Enhanced extrapolative machine learning for designing high-performance multi-principal-element superalloys

Machine learning (ML) has become a powerful tool for accelerating the design and development of new materials. Among various traditional ML algorithms, decision tree-based ensemble learning methods are frequently chosen for their strong predictive capabilities. However, decision trees are limited in regression tasks to interpolating within the data range of the training set, which restricts their usefulness for designing materials with enhanced properties. Herein, we focused on predicting and optimizing the L1₂-phase solvus temperature (T_L12) and density, two critical properties for multi-principal-element superalloys (MPESAs). To achieve this, we employed the piecewise symbolic regression tree (PS-Tree), which demonstrates excellent extrapolation capability. Our model successfully predicted high T_L12 values exceeding the training data range (1242 °C), with four candidate alloys achieving T_L12 values of 1246, 1249, 1254, and 1274 °C. Experimental validation confirmed the accuracy of these predictions, verifying the robust extrapolative capability of the PS-Tree method. Notably, one alloy exhibited a T_L12 of 1267 °C and a density of 7.94 g cm⁻³, outperforming most MPESAs. Additionally, another alloy exhibited a compressive yield strength of 897 MPa at 750 °C, with a specific yield strength at this temperature higher than that of most L1₂-strengthened alloys and Co/Ni-based superalloys. Moreover, the model provided generalized insights, indicating that alloys with δ_r > 5.3 and ∆H_mix < –12.8 J mol⁻¹ K⁻¹ tend to favor higher T_L12.