Tailoring materials to achieve a desired behaviour in specific applications is of significant scientific and industrial interest as design of materials is a key driver to innovation. Overcoming the rather slow and expertise-bound traditional forward approaches of trial and error, inverse design is attracting substantial attention. Targeting a property, the design algorithm proposes a candidate structure with the desired property. Architected materials are particularly suitable as their internal structure can be adapted to achieve the targeted properties. Spinodoid structures are a specific class of architected materials with advantageous properties like non-periodicity, smoothness, and a low-dimensional design space which make them a good candidate for the inverse design of resilient architected materials. In this contribution we introduce two data-efficient inverse design methods. We present a direct approach which uses a neural network-based surrogate model. By exploiting equivariance [3], i.e. the fact that a permutation of design variables will yield the same but rotated structure, we enable a very efficient training of the surrogate model. This way, we reduced the required data by several orders of magnitude compared to published approaches [1]. Alternatively, we propose an indirect inverse design approach based on Bayesian optimization [2] where a small initial data set is iteratively augmented by in silico generated data until a structure with the targeted properties is found. The application to the inverse design of spinodoid structures of desired mechanical demonstrates the applicability of both frameworks.

REFERENCES
[1] S Kumar, S Tan, L Zheng, DM Kochmann. Inverse-designed spinodoid metamaterials. npj Computational Materials, 2020.
[2] A Raßloff, P Seibert, KA Kalina, M Kästner. Inverse design of spinodoid structures using Bayesian optimization. Computational Mechanics, 2025.
[3] M Rosenkranz, M Kästner, IF Sbalzarini. Data-efficient inverse design of spinodoid metamaterials. arXiv arXiv:2505.03415, 2025.