The use of machine learning methods for accelerating the design of materials has become increasingly popular within the research field of integrated computational materials engineering (ICME). Particularly, supervised learning methods are used to learn the linkages of the well-known chain processing-structure-properties-performance and thereby enable efficient optimization along this chain. For processing spatially resolved microstructure information, recently, convolutional neural networks are used. In this regard, the microstructure can be represented in a lower dimensional feature space that can serve as basis for solving design problems. However, such models are challenging to train due to the typically large amount of model parameters. To decrease the number of trainable parameters, feature extraction techniques can be used upstream (e.g., 2-point spatial correlation functions) aiming to obtain a more compact microstructure representation.

In this contribution, we will show how to learn structure-properties relations for spatially resolved microstructures by extending an explainable geometrical shape learning approach. The proposed approach computes a low dimensional representation by making use of geometric information (relationships between general abstract objects like voxels, level sets, curves, meshes). Taking as input such low dimensional information and features or statistics of the voxelized microstructure, we predict its effective properties of interest. The approach contrasts to convolutional neural networks as it can be explained in the sense that the computed features and the meta-models are derived from first mathematical principles. Furthermore, the novel model is easier to train as it has a lower amount of model parameters and can therefore be applied to fewer training data. In other use cases, such as in car crash simulations, the novel model has shown to perform better than state of the art approaches.