# An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units

arXiv: https://arxiv.org/abs/2407.20251 · HTML: https://mlsanity.com/paper/2407.20251/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 87 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Uncertainty-Aware Deep Classifiers using Generative Models](https://mlsanity.com/paper/2006.04183/) (2020)
- [AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification](https://mlsanity.com/paper/2110.13511/) (2021)
- [Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling](https://mlsanity.com/paper/2306.14773/) (2023)
- [Uncertainty Quantification with Generative Models](https://mlsanity.com/paper/1910.10046/) (2019)
- [METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design](https://mlsanity.com/paper/2006.02142/) (2020)
- [Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design](https://mlsanity.com/paper/1612.07401/) (2016)
- [Probabilistic Deep Learning for Real-Time Large Deformation Simulations](https://mlsanity.com/paper/2111.01867/) (2021)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [A General Framework Combining Generative Adversarial Networks and Mixture Density Networks for Inverse Modeling in Microstructural Materials Design](https://mlsanity.com/paper/2101.10553/) (2021)
- [Probabilistic Deep Learning with Probabilistic Neural Networks and Deep Probabilistic Models](https://mlsanity.com/paper/2106.00120/) (2021)

## Built on by (most cited first, 2 of 2)

- [Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbation](https://mlsanity.com/paper/2608.22606/) (2026)
- [RAG: A Random-Forest-Based Generative Design Framework for Uncertainty-Aware Design of Metamaterials with Complex Functional Response Requirements](https://mlsanity.com/paper/2601.13233/) (2026)

## Abstract (arXiv)

Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered.