A Physics-Regulated Neural Framework for Learning 3D Grain Growth Dynamics

2026-07-06

AI Summary

This work addresses the longstanding challenge of balancing physical fidelity and computational scalability in three-dimensional grain growth simulations by introducing the 3D-PRIMME framework. The method leverages an interpretable neural network embedded with physical constraints to learn scale-invariant local evolution rules from only two consecutive time steps of microstructure data. Trained on a modest 100³ grid, the model generalizes accurately—without retraining—to systems as large as 1024³ (encompassing 512 to over 550,000 grains), faithfully reproducing the linear coarsening law over long timescales while preserving key grain topological statistics. This represents the first data-driven approach capable of physically consistent, highly scalable three-dimensional grain growth simulation across multiple orders of magnitude in system size.

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.

Problem

• grain growth
• 3D microstructure evolution
• physical invariants
• scaling laws
• computational scalability

Innovation

• physics-informed machine learning
• 3D grain growth
• scale-independent modeling
• microstructure evolution
• neural surrogate