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We leverage dimensional analysis and genetic programming (a type of machinelearning) to discover two strikingly simple but universal scaling laws, whichremain accurate for different materials, processing conditions, and machines inmetal three-dimensional (3D) printing. The first one is extracted fromhigh-fidelity high-speed synchrotron X-ray imaging, and defines a newdimensionless number, Keyhole number, to predict melt-pool vapor depressiondepth. The second predicts porosity using the Keyhole number and anotherdimensionless number, normalized energy density. By reducing the dimensions ofthese longstanding problems, the low-dimensional scaling laws will aid processoptimization and defect elimination, and potentially lead to a quantitativepredictive framework for the critical issues in metal 3D printing. Moreover,the method itself is broadly applicable to a range of scientific areas.

Discovering universal scaling laws in 3D printing of metals with genetic programming and dimensional analysis