Uncertainty-aware multi-objective optimization for high work output and low hysteresis in TiNiCuHfCo shape memory alloys

Designing shape memory alloys (SMAs) with both high work output and minimal thermal hysteresis (ΔT) is essential for advancing actuation technologies, yet it remains a challenging multi-objective optimization (MOO) problem. In this study, we develop an uncertainty-aware machine learning (ML) framework and showcase its efficiency to optimize TiNiCuHfCo SMAs. Starting from a vast composition space, ML models were employed to predict phase transformation temperatures and ΔT, effectively filtering out promising candidates. MOO was subsequently performed to balance the enthalpy change and hardness by minimizing the distance to a predefined target while accounting for prediction uncertainties. After four experimental iterations, the optimized alloys, Ti₅₀Ni₄₃Cu_6.3Hf_0.3Co_0.4 and Ti₅₀Ni_44.9Cu_4.9Hf_0.1Co_0.1, demonstrated good performance in high work output (∼ 21 MJ m⁻³) and low ΔT (∼ 25 °C). These improvements are attributed to enhanced lattice compatibility between phases and matrix strengthening achieved through dense grain boundaries and residual dislocations. This study underscores the effectiveness of integrating ML, uncertainty quantification, and domain knowledge, providing an alternative approach for multi-properties optimization in alloys.