# IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

arXiv: https://arxiv.org/abs/2103.02588 · HTML: https://mlsanity.com/paper/2103.02588/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 109 references that are in the map.
- First posted on arXiv 3 Mar 2021.

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

- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [A Generative Model for Inverse Design of Metamaterials](https://mlsanity.com/paper/1805.10181/) (2018)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [MO-PaDGAN: Reparameterizing Engineering Designs for Augmented Multi-objective Optimization](https://mlsanity.com/paper/2009.07110/) (2020)
- [Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process](https://mlsanity.com/paper/2006.15273/) (2020)
- [Two-Scale Topology Optimization with Microstructures](https://mlsanity.com/paper/1706.03189/) (2017)

## Built on by (most cited first, 19 of 19)

- [3D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Models](https://mlsanity.com/paper/2212.00842/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis](https://mlsanity.com/paper/2103.06230/) (2021)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Dynamically configured physics-informed neural network in topology optimization applications](https://mlsanity.com/paper/2312.06993/) (2023)
- [How well do generative models solve inverse problems? A benchmark study](https://mlsanity.com/paper/2601.23238/) (2026)
- [GrainPaint: A multi-scale diffusion-based generative model for microstructure reconstruction of large-scale objects](https://mlsanity.com/paper/2503.04776/) (2025)
- [Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions](https://mlsanity.com/paper/2306.10055/) (2023)
- [Machine Learning-Guided Design of Non-Reciprocal and Asymmetric Elastic Chiral Metamaterials](https://mlsanity.com/paper/2404.13215/) (2024)
- [Smooth Like Butter: Evaluating Multi-Lattice Transitions in Property-Augmented Latent Spaces](https://mlsanity.com/paper/2407.08074/) (2024)
- [Development and Comparison of Model-Based and Data-Driven Approaches for the Prediction of the Mechanical Properties of Lattice Structures](https://mlsanity.com/paper/2501.05762/) (2025)
- [DeepJEB++: Foundation Model-Driven Large-Scale 3D Engineering Dataset via 2D Latent Space Augmentation](https://mlsanity.com/paper/2606.12994/) (2026)
- [CertMix: Certified, Data-Efficient Metamaterial Design by Affine Mixing of Aligned Neural-Implicit Weight Spaces](https://mlsanity.com/paper/2607.04123/) (2026)

## Abstract (arXiv)

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignores the effects of unit cell geometry on properties, or considers the geometry-property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. We further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R2-scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.