovery.