The Algebra of Units: From Buckingham's Pi-grec Theorem to Latent-Variable Learning
A new paper proposes a method to automatically discover dimensionless groups from data, bypassing the need for expert physical insight. The technique leverages singular value decomposition (SVD) on logarithmically transformed measurements to identify a low-dimensional manifold, from which dimensionless quantities can be recovered. This approach has been demonstrated on a synthetic compressor dataset, accurately reproducing performance maps and highlighting a connection between dimensional analysis and data-driven learning. AI