A data-driven framework for molten pool morphology prediction in laser welding with dimensionless numbers discovery

Machine learning-based monitoring of laser welding processes enables accurate and real-time perception of molten pool morphology by efficiently analyzing complex and high-dimensional welding signals, thereby facilitating intelligent control and enhancing weld quality assurance. However, the inherent “black-box” nature of the neural network undermines the physical interpretability of the molten pool morphology predictions and may produce results that diverge from the underlying physical mechanisms. To alleviate this challenge, this research proposes a data-driven framework for molten pool morphology prediction in laser welding, incorporating dimensional constraints for dimensionless numbers discovery. Based on Buckingham's Pi theorem, a dimensionless learning network (DimensionlessNet) is developed to predict the dimensionless width and aspect ratio of the molten pool. By combining the coefficient sparsity regularization term and the norm constraint term into the loss function, the framework can automatically mine the dimensionless numbers that are most relevant to the molten pool morphology. The experimental results illustrate that the proposed method is comparable to the traditional machine learning models in terms of prediction accuracy, while significantly enhancing physical interpretability and generalization across different welding conditions. This work offers a novel approach for interpretable prediction of molten pool morphology in complex laser welding processes. • A DimensionlessNet based on Buckingham-Π theorem is developed to discover dimensionless numbers in laser welding. • Sparsity and norm constraints help select meaningful expressions, improving interpretability and consistency. • The model extracts two meaningful dimensionless numbers, improving interpretability and aligning with Rosenthal equation.