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Deep Neural Networks For Learning Geometric Features In Topology Optimization

Nivesh Dommaraju, Mariusz Bujny, Stefan Menzel, Markus Olhofer, Fabian Duddeck, "Deep Neural Networks For Learning Geometric Features In Topology Optimization", ECCOMAS Congress 2020, 2021.


Topology Optimization (TO) redistributes material in a defined design space to provide optimal designs for multiple objectives under prescribed constraints. In the early design phase, due to flexibility in optimization constraints or boundary conditions, TO can be used to generate a large dataset of different design concepts. A few of the resulting designs can then be picked for further analysis of requirements not considered in the TO. Since the designer cannot review all designs generated by TO, different design exploration methods are suggested. For example [1, 2] propose to select a few representative designs in the dataset based on geometric or performance features. These methods are based on a feature extraction step followed by a design selection step. The extracted features such as weight, position of center of gravity, stiffness, or task-specific features influence heavily the design selection step which involves ranking or clustering [1-3] of designs with similar features. Often, user-specified features might not be effective in the selection of designs with novel geometry, i.e. designs with different topology, size or shape. Hence, a method is proposed here to learn features using a deep autoencoder neural network [4]. We adapt this method to more topologically complex datasets. A large training-dataset is generated using TO (Solid Isotropic Material with Penalization [5]) by varying prescribed boundary conditions. Since the autoencoder requires a point cloud representation of designs, we convert designs first into a surface mesh and then to a point cloud. The surface mesh is generated using the marching cubes method [6] and the point cloud using uniform mesh sampling [7]. Then, the point cloud autoencoder is trained to learn geometric features characterized by higher generalization ability compared to the hand-engineered features. The learned features are compared to commonly used geometry similarity metrics such as voxel differences, chamfer distance, and earth mover distance [4]. Based on evaluation of the proposed method, we find it promising in identifying novel geometries and supporting engineering design process via TO.

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