A Physics-Regularized Machine Learning Approach for Predicting Time-Temperature-Transformation Curves in Alloys: Application to Uranium-Based Alloys

A physics-regularized machine learning (ML) approach is developed for predicting time-temperature-transformation (TTT) diagrams from alloy composition in uranium (U)-based systems. To ensure physically realistic C-curve shape while maintaining predictive accuracy, four loss function formulations are systematically evaluated: (1) baseline mean squared error (MSE), (2) MSE regularized with a semi-empirical nucleation-based model, (3) MSE regularized with shape constraints that enforce characteristic C-curve convexity, and (4) a hybrid approach that combines both semi-empirical regularization and shape constraints. Models that incorporate shape-constrained loss functions generate TTT predictions exhibiting a physically consistent C-curve form and demonstrate good agreement with experimental isothermal transformation data. Post hoc model explanation using global feature importance and partial dependency plots reveals systematic changes in the learned composition-TTT relationships as a function of the loss function formulation. The optimized ML model, which used a hybrid loss function, was applied to previously unexplored U-Mo-X ternary systems. This analysis identified U-Mo-Pt, U-Mo-Au, U-Mo-Ta, U-Mo-W, and U-Mo-Fe as candidate alloys that exhibit enhanced kinetic stability against $\gamma$-to-$\alpha$ phase decomposition during isothermal holds compared to the U-Mo binary baseline. Furthermore, TTT nose time predictions from the optimized ML model are compared with those from a Gaussian Process Regression (GPR) model using MSE loss. The developed physics-regularized ML framework offers potential for accelerating alloy discovery in U-based systems, where traditional TTT experimental determination is time and resource-intensive.