Machine Learning Surrogates For Phase-Field Modelling Of Solidification

Phase-field models offer a physically accurate framework for simulating microstructure evolution, but they are too slow for certain industrial applications, such as metal additive manufacturing. The goal of this thesis was to investigate whether a machine learning surrogate could replace the phase-field model in predicting the microstructural evolution of an aluminium–copper alloy during rapid solidification, therefore accelerating the modelling of solidification for industrial use.
We framed the problem as a supervised learning task, with deep learning used to learn the evolution of phase and concentration fields from one time step to the next. We generated a dataset of 12 simulations using a phase-field model, varying one process parameter, thermal gradient, which affected the solidification dynamics. Each simulation contains 201 spatial snapshots of the phase and concentration fields at 1.97\,\mu \mathrm {s} intervals between each snapshot. We generated additional training data through data augmentation.
Four deep learning architectures were compared: UNet, UNet FiLM, U-AFNO, and U-AFNO FiLM. Models were evaluated based on metrics that measured pixel-wise and channel-wise error, as well as long-term prediction accuracy. The models with FiLM were conditioned on the process parameter, thermal gradient; the models without were not conditioned on any process parameter. We compared these models to a naive baseline, which assumed that the microstructure remains unchanged from one time step to the next.
All models outperformed the baseline model in terms of mean squared error. They captured the general features of the microstructures; however, they failed to accurately reproduce the finegrained dendritic structure of the solid–liquid interface. The best-performing model was U-AFNO FiLM, which achieved the best results among all single-step error metrics, except for one. For autoregressive prediction, U-AFNO FiLM maintained the lowest prediction error under baseline metrics for the longest sequence of predicted time steps. Depending on the model, microstructure evolution was predicted with speed-up factors ranging from approximately 4900 to 6700 times faster than the phase field model. A blurring of the solid–liquid interface was observed across all surrogate models’ predictions, making them unfit for replacing the phase field model. The reasons for the inability to make accurate predictions were analysed, and it was concluded that the training time was too short and that the use of mean squared error as the training loss limited the model’s ability to prioritise the interface structure.