# Neural Metamaterial Networks for Nonlinear Material Design

arXiv: https://arxiv.org/abs/2309.10600 · HTML: https://mlsanity.com/paper/2309.10600/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 79 references that are in the map.
- First posted on arXiv 15 Sep 2023.

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

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Two-Scale Topology Optimization with Microstructures](https://mlsanity.com/paper/1706.03189/) (2017)
- [Learning Elastic Constitutive Material and Damping Models](https://mlsanity.com/paper/1909.01875/) (2019)
- [Differentiable Simulation of Inertial Musculotendons](https://mlsanity.com/paper/2202.02344/) (2022)
- [Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties](https://mlsanity.com/paper/2005.09111/) (2020)
- [Analysis of a Reduced-Order Model for the Simulation of Elastic Geometric Zigzag-Spring Meta-Materials](https://mlsanity.com/paper/2010.08070/) (2020)

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

- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains](https://mlsanity.com/paper/2410.09417/) (2024)
- [Learning 3D Garment Animation from Trajectories of A Piece of Cloth](https://mlsanity.com/paper/2501.01393/) (2025)
- [Neural Co-Optimization of Structural Topology, Manufacturable Layers, and Path Orientations for Fiber-Reinforced Composites](https://mlsanity.com/paper/2505.03779/) (2025)
- [Data-Driven Nonlinear Deformation Design of 3D-Printable Shells](https://mlsanity.com/paper/2408.15097/) (2024)

## Abstract (arXiv)

Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.