Point cloud autoencoders were recently introduced as powerful models for data compression. They learn a lowdimensional set of variables that are suitable as design parameters for shape generation... Show morePoint cloud autoencoders were recently introduced as powerful models for data compression. They learn a lowdimensional set of variables that are suitable as design parameters for shape generation and optimization problems. In engineering tasks, 3D point clouds are often derived from fine polygon meshes, which are the most suitable representations for physics simulation, e.g., computational fluid dynamics (CFD). Yet, the reconstruction of high-quality meshes from autoencoder-based point clouds is challenging, often requiring supervised and manual work, which is prohibitive during the optimization. Target shape matching optimization using existing mesh prototypes overcomes the difficulties of recovering shape information from the point coordinates. However, for autoencoders trained on data sets comprising shapes with high degree of dissimilarity, there is not a single mesh prototype that can fit any autoencoder-based point cloud, and the selection of a set of prototypes is nontrivial. In the present paper we propose a method for optimizing a selection of prototypical meshes to match the maximum number of shapes in the autoencoder output space as possible, which is achieved by linking the advantages of the latent space representation of an autoencoder and the state-of-the-art free form deformation (FFD) method. Furthermore, we approached the balance between costs (number of mesh prototypes) and number of covered shapes by varying the number of prototypes and the dimensionality of the autoencoder latent space, showing that higher-dimensional latent spaces encode finer geometric changes, requiring more sophisticated FFD setups. Show less
Rios, T.; Wollstadt, P.; Stein, B. van; Bäck, T.H.W.; Xu, Z.; Sendhoff, B.; Menzel, S. 2019
Geometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network... Show moreGeometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network models on geometric input requires considerable computational effort. Even more so, if one considers typical problem sizes found in application domains such as engineering tasks, where geometric data are often orders of magnitude larger than the inputs currently considered in GDL literature. Hence, an assessment of the scalability of the training task is necessary, where model and data set parameters can be mapped to the computational demand during training. The present paper therefore studies the effects of data set size and the number of free model parameters on the computational effort of training a Point Cloud Autoencoder (PC-AE). We further review pre-processing techniques to obtain efficient representations of high-dimensional inputs to the PC-AE and investigate the effects of these techniques on the information abstracted by the trained model. We perform these experiments on synthetic geometric data inspired by engineering applications using computing hardware with particularly recent graphics processing units (GPUs) with high memory specifications. The present study thus provides a comprehensive evaluation of how to scale geometric deep learning architectures to high-dimensional inputs to allow for an application of state-of-the-art deep learning methods in real-world tasks. Show less
Rios, T.; Sendhoff, B.; Menzel, S.; Bäck, T.H.W.; Stein, B. van 2019
A crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off... Show moreA crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off between exploring feasible solutions in the design space and maintaining admissible computational effort. In order to achieve such balance in optimization problems with Computer Aided Engineering (CAE) models, the conventional constructive geometric representations are substituted by deformation methods, e.g. free form deformation, where the position of a few control points might be capable of handling large scale shape modifications. In light of the recent developments in the field of geometric deep learning, autoencoders have risen as a promising alternative for efficiently condensing high-dimensional models into compact representations. In this paper, we present a novel perspective on geometric deep learning models by exploring the applicability of the latent space of a point cloud autoencoder in shape optimization problems with evolutionary algorithms. Focusing on engineering applications, a target shape matching optimization is used as a surrogate to the computationally expensive CAE simulations required in engineering optimizations. Through the quality assessment of the solutions achieved in the optimization and further aspects, such as shape feasibility, point cloud autoencoders showed to be consistent and suitable geometric representations for such problems, adding a new perspective on the approaches for handling high-dimensional models to optimization tasks. Show less
