Back To Meshes: Optimal Simulation-ready Mesh Prototypes For Autoencoder-based 3D Car Point Clouds

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 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.

I. Introduction

Point cloud autoencoders stand out from the literature on geometric deep learning as powerful shape generation techniques. These architectures compress 3D geometric data into a compact set of design variables, the so-called latent space, while learning an efficient method for reconstructing geometries [1], [2]. In automated computational shape optimization problems, e.g. aerodynamic design optimization of vehicles, the latent variables could perform as shape parameters. While the optimization algorithm searches iteratively for solutions in the latent space, the trained decoder retrieves the shapes as 3D point clouds, which serve as input to downstream tasks. Nevertheless, different aspects hinder the implementation of these methods. Among them are the interpretability of the latent variables [3], [4], the sparsity of engineering data sets and, ultimately, the need to recover surface meshes from the 3D point clouds generated by the autoencoder for performing downstream tasks, such as automated performance simulations of novel design proposals.