# GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

arXiv: https://arxiv.org/abs/2204.06682 · HTML: https://mlsanity.com/paper/2204.06682/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 79 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions](https://mlsanity.com/paper/1904.04205/) (2019)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process](https://mlsanity.com/paper/2006.15273/) (2020)
- [Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization](https://mlsanity.com/paper/2106.06478/) (2021)
- [AuTO: A Framework for Automatic differentiation in Topology Optimization](https://mlsanity.com/paper/2104.01965/) (2021)
- [De-homogenization of optimal multi-scale 3D topologies](https://mlsanity.com/paper/1910.13002/) (2019)
- [Design and Optimization of Conforming Lattice Structures](https://mlsanity.com/paper/1905.02902/) (2019)
- [Integrating Material Selection with Design Optimization via Neural Networks](https://mlsanity.com/paper/2112.12566/) (2021)

## Built on by (most cited first, 3 of 3)

- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks](https://mlsanity.com/paper/2209.08168/) (2022)

## Abstract (arXiv)

Multiscale topology optimization (M-TO) entails generating an optimal global topology, and an optimal set of microstructures at a smaller scale, for a physics-constrained problem. With the advent of additive manufacturing, M-TO has gained significant prominence. However, generating optimal microstructures at various locations can be computationally very expensive. As an alternate, graded multiscale topology optimization (GM-TO) has been proposed where one or more pre-selected and graded (parameterized) microstructural topologies are used to fill the domain optimally. This leads to a significant reduction in computation while retaining many of the benefits of M-TO. A successful GM-TO framework must: (1) be capable of efficiently handling numerous pre-selected microstructures, (2) be able to continuously switch between these microstructures during optimization, (3) ensure that the partition of unity is satisfied, and (4) discourage microstructure mixing at termination. In this paper, we propose to meet these requirements by exploiting the unique classification capacity of neural networks. Specifically, we propose a graded multiscale topology optimization using neural-network (GM-TOuNN) framework with the following features: (1) the number of design variables is only weakly dependent on the number of pre-selected microstructures, (2) it guarantees partition of unity while discouraging microstructure mixing, and (3) it supports automatic differentiation, thereby eliminating manual sensitivity analysis. The proposed framework is illustrated through several examples.