A dual-learning framework accelerating the design of ultra-high hardness high-entropy alloys

High-entropy alloys (HEAs) provide a pathway to achieve ultra-high hardness through multi-element configuration tuning, yet their development is hindered by the vast composition and processing-parameter spaces. In this work, we propose a dual-learning framework that integrates supervised machine learning for composition screening with Bayesian optimization for efficient processing-parameter design. A customized HEA database was constructed to train the supervised machine learning model, XGBoost model, achieving 99.9% and 97.7% accuracy on training and test, respectively, directing a non-equiatomic ratio Co 11 Cr 20 Fe 24 Ni 12 Al 23 Mo 10 as the top candidate. Bayesian optimization, requiring only five and six process trials for annealing temperatures and times in successive iterations, respectively, rapidly gives rise to optimal annealing conditions. The resulting alloy exhibits an ultra-high hardness of 907 HV 0.5 at 25 °C and maintains 739 HV 0.5 at 800 °C, with a compressive strength of 2.38 GPa and a yield strength of 2.12 GPa. Furthermore, our interpretability analysis underscores the critical roles of valence electron concentration (VEC) and atomic size difference ( δ ) in designing high hardness HEAs. Accordingly, we establish VEC <7.45 and δ >0.054 as design principle for achieving a hardness of no less than 500 HV. Finally, synchrotron X-ray diffraction, combining electron microscopic analyses, reveals mixing enthalpy-driven nano-precipitates induced precipitation strengthening as the mechanism for realizing high strength. Our framework simplifies the search space from ∼2.1×10 5 compositions and ∼1.9×10 3 processing conditions into only 11 trials finished within three days, providing a powerful tool for accelerating HEAs development with excellent mechanical properties.