Table 1 Overview of some data-driven dimensionless learning methods and their capabilities

Method	ODE/PDE	Model-	Input	Regime	Self-	Characteristic	Irreducible	Model
		Free	Ranking	Detection	Similar	Scales	Error	Efficiency
Scaling LAWs¹¹	×	×	✓	×	–	–	×	×
Active Subspaces¹⁷	✓	×	✓	×	–	–	×	×
AI Feynman¹³	×	×	×	×	–	–	×	×
Clustering²⁰	✓	×	✓	✓	–	–	×	×
PyDimension¹²	✓	×	×	×	✓	✓	×	×
BuckiNet¹⁵	✓	×	✓	×	✓	✓	×	×
BSM²¹	✓	×	×	×	✓	✓	×	×
IT-π (Current)	✓	✓	✓	✓	✓	✓	✓	✓

These capabilities include whether each method is applicable to ODEs/PDEs, operates in a model-free manner, ranks inputs by predictability, identifies distinct physical regimes, uncovers self-similarity, determines characteristic scales and dimensionless parameters, provides a bound on the irreducible error, and evaluates model efficiency. Entries marked with “–” indicate that although the method could potentially be extended to infer the corresponding physical property after deriving the dimensionless variables, the authors did not explicitly perform this step.

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