# An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

arXiv: https://arxiv.org/abs/2301.08911 · HTML: https://mlsanity.com/paper/2301.08911/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2023.

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

- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Fourier-Latent Diffusion for Constrained Generation of Triply Periodic Minimal Surfaces](https://mlsanity.com/paper/2608.02151/) (2026)

## Abstract (arXiv)

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3=134.2 million finite elements run in less than 40 seconds per iteration with a peak GPU memory of 9 GB on an NVIDIA GeForce GTX 1080Ti GPU. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d.