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

We leverage dimensional analysis and genetic programming (a type of machine learning) to discover two strikingly simple but universal scaling laws, which remain accurate for different materials, processing conditions, and machines in metal three-dimensional (3D) printing. The first one is extracted from high-fidelity high-speed synchrotron X-ray imaging, and defines a new dimensionless number, Keyhole number, to predict melt-pool vapor depression depth. The second predicts porosity using the Keyhole number and another dimensionless number, normalized energy density. By reducing the dimensions of these longstanding problems, the low-dimensional scaling laws will aid process optimization and defect elimination, and potentially lead to a quantitative predictive framework for the critical issues in metal 3D printing. Moreover, the method itself is broadly applicable to a range of scientific areas.