用物理约束神经网络模拟三维晶粒长大，高效且跨尺度准确。
A Physics-Regulated Neural Framework for Learning 3D Grain Growth Dynamics
- 引入物理规律约束神经网络，确保演化符合能量降低和统计规律。
- 仅用两步训练数据，就能准确预测大尺寸系统中晶粒长大过程。
- 适合需要快速、稳定模拟大规模材料微结构演化的研究人员。
晶粒长大由晶界能降低驱动，并遵循明确的统计标度律。构建既能保持物理守恒量又计算高效的3D数据驱动代理模型仍具挑战。本文提出3D-PRIMME（物理约束可解释机器学习用于微结构演化），用于学习三维晶粒生长动力学。模型仅需两个连续时间步的数据即可训练，却能准确复现线性粗化定律，并在长时间尺度上保持拓扑统计特性。尽管训练基于100³网格点、512个晶粒，该学习到的演化算子可直接应用于高达1024³网格点、55万晶粒的大域，无需重训，且在系统规模扩大数个数量级后仍保持一致的动力学与晶粒拓扑。结果表明，3D-PRIMME学习到了一种尺度无关、时间稳定的局部演化规则，实现了高效且鲁棒的大规模三维微结构演化代理预测。
原文摘要 · Abstract (English)
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.
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