Supplemental data for "Robust inverse material design with physical guarantees using the Voigt-Reuss Net"

We use an open 3D microstructure dataset (90,000 stochastic microstructures, resolution 192x192x192), together with 236 scalar, image-derived morphological descriptors per microstructure [2]. For each microstructure, we sample three non-dimensional parameters that encode the bulk and shear moduli of the two phases, and compute the corresponding effective stiffness tensor (symmetric positive definite, 6x6 in Mandel notation).

Overall, the dataset contains ~1.18 million microstructure-material combinations and includes the train/validation/test splits used in the paper. (ii) 2D plane-strain elasticity. We use periodic microstructures obtained from thresholded trigonometric fields parameterized by an amplitude matrix A and a threshold [3].

For each sample, we provide the generator parameters, the rendered microstructure image, and the homogenized plane-strain stiffness tensor (symmetric positive definite, 3x3 in Voigt notation). The same split definitions and metadata used for training and evaluation are included to reproduce the forward-prediction comparisons and inverse-design experiments. Further details on file formats, naming conventions, and the exact contents of each file are provided in README.md.

[1] Keshav, S., and Fritzen, F. (2026). Robust inverse material design with physical guarantees using the Voigt-Reuss Net, International Journal for Numerical Methods in Engineering. doi.org/10.1002/nme.70296 [2] Prifling, B., Röding, M., Townsend, P., Neumann, M., and Schmidt, V. (2020). Large-scale statistical learning for mass transport prediction in porous materials using 90,000 artificially generated microstructures [dataset].

Zenodo. doi.org/10.5281/zenodo.4047774 [3] Boddapati, J., & Daraio, C. (2024). Planar structured materials with extreme elastic anisotropy. Materials & Design, 246, 113348. doi.org/10.1016/j.matdes.2024.113348 [4] Leuschner, M., and Fritzen, F. (2018).

Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems. Computational Mechanics, 62(3), 359-392. doi.org/10.1007/s00466-017-1501-5