# Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design

arXiv: https://arxiv.org/abs/2302.00557 · HTML: https://mlsanity.com/paper/2302.00557/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 11 of 11)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)
- [Surrogate Modeling of Fluid Dynamics with a Multigrid Inspired Neural Network Architecture](https://mlsanity.com/paper/2105.03854/) (2021)
- [U-Net-Based Surrogate Model For Evaluation of Microfluidic Channels](https://mlsanity.com/paper/2105.05173/) (2021)

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

- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [An Implicit GNN Solver for Poisson-like problems](https://mlsanity.com/paper/2302.10891/) (2023)
- [Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics](https://mlsanity.com/paper/2510.25683/) (2025)
- [Attention to Detail: Fine-Scale Feature Preservation-Oriented Geometric Pre-training for AI-Driven Surrogate Modeling](https://mlsanity.com/paper/2504.20110/) (2025)
- [Conservative Hybrid Graph Networks for Process Systems with Learned Routing](https://mlsanity.com/paper/2608.28896/) (2026)

## Abstract (arXiv)

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many scientific and engineering problems involving geometrical design, it is desirable for the surrogate models to precisely describe the change in geometry and predict the consequences. In that context, we develop graph neural networks (GNNs) as fast surrogate models for physics simulation, which allow us to directly train the models on 2/3D geometry designs that are represented by an unstructured mesh or point cloud, without the need for any explicit or hand-crafted parameterization. We utilize an encoder-processor-decoder-type architecture which can flexibly make prediction at both node level and graph level. The performance of our proposed GNN-based surrogate model is demonstrated on 2 example applications: feature designs in the domain of additive engineering and airfoil design in the domain of aerodynamics. The models show good accuracy in their predictions on a separate set of test geometries after training, with almost instant prediction speeds, as compared to O(hour) for the high-fidelity simulations required otherwise.