Transfer-learning-based refinement of volume size factors from first-principles calculations

The volume size factor (VSF) is a key descriptor associated with lattice distortion and related phenomena such as solid-solution strengthening. However, experimental VSF data remain scarce because of the difficulty and cost of preparing solid solutions, while first-principles calculations often exhibit systematic discrepancies from experiments in specific alloy systems. Here, we demonstrate that these discrepancies can be treated not as random errors but as learnable physical information. A transfer-learning framework was developed to refine first-principles VSF predictions using limited experimental data while preserving extrapolative reliability. First-principles calculations were performed for 1,998 binary solid-solution systems, producing one of the largest VSF datasets reported to date. Six transfer-learning strategies and six machine-learning models were systematically evaluated with respect to generalization and extrapolation performance. Conventional machine-learning approaches exhibited substantial degradation outside the experimental-data distribution, whereas transformation-based approaches maintained predictive reliability under extrapolation conditions. Pareto analysis identified optimal models balancing agreement with experiments and consistency with first-principles calculations, and their ensemble average was adopted to construct the final refined VSF dataset. Descriptor analysis revealed that discrepancies between first-principles and experimental VSFs are dominated by electronic-structure-related factors, particularly the period of the solute element, suggesting insufficient treatment of relativistic effects and strong electron correlation in conventional first-principles approaches. The proposed framework establishes a practical route for integrating first-principles calculations and experimental data toward reliable alloy design, and the refined dataset may serve as a useful resource for the design and exploration of advanced structural alloys, including high-entropy alloys, particularly for experimentally unexplored alloy systems.