# Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling

arXiv: https://arxiv.org/abs/2306.14773 · HTML: https://mlsanity.com/paper/2306.14773/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2023.

## Built on by (most cited first, 21 of 21)

- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials](https://mlsanity.com/paper/2410.05281/) (2024)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Deep learning-aided inverse design of porous metamaterials](https://mlsanity.com/paper/2507.17907/) (2025)
- [Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity](https://mlsanity.com/paper/2507.12233/) (2025)
- [LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures](https://mlsanity.com/paper/2402.01045/) (2024)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)
- [MetamatBench: Integrating Heterogeneous Data, Computational Tools, and Visual Interface for Metamaterial Discovery](https://mlsanity.com/paper/2505.20299/) (2025)
- [UniMate: A Unified Model for Mechanical Metamaterial Generation, Property Prediction, and Condition Confirmation](https://mlsanity.com/paper/2506.15722/) (2025)
- [AI-guided inverse design and discovery of recyclable vitrimeric polymers](https://mlsanity.com/paper/2312.03690/) (2023)
- [Inverse designing metamaterials with programmable nonlinear functional responses in graph space](https://mlsanity.com/paper/2408.06300/) (2024)
- [Deep Electromagnetic Structure Design Under Limited Evaluation Budgets](https://mlsanity.com/paper/2506.19384/) (2025)
- [Robust inverse material design with physical guarantees using the Voigt-Reuss Net](https://mlsanity.com/paper/2511.11388/) (2025)
- [Scientific feedback reveals productive regimes beyond training conventions](https://mlsanity.com/paper/2512.15756/) (2025)
- [Enhanced Data-Driven Product Development via Gradient Based Optimization and Conformalized Monte Carlo Dropout Uncertainty Estimation](https://mlsanity.com/paper/2601.00932/) (2026)
- [Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials](https://mlsanity.com/paper/2603.15917/) (2026)
- [CertMix: Certified, Data-Efficient Metamaterial Design by Affine Mixing of Aligned Neural-Implicit Weight Spaces](https://mlsanity.com/paper/2607.04123/) (2026)
- [Harnessing disorder to decouple extension and shear in kirigami metamaterials](https://mlsanity.com/paper/2607.16583/) (2026)
- [ReGDiff: Guided Diffusion in Regulated Latent Space for Exploring Metamaterial Voxel Geometry](https://mlsanity.com/paper/2609.34231/) (2026)

## Abstract (arXiv)

The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials--truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, pentamode-like, and tailored nonlinear behaviors. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.