Nivesh Dommaraju, Mariusz Bujny, Stefan Menzel, Markus Olhofer, Fabian Duddeck, "Evaluation of geometric similarity metrics for structural clusters generated using topology optimization", Applied Intelligence, 2022.

In an engineering design process, multitudes of feasible designs can be automatically generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Design exploration of such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives as designs for review. Similarity can be defined on a purely functional level but also based on the geometric properties, such as size, shape, and topology, which are important at the early stages of design engineering. Different metrics exist to measure geometrical differences, e.g., voxel distance, chamfer distances, or Euclidean distance in the reduced representation of the high-dimensional 3D geometric data. It is not clear which of the numerous metrics is best suited for exploring designs obtained in structural optimization. For example, chamfer distance intuitively measures the geometrical differences but is expensive. Euclidean distance with low-dimensional geometric features, when meaningful, provides features that can be associated with designs, which eases the visualization and exploration of a design dataset. To evaluate different metrics in the context of design exploration, we propose a novel approach to quantify certain useful properties of a metric such as the ability to capture intuitive geometrical differences and to identify similar designs in topologically-complex synthetic datasets using clustering, an unsupervised machine learning method. From our results, we conclude that dimensionality reduction techniques, namely, UMAP (Uniform Manifold Approximation and Projection), and PCAE (Pointcloud Autoencoder) are promising in encoding geometric features that enable us to integrate geometrical properties with performance attributes.