# Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending

arXiv: https://arxiv.org/abs/2112.00648 · HTML: https://mlsanity.com/paper/2112.00648/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 73 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process](https://mlsanity.com/paper/2006.15273/) (2020)
- [METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design](https://mlsanity.com/paper/2006.02142/) (2020)
- [Two-Scale Topology Optimization with Microstructures](https://mlsanity.com/paper/1706.03189/) (2017)

## 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)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Integrating Material Selection with Design Optimization via Neural Networks](https://mlsanity.com/paper/2112.12566/) (2021)
- [Smooth Like Butter: Evaluating Multi-Lattice Transitions in Property-Augmented Latent Spaces](https://mlsanity.com/paper/2407.08074/) (2024)

## Abstract (arXiv)

To create heterogeneous, multiscale structures with unprecedented functionalities, recent topology optimization approaches design either fully aperiodic systems or functionally graded structures, which compete in terms of design freedom and efficiency. We propose to inherit the advantages of both through a data-driven framework for multiclass functionally graded structures that mixes several families, i.e., classes, of microstructure topologies to create spatially-varying designs with guaranteed feasibility. The key is a new multiclass shape blending scheme that generates smoothly graded microstructures without requiring compatible classes or connectivity and feasibility constraints. Moreover, it transforms the microscale problem into an efficient, low-dimensional one without confining the design to predefined shapes. Compliance and shape matching examples using common truss geometries and diversity-based freeform topologies demonstrate the versatility of our framework, while studies on the effect of the number and diversity of classes illustrate the effectiveness. The generality of the proposed methods supports future extensions beyond the linear applications presented.