# Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models

arXiv: https://arxiv.org/abs/2305.19836 · HTML: https://mlsanity.com/paper/2305.19836/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2023.

## Built on by (most cited first, 30 of 48)

- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [An operator learning perspective on parameter-to-observable maps](https://mlsanity.com/paper/2402.06031/) (2024)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics](https://mlsanity.com/paper/2407.21314/) (2024)
- [Conditional score-based diffusion models for solving inverse problems in mechanics](https://mlsanity.com/paper/2406.13154/) (2024)
- [Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials](https://mlsanity.com/paper/2410.05281/) (2024)
- [DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling](https://mlsanity.com/paper/2502.06250/) (2025)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [Nonlinear Inverse Design of Mechanical Multi-Material Metamaterials Enabled by Video Denoising Diffusion and Structure Identifier](https://mlsanity.com/paper/2409.13908/) (2024)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (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)
- [FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design](https://mlsanity.com/paper/2408.13532/) (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)
- [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025)
- [Geometry-Aware Neural Optimizer for Shape Optimization and Inversion](https://mlsanity.com/paper/2605.04474/) (2026)
- [Inverse designing metamaterials with programmable nonlinear functional responses in graph space](https://mlsanity.com/paper/2408.06300/) (2024)
- [Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturing](https://mlsanity.com/paper/2410.17518/) (2024)
- [Reduced-order structure-property linkages for stochastic metamaterials](https://mlsanity.com/paper/2505.01283/) (2025)
- [Friction on Demand: A Generative Framework for the Inverse Design of Metainterfaces](https://mlsanity.com/paper/2511.03735/) (2025)
- [A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials](https://mlsanity.com/paper/2603.18225/) (2026)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Learning Physics-Consistent Material Behavior from Dynamic Displacements](https://mlsanity.com/paper/2407.20273/) (2024)
- [Inverse design of Non-parameterized Ventilated Acoustic Resonator via Variational Autoencoder with Acoustic Response-encoded Latent Space](https://mlsanity.com/paper/2408.05917/) (2024)
- [AI-driven Inverse Design of Band-Tunable Mechanical Metastructures for Tailored Vibration Mitigation](https://mlsanity.com/paper/2412.12122/) (2024)

## Abstract (arXiv)

The accelerated inverse design of complex material properties - such as identifying a material with a given stress-strain response over a nonlinear deformation path - holds great potential for addressing challenges from soft robotics to biomedical implants and impact mitigation. While machine learning models have provided such inverse mappings, they are typically restricted to linear target properties such as stiffness. To tailor the nonlinear response, we here show that video diffusion generative models trained on full-field data of periodic stochastic cellular structures can successfully predict and tune their nonlinear deformation and stress response under compression in the large-strain regime, including buckling and contact. Unlike commonly encountered black-box models, our framework intrinsically provides an estimate of the expected deformation path, including the full-field internal stress distribution closely agreeing with finite element simulations. This work has thus the potential to simplify and accelerate the identification of materials with complex target performance.