Machine learning surrogates for CALPHAD inputs in mean-field precipitation modelling of IN738LC

This study presents a novel application of a machine learning-based surrogate modelling approach to replace CALPHAD-based inputs in the mean-field simulation of precipitation in the nickel-based superalloy IN738LC. A multi-component mean-field precipitation model is employed to describe the nucleation, growth and coarsening of precipitates. This model requires composition and temperature-dependent inputs, including chemical driving force and grouped mobility, which are calculated using CALPHAD tool (Thermo-Calc). To overcome the high computational cost of these calculations, feed-forward neural network surrogate models are developed to replace the thermodynamic calculations needed for the chemical driving force and grouped mobility parameters. Ensemble neural networks trained with different optimisation strategies (Adam, Rprop and a dynamic approach) are evaluated in terms of accuracy and robustness. The precipitation kinetics of phase were experimentally characterized under different heat treatments by varying cooling rates after sub-solvus solid solution heat treatments, and the surrogate predictions are verified against Thermo-Calc results and validated by comparing predicted size distributions with experimental microstructures. The experimental dispersions exhibit strong sensitivity to the cooling rates, with multi-modal size distributions. A two-step training process that involves optimiser switching is shown to improve the robustness and accuracy of the results. The error incurred when calculating the solvus temperature and property diagram is within the range of typical experimental data. The surrogate modelling error propagated into the calculation of precipitation kinetics can be absorbed into the model calibration, as demonstrated for the complex application of modelling a sub-solvus solid solution treatment followed by aging. • The evolution of the microstructure during solid solution treatment and aging in the IN738LC nickel-based superalloy is clarified, and the precipitation behaviour is shown to be highly sensitive to the quench rate. • A physics-based precipitation model for IN738LC is established by integrating mean-field theory with thermodynamic and mobility calculations driven by temperature and gamma prime phase fraction. • A machine learning surrogate model based on feed-forward neural networks is developed to predict thermodynamic driving force and atomic mobility with prediction accuracy exceeding ninety-nine percent. • The surrogate model demonstrates strong agreement with experimental observations of gamma prime precipitation kinetics in IN738LC across various quench conditions, confirming its capability to replace conventional computational thermodynamics and mobility calculations in precipitation simulations. • A dynamic optimiser switching strategy and ensemble neural network approach improve training robustness and accuracy, establishing a new pathway for predictive microstructure design in alloys.