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, 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. Alternatively, we propose an indirect inverse design approach based on Bayesian optimization, 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.