Prediction of Directional Growth Proportion in Laser-Directed Energy Deposition of DD6 Single-Crystal Superalloy Based on Physically Constrained Neural Networks

Accurate prediction of the directional growth proportion in laser-directed energy deposition (L-DED) of single-crystal superalloys remains a significant challenge due to the difficulty in controlling directional growth behavior and the limitations of small-sample data. To this end, this article proposes a neural network prediction method integrating outlier identification and physical constraints. First, based on 75 sets of L-DED experimental characterization data and finite element simulation data, a prediction dataset containing processing parameters, linear energy density, temperature gradient G , and solidification rate R was constructed. Subsequently, the DBSCAN algorithm was employed for outlier identification and denoising, and a physically constrained BP neural network was constructed leveraging the physical correlation between G / R and the directional growth proportion to enhance the physical consistency and generalization ability of the model. The results show that the predictive accuracy of algorithms such as support vector regression and random forest was improved after data denoising. Among them, the physically constrained BP neural network exhibited the best performance, with the test set R 2 increasing from 0.776 to 0.864. This method can provide an effective predictive tool for regulating crystal directional growth in the additive manufacturing of single-crystal superalloys.