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

arXiv: https://arxiv.org/abs/2607.04680 · HTML: https://mlsanity.com/paper/2607.04680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [Randomness In Neural Network Training: Characterizing The Impact of Tooling](https://mlsanity.com/paper/2106.11872/) (2021)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator](https://mlsanity.com/paper/2503.14568/) (2025)
- [High-fidelity Grain Growth Modeling: Leveraging Deep Learning for Fast Computations](https://mlsanity.com/paper/2505.05354/) (2025)

## Abstract (arXiv)

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 1003 grid points with 512 grains, the learned evolution operator is applied to domains up to 10243 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.