# Differentiable graph-structured models for inverse design of lattice materials

arXiv: https://arxiv.org/abs/2304.05422 · HTML: https://mlsanity.com/paper/2304.05422/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 11 Apr 2023.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [Convolutional Networks for Fast, Energy-Efficient Neuromorphic Computing](https://mlsanity.com/paper/1603.08270/) (2016)
- [A Generalist Neural Algorithmic Learner](https://mlsanity.com/paper/2209.11142/) (2022)
- [Neuromorphic Hardware In The Loop: Training a Deep Spiking Network on the BrainScaleS Wafer-Scale System](https://mlsanity.com/paper/1703.01909/) (2017)
- [Accelerated physical emulation of Bayesian inference in spiking neural networks](https://mlsanity.com/paper/1807.02389/) (2018)

## Built on by (most cited first, 8 of 8)

- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [CLOUD: A Scalable and Physics-Informed Foundation Model for Crystal Representation Learning](https://mlsanity.com/paper/2506.17345/) (2025)
- [A Method for Auto-Differentiation of the Voronoi Tessellation](https://mlsanity.com/paper/2312.16192/) (2023)
- [Inverse designing metamaterials with programmable nonlinear functional responses in graph space](https://mlsanity.com/paper/2408.06300/) (2024)
- [Data-Driven Nonlinear Deformation Design of 3D-Printable Shells](https://mlsanity.com/paper/2408.15097/) (2024)
- [Self-Supervised Coarsening of Unstructured Grid with Automatic Differentiation](https://mlsanity.com/paper/2507.18297/) (2025)
- [Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials](https://mlsanity.com/paper/2603.15917/) (2026)
- [Harnessing disorder to decouple extension and shear in kirigami metamaterials](https://mlsanity.com/paper/2607.16583/) (2026)

## Abstract (arXiv)

Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into lattice topologies enable a degree of property customization not afforded to bulk materials. A promising venue for inspiration toward their design is in the irregular micro-architectures of nature. However, the immense design variability unlocked by such irregularity is challenging to probe analytically. Here, we propose a new computational approach using graph-based representation for regular and irregular lattice materials. Our method uses differentiable message passing algorithms to calculate mechanical properties, therefore allowing automatic differentiation with surrogate derivatives to adjust both geometric structure and local attributes of individual lattice elements to achieve inversely designed materials with desired properties. We further introduce a graph neural network surrogate model for structural analysis at scale. The methodology is generalizable to any system representable as heterogeneous graphs.