# De-homogenization of optimal multi-scale 3D topologies

arXiv: https://arxiv.org/abs/1910.13002 · HTML: https://mlsanity.com/paper/1910.13002/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2204.06682/) (2022)
- [Consistent machine learning for topology optimization with microstructure-dependent neural network material models](https://mlsanity.com/paper/2408.13843/) (2024)

## Abstract (arXiv)

This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal multi-scale designs on a very fine mesh (de-homogenization). By performing homogenization-based topology optimization, optimal multi-scale designs are obtained on a relatively coarse mesh resulting in a low computational cost. As microstructure parameterization we use orthogonal rank-3 microstructures, which are known to be optimal for a single loading case. Furthermore, a method to get explicit control of the minimum feature size and complexity of the final shapes will be discussed. Numerical examples show excellent performance of these fine-scale designs resulting in objective values similar to the homogenization-based designs. Comparisons with well-established density-based topology optimization methods show a reduction in computational cost of 3 orders of magnitude, paving the way for giga-scale designs on a standard PC.