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 y 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 y size distributions with experimental microstructures. The experimental y 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.