Fig. 1 General process of machine learning in materials science [12]

Fig. 2 General process of feature engineering in Ni-based superalloys

Fig. 3 Sources and number of databases in Ni-based superalloys

Fig. 4 Applications of machine learning in the composition screening and optimization of Ni-based superalloys

Fig. 5 Predicted results showing a the distribution and b ZPF line of TCP phases by ML and c Thermo-Calc; d the distribution and e ZPF line of GGP phases by ML and f Thermo-Calc; and the phase diagram by g experimental, h ML, i Thermo-Calc in NiX-6W-4Nb diffusion triple [34]

Fig. 6 Creep resistance of designed alloys and several typical polycrystalline superalloys: U720Li, N18, Alloy 718 and GH4169 [38]

Fig. 7 Comparison of prediction results between the strain-compensated Arrhenius model and ANN model at a 1060 °C, b 1105 °C, c 1138 °C, d 1165 °C [60]

Fig. 8 3D relationships among temperature, strain rate, strain, and stress: a 3D continuous interaction space, 3D continuous mapping relationships under different, b temperatures, c strain rates, d strains [62]

Fig. 9 Flowchart of ASOA [63]

Fig. 10 a Pearson correlation coefficients of features for the Ni-based superalloys, b maximal information coefficient of features for the Ni-based superalloys [68]

Fig. 11 Interpretability analysis of the model. a, c low-temperature data predicting high-temperature data: a SHAP value summary plot, c mean |SHAP value| bar graph; b, d GH4169 data predicting GH4169D Data: b SHAP value summary plot, d mean |SHAP value| radar graph [72]

Fig. 12 Procedure of DCSA for modeling the creep rupture life. The input of DCSA is the alloy samples with various creep mechanisms. The division algorithm automatically classifies the samples into several clusters with different creep mechanisms. The selection algorithm is used to self-adaptively choose the optimal regression from five common regression models, i.e., RF, SVR, GPR, LR, and RR for each cluster. The final output of DCSA is a group of optimal models for the description of different creep mechanisms for each cluster [76]

Fig. 13 a Predicted and experimental oxidation data for 0Cr-15Cr alloys at 900 °C; b normalized mass gains from a; c parabolic curves of mass gains vs t1/2 from a; d normalized mass gains vs t1/2 from c [91]

Fig. 14 Computational flow of the constructed CKM relationship model. Consists of two core components, where the upper side of the flow chart shows the construction of the prediction model for the Kp by using two strategies, including data collection, model selection, feature engineering, and the integration of physical formula-driven data mining and ML. The lower part outlines the construction of the near-surface degraded γ′ features datasets and prediction ML model of γ′ features, DICTRA in Thermo-Calc is used to connect Kp and the prediction of the near-surface degraded microstructure [94]