# LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures

arXiv: https://arxiv.org/abs/2402.01045 · HTML: https://mlsanity.com/paper/2402.01045/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [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)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Graph Element Networks: adaptive, structured computation and memory](https://mlsanity.com/paper/1904.09019/) (2019)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling](https://mlsanity.com/paper/2306.14773/) (2023)
- [ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling](https://mlsanity.com/paper/1903.05631/) (2019)
- [Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecasting](https://mlsanity.com/paper/2206.09450/) (2022)

## Built on by (most cited first, 2 of 2)

- [Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads](https://mlsanity.com/paper/2510.02472/) (2025)
- [Provably Communication-Efficient and Privacy-Preserving Federated Graph Neural Networks](https://mlsanity.com/paper/2605.26243/) (2026)

## Abstract (arXiv)

This study introduces a two-scale Graph Neural Operator (GNO), namely, LatticeGraphNet (LGN), designed as a surrogate model for costly nonlinear finite-element simulations of three-dimensional latticed parts and structures. LGN has two networks: LGN-i, learning the reduced dynamics of lattices, and LGN-ii, learning the mapping from the reduced representation onto the tetrahedral mesh. LGN can predict deformation for arbitrary lattices, therefore the name operator. Our approach significantly reduces inference time while maintaining high accuracy for unseen simulations, establishing the use of GNOs as efficient surrogate models for evaluating mechanical responses of lattices and structures.