Uncertainty-Aware Prediction of Mixing Enthalpy in Binary Alloys with Symmetry-Augmented Embeddings

The modeling of the enthalpy of mixing in binary alloys is essential to thermodynamic assessments and computational alloy design, particularly in data-scarce systems where experimental measurements are limited or incomplete. In this work, we propose a machine learning framework for the prediction of mixing enthalpy in binary alloys under conditions of limited data availability. The method integrates symmetry-augmented embeddings, which enforce physical invariances such as element permutation and compositional mirroring, ensuring consistency across chemically equivalent representations and capturing chemically meaningful similarities between elements, thereby supporting knowledge transfer across alloy systems. To account for data uncertainty and improve trust in predictions, we incorporate Bayesian neural networks, enabling the estimation of predictive confidence, especially in composition ranges lacking experimental data. The model is trained jointly across multiple binary alloy systems, allowing it to share structural insights and improve prediction quality in data-limited concentration intervals. The method achieves a reduction in mean absolute error by more than a factor of eight compared with the classical Miedema model (0.53 kJ·mol−1 vs. 4.27 kJ·mol−1) while maintaining consistent accuracy even when trained on only 25% of the experimental measurements, confirming its robustness thanks to cross-alloy knowledge transfer and symmetry-based data augmentation. We evaluate the method on a benchmark dataset containing both fully and partially characterized binary alloy systems and demonstrate its effectiveness in interpolating and extrapolating enthalpy values while providing reliable uncertainty estimates. The results highlight the value of incorporating domain-specific symmetries and uncertainty-aware learning in data-driven material modeling and suggest that this approach can support predictive thermodynamic assessments even in under-sampled systems.