# FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks

arXiv: https://arxiv.org/abs/2209.08168 · HTML: https://mlsanity.com/paper/2209.08168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 56 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (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)
- [GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2204.06682/) (2022)

## Abstract (arXiv)

Fluid-flow devices with low dissipation, but high contact area, are of importance in many applications. A well-known strategy to design such devices is multi-scale topology optimization (MTO), where optimal microstructures are designed within each cell of a discretized domain. Unfortunately, MTO is computationally very expensive since one must perform homogenization of the evolving microstructures, during each step of the homogenization process. As an alternate, we propose here a graded multiscale topology optimization (GMTO) for designing fluid-flow devices. In the proposed method, several pre-selected but size-parameterized and orientable microstructures are used to fill the domain optimally. GMTO significantly reduces the computation while retaining many of the benefits of MTO. In particular, GMTO is implemented here using a neural-network (NN) since: (1) homogenization can be performed off-line, and used by the NN during optimization, (2) it enables continuous switching between microstructures during optimization, (3) the number of design variables and computational effort is independent of number of microstructure used, and, (4) it supports automatic differentiation, thereby eliminating manual sensitivity analysis. Several numerical results are presented to illustrate the proposed framework.