A Physics-Regulated Neural Framework for Learning 3D Grain Growth Dynamics
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a machine learning model called 3D-PRIMME to predict how the tiny crystal structures inside materials change shape over time in three dimensions. Their model learns from just two snapshots and can accurately mimic how grains grow and change even when applied to much larger systems than it was trained on. This approach respects important physical rules and keeps the grain shapes and statistics consistent over long periods. It shows that the model can efficiently predict large-scale changes without needing to be retrained.
grain growthgrain boundary energymicrostructure evolutionmachine learning surrogatestatistical scaling laws3D modelingtopological statisticscoarsening lawlocal evolution rule
Authors
Zhihui Tian, Kang Yang, Michael Tonks, Amanda R. Krause, Joel B. Harley
Abstract
Grain growth is governed by the reduction in grain boundary energy and exhibits well-established statistical scaling laws. Developing data-driven surrogates that preserve these physical invariants while remaining computationally scalable remains challenging, especially in 3D. We present 3D-PRIMME (Physics-Regulated Interpretable Machine Learning for Microstructure Evolution) for learning three-dimensional grain growth dynamics. The model is trained using only two consecutive time steps yet accurately reproduces the linear coarsening law and preserves topological statistics over extended time scales. Despite being trained on a $100^3$ grid points with 512 grains, the learned evolution operator is applied to domains up to $1024^3$ grid points with 550000 grains without retraining, maintaining consistent kinetics and grain topology across orders-of-magnitude increases in system size. These results demonstrate that 3D-PRIMME learns a scale-independent and temporally stable local evolution rule, enabling efficient and robust large-scale surrogate prediction of 3D microstructure evolution.