# A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations

arXiv: https://arxiv.org/abs/2402.13101 · HTML: https://mlsanity.com/paper/2402.13101/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Physically recurrent neural networks for path-dependent heterogeneous materials: embedding constitutive models in a data-driven surrogate](https://mlsanity.com/paper/2209.07320/) (2022)
- [Finite electro-elasticity with physics-augmented neural networks](https://mlsanity.com/paper/2206.05139/) (2022)
- [Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity](https://mlsanity.com/paper/2208.00246/) (2022)
- [GNN-based physics solver for time-independent PDEs](https://mlsanity.com/paper/2303.15681/) (2023)
- [Prediction and optimization of mechanical properties of composites using convolutional neural networks](https://mlsanity.com/paper/1906.00094/) (2019)
- [Mesh-based graph convolutional neural networks for modeling materials with microstructure](https://mlsanity.com/paper/2107.00090/) (2021)
- [A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features](https://mlsanity.com/paper/2012.11330/) (2020)

## Built on by (most cited first, 7 of 7)

- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity](https://mlsanity.com/paper/2507.05291/) (2025)
- [Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamics](https://mlsanity.com/paper/2503.19712/) (2025)
- [Towards scientific machine learning for granular material simulations -- challenges and opportunities](https://mlsanity.com/paper/2504.08766/) (2025)
- [A Comparison of Surrogate Constitutive Models for Viscoplastic Creep Simulation of HT-9 Steel](https://mlsanity.com/paper/2509.22667/) (2025)
- [Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks](https://mlsanity.com/paper/2606.10909/) (2026)
- [Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites](https://mlsanity.com/paper/2607.13688/) (2026)

## Abstract (arXiv)

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of this approach. The costs originate from microscale Finite Element (FE) models that must be solved at every macroscopic integration point. A plethora of surrogate modeling strategies attempt to alleviate this cost by learning to predict macroscopic stresses from macroscopic strains, completely replacing the microscale models. In this work, we introduce an alternative surrogate modeling strategy that allows for keeping the multiscale nature of the problem, allowing it to be used interchangeably with an FE solver for any time step. Our surrogate provides all microscopic quantities, which are then homogenized to obtain macroscopic quantities of interest. We achieve this for an elasto-plastic material by predicting full-field microscopic strains using a graph neural network (GNN) while retaining the microscopic constitutive material model to obtain the stresses. This hybrid data-physics graph-based approach avoids the high dimensionality originating from predicting full-field responses while allowing non-locality to arise. By training the GNN on a variety of meshes, it learns to generalize to unseen meshes, allowing a single model to be used for a range of microstructures. The embedded microscopic constitutive model in the GNN implicitly tracks history-dependent variables and leads to improved accuracy. We demonstrate for several challenging scenarios that the surrogate can predict complex macroscopic stress-strain paths. As the computation time of our method scales favorably with the number of elements in the microstructure compared to the FE method, our method can significantly accelerate FE2 simulations.