Scalability of Learning Tasks on 3D CAE Models Using Point Cloud Autoencoders

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 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.