# Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems

arXiv: https://arxiv.org/abs/2006.15274 · HTML: https://mlsanity.com/paper/2006.15274/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2020.

## Built on by (most cited first, 30 of 52)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Design](https://mlsanity.com/paper/2302.02913/) (2023)
- [A deep learning energy method for hyperelasticity and viscoelasticity](https://mlsanity.com/paper/2201.08690/) (2022)
- [IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures](https://mlsanity.com/paper/2103.02588/) (2021)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [FRAMED: An AutoML Approach for Structural Performance Prediction of Bicycle Frames](https://mlsanity.com/paper/2201.10459/) (2022)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [Challenges and opportunities for machine learning in multiscale computational modeling](https://mlsanity.com/paper/2303.12261/) (2023)
- [Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal](https://mlsanity.com/paper/2408.07847/) (2024)
- [An adaptive artificial neural network-based generative design method for layout designs](https://mlsanity.com/paper/2101.12410/) (2021)
- [Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis](https://mlsanity.com/paper/2103.06230/) (2021)
- [How to See Hidden Patterns in Metamaterials with Interpretable Machine Learning](https://mlsanity.com/paper/2111.05949/) (2021)
- [BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraints](https://mlsanity.com/paper/2508.00830/) (2025)
- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending](https://mlsanity.com/paper/2112.00648/) (2021)
- [VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems](https://mlsanity.com/paper/2302.11173/) (2023)
- [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)
- [Deep learning-aided inverse design of porous metamaterials](https://mlsanity.com/paper/2507.17907/) (2025)
- [Deep learning for size-agnostic inverse design of random-network 3D printed mechanical metamaterials](https://mlsanity.com/paper/2212.12047/) (2022)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [Investigating Deep Learning Model Calibration for Classification Problems in Mechanics](https://mlsanity.com/paper/2212.00881/) (2022)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)

## Abstract (arXiv)

Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven metamaterial design framework based on deep generative modeling. A variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encode meaningful patterns of variation in geometries and properties. Based on these insights, systematic data-driven methods are proposed for the design of microstructure, graded family, and multiscale system. For microstructure design, the tuning of mechanical properties and complex manipulations of microstructures are easily achieved by simple vector operations in the latent space. The vector operation is further extended to generate metamaterial families with a controlled gradation of mechanical properties by searching on a constructed graph model. For multiscale metamaterial systems design, a diverse set of microstructures can be rapidly generated using VAE for target properties at different locations and then assembled by an efficient graph-based optimization method to ensure compatibility between adjacent microstructures. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems that achieve desired distortion behaviors.