# Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process

arXiv: https://arxiv.org/abs/2006.15273 · HTML: https://mlsanity.com/paper/2006.15273/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2020.

## Built on by (most cited first, 16 of 16)

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- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization](https://mlsanity.com/paper/2106.06478/) (2021)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending](https://mlsanity.com/paper/2112.00648/) (2021)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2204.06682/) (2022)
- [Interpretable Multi-Source Data Fusion Through Latent Variable Gaussian Process](https://mlsanity.com/paper/2402.04146/) (2024)
- [Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process](https://mlsanity.com/paper/2407.11268/) (2024)
- [Multi-objective robust optimization using adaptive surrogate models for problems with mixed continuous-categorical parameters](https://mlsanity.com/paper/2203.01996/) (2022)
- [On the Performance of Machine Learning Methods for Breakthrough Curve Prediction](https://mlsanity.com/paper/2204.11719/) (2022)
- [FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks](https://mlsanity.com/paper/2209.08168/) (2022)
- [Smooth Like Butter: Evaluating Multi-Lattice Transitions in Property-Augmented Latent Spaces](https://mlsanity.com/paper/2407.08074/) (2024)

## Abstract (arXiv)

The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or distance measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.