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Liu et al. J. Mater. Inf. 2026, 6, 18 Page 9 of 29

SVR-C 1
SVR-epsilon 0.1
RF- n_estimators 100
RF- max_depth -1
Stacking
RF- min_samples_split 2
GBRT- learning_rate 0.1
GBRT- max_depth 3
GBRT- n_estimators 100
C 100
gamma 0.1
SVR epsilon 0.1
degree 3
tol 0.001
n_estimators 100
learning_rate 0.3
max_depth 6
XGBoost
min_child_weight 1
subsample 1
gamma 0
ML: Machine learning; AdaBoost: adaptive boosting; ANN: artificial neural network; Bagging: bootstrap aggregating; DT: decision tree; ExtraTrees:
extremely randomized trees; GBRT: gradient boosting regression tree; KNN: K-nearest neighbor; LightGBM: light gradient boosting machine; RF:
random forest; SVR: support vector regression; XGBoost: eXtreme gradient boosting.

resulting high-confidence Pareto frontier, achieved through the systematic integration of mechanical
properties and engineering constraints, demonstrates a high degree of experimental reliability.

Thermo-Calc thermodynamic phase diagram calculation
Thermo-Calc calculations were performed to locate titanium alloys on the Pareto frontier within equivalent
phase and phase fraction diagrams under different equilibrium states. These results reveal the evolution of
phase fractions under various heat treatment conditions. The thermodynamic equilibrium state of titanium
alloys is determined by establishing mathematical models of Gibbs free energy for each phase and applying
optimized database parameters. Phase fraction calculations and equivalent diagram generation are direct
applications of these thermodynamic models. For instance, a single equilibrium calculation at fixed
composition and temperature directly yields the phase fractions under those conditions. By systematically
varying temperatures at fixed composition and performing multiple equilibrium calculations, phase
fraction-temperature curves can be obtained. These curves can be combined to construct equivalent
diagrams, thereby revealing phase evolution during heat treatment. For the calculation of derived properties
such as specific heat capacity, the software computes the system enthalpy through equilibrium analysis and
employs numerical differentiation to determine enthalpy changes over small temperature intervals. This
enables the calculation of specific heat capacity. This method captures latent heat effects during phase
transitions, allowing the calculated results to reproduce characteristic peaks observed in experimental data.

Johnson–Cook model validation
This work aims to investigate the stress-strain relationship in various alloys under dynamic impact
conditions. However, the classical Johnson–Cook (J–C) model cannot accurately and efficiently capture the
[69]
combined effects of dynamic loading, strain hardening, and thermal softening. To address this limitation, the
initial segment equation was modified to describe elastic deformation, leading to the development of the