# Physics-Informed GCN-LSTM Framework for Long-Term Forecasting of 2D and 3D Microstructure Evolution

arXiv: https://arxiv.org/abs/2509.15029 · HTML: https://mlsanity.com/paper/2509.15029/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Deep Convolutional AutoEncoder-based Lossy Image Compression](https://mlsanity.com/paper/1804.09535/) (2018)
- [An End-to-End Compression Framework Based on Convolutional Neural Networks](https://mlsanity.com/paper/1708.00838/) (2017)
- [GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure](https://mlsanity.com/paper/2401.03661/) (2024)

## Built on by (most cited first, 1 of 1)

- [Efficient and Scalable Physics-Guided Fully Convolutional Spatiotemporal Learning for 3D Microstructure Evolution Prediction](https://mlsanity.com/paper/2609.36504/) (2026)

## Abstract (arXiv)

This paper presents a physics-informed framework that integrates graph convolutional networks (GCN) with long short-term memory (LSTM) architecture to forecast microstructure evolution over long time horizons in both 2D and 3D with remarkable performance across varied metrics. The proposed framework is composition-aware, trained jointly on datasets with different compositions, and operates in latent graph space, which enables the model to capture compositions and morphological dynamics while remaining computationally efficient. Compressing and encoding phase-field simulation data with convolutional autoencoders and operating in Latent graph space facilitates efficient modeling of microstructural evolution across composition, dimensions, and long-term horizons. The framework captures the spatial and temporal patterns of evolving microstructures while enabling long-range forecasting at reduced computational cost after training.