On the Efficiency of a Point Cloud Autoencoder as a Geometric Representation for Shape Optimization

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 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.Algorithms and the Foundations of Software technolog

AI based geometric similarity search supporting component reuse in engineering design

Today, companies are faced with the challenge to develop and produce individualized products in the shortest possible time at very low cost in order to remain attractive under strong competitive pressure. For reasons of efficiency, products are therefore often developed in generations. Proven components are adopted in a new product generation and only some of the components are newly developed to meet new customer requirements. Many companies, therefore, have a large database of 3D CAD product models containing years of engineering experience. Nevertheless, it is often difficult to execute database queries to find which products or components already exist and could be reused or adapted for a new product generation or variant. As a result, many duplicates are created, which are associated with high effort and costs, and the risk of introducing design errors increases. Therefore, the aim of this paper is to develop an automated approach for geometric similarity search that also takes company-specific features of components into account. Machine learning methods are capable of automatically extracting relevant geometric features by learning a suitable representation of the corresponding 3D object. For this purpose, an autoencoder is developed which is trained to extract class-specific feature vectors. To improve the representativeness of those vectors for the similarity search, the architecture and hyperparameters of the autoencoder are optimized based on several experiments. Considering a real use case with a data set from the field of mechanical engineering, it is shown that geometrically similar CAD models can be found very quickly using the learned representation, and that better results are obtained than with conventional methods based on meta information, e.g. volume and bounding box. On the one hand, the fast finding of similar models encourages the reuse of existing solutions. On the other hand, standardization and, thus, economy of scale is promoted

Surface Networks

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curvature directions --- this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models \emph{Surface Networks (SN)}. We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs

Large Language and Text-to-3D Models for Engineering Design Optimization

The current advances in generative AI for learning large neural network models with the capability to produce essays, images, music and even 3D assets from text prompts create opportunities for a manifold of disciplines. In the present paper, we study the potential of deep text-to-3D models in the engineering domain, with focus on the chances and challenges when integrating and interacting with 3D assets in computational simulation-based design optimization. In contrast to traditional design optimization of 3D geometries that often searches for the optimum designs using numerical representations, such as B-Spline surface or deformation parameters in vehicle aerodynamic optimization, natural language challenges the optimization framework by requiring a different interpretation of variation operators while at the same time may ease and motivate the human user interaction. Here, we propose and realize a fully automated evolutionary design optimization framework using Shap-E, a recently published text-to-3D asset network by OpenAI, in the context of aerodynamic vehicle optimization. For representing text prompts in the evolutionary optimization, we evaluate (a) a bag-of-words approach based on prompt templates and Wordnet samples, and (b) a tokenisation approach based on prompt templates and the byte pair encoding method from GPT4. Our main findings from the optimizations indicate that, first, it is important to ensure that the designs generated from prompts are within the object class of application, i.e. diverse and novel designs need to be realistic, and, second, that more research is required to develop methods where the strength of text prompt variations and the resulting variations of the 3D designs share causal relations to some degree to improve the optimization.Comment: 9 pages, 13 figures, IEEE conference templat

Multi-task shape optimization using a 3D point cloud autoencoder as unified representation

Algorithms and the Foundations of Software technolog