# Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization

arXiv: https://arxiv.org/abs/2106.06478 · HTML: https://mlsanity.com/paper/2106.06478/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 53 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 2 of 2)

- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process](https://mlsanity.com/paper/2006.15273/) (2020)

## Built on by (most cited first, 9 of 9)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2204.06682/) (2022)
- [Dynamically configured physics-informed neural network in topology optimization applications](https://mlsanity.com/paper/2312.06993/) (2023)
- [Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions](https://mlsanity.com/paper/2306.10055/) (2023)
- [FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks](https://mlsanity.com/paper/2209.08168/) (2022)
- [Smooth Like Butter: Evaluating Multi-Lattice Transitions in Property-Augmented Latent Spaces](https://mlsanity.com/paper/2407.08074/) (2024)
- [Flow Battery Manifold Design with Heterogeneous Inputs Through Generative Adversarial Neural Networks](https://mlsanity.com/paper/2508.08863/) (2025)

## Abstract (arXiv)

For natural frequency optimization of engineering structures, cellular composites have been shown to possess an edge over solid. However, existing multiscale design methods for cellular composites are either computationally exhaustive or confined to a single class of microstructures. In this paper, we propose a data-driven topology optimization (TO) approach to enable the multiscale design of cellular structures with various choices of microstructure classes. The key component is a newly proposed latent-variable Gaussian process (LVGP) model through which different classes of microstructures are mapped into a low-dimensional continuous latent space. It provides an interpretable distance metric between classes and captures their effects on the homogenized stiffness tensors. By introducing latent vectors as design variables, a differentiable transition of stiffness matrix between classes can be easily achieved with an analytical gradient. After integrating LVGP with the density-based TO, an efficient data-driven cellular composite optimization process is developed to enable concurrent exploration of microstructure concepts and the associated volume fractions for natural frequency optimization. Examples reveal that the proposed cellular designs with multiclass microstructures achieve higher natural frequencies than both single-scale and single-class designs. This framework can be easily extended to other multi-scale TO problems, such as thermal compliance and dynamic response optimization.