Physics-Guided Neural Network for Regularization and Learning Unbalanced Data Sets: A Priori Prediction of Melt Pool Width Variation in Directed Energy Deposition

Directed energy deposition is of interest to the aerospace and defense industries for the production of novel and complex geometries, as well as repair applications. However, variability during the build process can result in deviations in final component geometry, structure, and mechanical properties, which adds to the complexity of process planning and slows down adoption of this technology. To address geometric tolerances, neural networks were trained to predict melt pool width, given input drivers such as build height, laser power, laser speed, and thin wall length. Physical constraints on the relationships between the 1st and 2nd derivatives of input drivers and melt pool width were enforced using custom loss functions, yielding physics-guided neural networks (PGNNs). PGNNs predicted the melt pool width with a higher performance (R-square = 0.991) than traditional neural networks (R-square = 0.884). Physics-based loss functions performed superior to traditional methods of regularization and were a superior method of training on unbalanced data sets versus sample/class weighting. This work demonstrates the benefits of enforcing physical constraints on machine learning predictions of additive manufacturing processes using finite estimates of mathematical expressions of physical laws.