# Two-Scale Topology Optimization with Microstructures

arXiv: https://arxiv.org/abs/1706.03189 · HTML: https://mlsanity.com/paper/1706.03189/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2017.

## Built on by (most cited first, 10 of 10)

- [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)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [Neural Metamaterial Networks for Nonlinear Material Design](https://mlsanity.com/paper/2309.10600/) (2023)
- [eFlesh: Highly customizable Magnetic Touch Sensing using Cut-Cell Microstructures](https://mlsanity.com/paper/2506.09994/) (2025)
- [Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending](https://mlsanity.com/paper/2112.00648/) (2021)
- [Designing Composites with Target Effective Young's Modulus using Reinforcement Learning](https://mlsanity.com/paper/2110.05260/) (2021)
- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Neural Co-Optimization of Structural Topology, Manufacturable Layers, and Path Orientations for Fiber-Reinforced Composites](https://mlsanity.com/paper/2505.03779/) (2025)

## Abstract (arXiv)

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut -- the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.