# Inverse designing metamaterials with programmable nonlinear functional responses in graph space

arXiv: https://arxiv.org/abs/2408.06300 · HTML: https://mlsanity.com/paper/2408.06300/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 52 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling](https://mlsanity.com/paper/2306.14773/) (2023)
- [Differentiable graph-structured models for inverse design of lattice materials](https://mlsanity.com/paper/2304.05422/) (2023)
- [Computational Discovery of Microstructured Composites with Optimal Stiffness-Toughness Trade-Offs](https://mlsanity.com/paper/2302.01078/) (2023)
- [Experiment-informed finite-strain inverse design of spinodal metamaterials](https://mlsanity.com/paper/2312.11648/) (2023)

## Built on by (most cited first, 1 of 1)

- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)

## Abstract (arXiv)

Material responses to static and dynamic stimuli, represented as nonlinear curves, are design targets for engineering functionalities like structural support, impact protection, and acoustic and photonic bandgaps. Three-dimensional metamaterials offer significant tunability due to their internal structure, yet existing methods struggle to capture their complex behavior-to-structure relationships. We present GraphMetaMat, a graph-based framework capable of designing three-dimensional metamaterials with programmable responses and arbitrary manufacturing constraints. Integrating graph networks, physics biases, reinforcement learning, and tree search, GraphMetaMat can target stress-strain curves spanning four orders of magnitude and complex behaviors, as well as viscoelastic transmission responses with varying attenuation gaps. GraphMetaMat can create cushioning materials for protective equipment and vibration-damping panels for electric vehicles, outperforming commercial materials, and enabling the automatic design of materials with on-demand functionalities.