Random-Walk Microstructures for Differentiable Topology Optimization

This repository contains the code for our ACM SCF 2025 paper “Random-Walk Microstructures for Differentiable Topology Optimization.”

Samuel Silverman, Dylan Balter, Keith A. Brown, Emily Whiting
Random-Walk Microstructures for Differentiable Topology Optimization
Proceedings of the ACM Symposium on Computational Fabrication (2025)

Data

The C++ libraries rwmicro and monad provide the random-walk generation and homogenized stiffness tensor simulation used to construct the dataset.

data/ contains:

• inputs.npz: (100000, 1, 32, 32) NumPy array of microstructure designs
• outputs.npz: (100000, 6) NumPy array of unique coefficients of the homogenized stiffness tensor ($\overline{\mathbf{C}}_{11}$, $\overline{\mathbf{C}}_{22}$, $\overline{\mathbf{C}}_{33}$, $\overline{\mathbf{C}}_{12}$, $\overline{\mathbf{C}}_{13}$, $\overline{\mathbf{C}}_{23}$)
• topopt_designs/: CSV and OBJ files for each of the topology optimization results (isotropic and orthotropic at 50%, 60%, 70%, and 80% density)

Code

The following scripts are provided in python/:

Script	Description	Image
train.py	Script for training the surrogate CNN model.
test.py	Script for testing the surrogate CNN model.
topology_optimization.py	Gradient-based topology optimization using the trained CNN surrogate.
visualize_design.py	Visualize a CSV microstructure design (supports periodic tiling).
export_to_mesh.py	Script for microstructure design CSV → OBJ export.

Note

A Conda environment is provided:

conda env create -f /path/to/environment.yml
conda activate random-walk-microstructures

Maintainers

• Sam Silverman - sssilver@bu.edu

Acknowledgements

The authors would like to thank Ruichen Liu for fabricating the optimized microstructure designs and Alec Ewe for running the compression tests on the fabricated samples. This work was supported by a Focused Research Program from the Rafik B. Hariri Institute for Computing and Computational Science & Engineering at Boston University and by the National Science Foundation (DMR-2323728).

Citation

@inproceedings{Silverman:2025:RandomWalkMicrostructures,
author = {Silverman, Samuel and Balter, Dylan and Brown, Keith A. and Whiting, Emily},
title = {Random-Walk Microstructures for Differentiable Topology Optimization},
year = {2025},
isbn = {9798400720345},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3745778.3766645},
doi = {10.1145/3745778.3766645},
booktitle = {Proceedings of the ACM Symposium on Computational Fabrication},
articleno = {25},
numpages = {11},
keywords = {microstructures, random walks, inverse design, neural networks, homogenization},
location = {},
series = {SCF '25}
}

License

Released under the MIT License.