# Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator

arXiv: https://arxiv.org/abs/2503.14568 · HTML: https://mlsanity.com/paper/2503.14568/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 69 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Learning two-phase microstructure evolution using neural operators and autoencoder architectures](https://mlsanity.com/paper/2204.07230/) (2022)
- [Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures](https://mlsanity.com/paper/2001.01575/) (2019)
- [Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone](https://mlsanity.com/paper/2406.17119/) (2024)
- [Accelerating phase-field-based simulation via machine learning](https://mlsanity.com/paper/2205.02121/) (2022)

## Built on by (most cited first, 5 of 5)

- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [Scaling Kinetic Monte-Carlo Simulations of Grain Growth with Combined Convolutional and Graph Neural Networks](https://mlsanity.com/paper/2511.17848/) (2025)
- [ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics](https://mlsanity.com/paper/2512.03290/) (2025)
- [Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs. implicit conditioning](https://mlsanity.com/paper/2604.21753/) (2026)
- [A Physics-Regulated Neural Framework for Learning 3D Grain Growth Dynamics](https://mlsanity.com/paper/2607.04680/) (2026)

## Abstract (arXiv)

Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is computationally intensive, especially for large systems and fine spatial resolutions. While machine learning approaches have been employed to accelerate simulations, they often struggle with resolution dependence and generalization across different grain scales. This study introduces a novel approach utilizing Fourier Neural Operator (FNO) to achieve resolution-invariant modeling of microstructure evolution in multi-grain systems. FNO operates in the Fourier space and can inherently handle varying resolutions by learning mappings between function spaces. By integrating FNO with the phase field method, we developed a surrogate model that significantly reduces computational costs while maintaining high accuracy across different spatial scales. We generated a comprehensive dataset from phase-field simulations using the Fan Chen model, capturing grain evolution over time. Data preparation involved creating input-output pairs with a time shift, allowing the model to predict future microstructures based on current and past states. The FNO-based neural network was trained using sequences of microstructures and demonstrated remarkable accuracy in predicting long-term evolution, even for unseen configurations and higher-resolution grids not encountered during training.