NeuroNURBS: Learning Efficient Surface Representations for 3D Solids

Boundary Representation (B-Rep) is the de facto representation of 3D solids in Computer-Aided Design (CAD). B-Rep solids are defined with a set of NURBS (Non-Uniform Rational B-Splines) surfaces forming a closed volume. To represent a surface, current works often employ the UV-grid approximation, i.e., sample points uniformly on the surface. However, the UV-grid method is not efficient in surface representation and sometimes lacks precision and regularity. In this work, we propose NeuroNURBS, a representation learning method to directly encode the parameters of NURBS surfaces. Our evaluation in solid generation and segmentation tasks indicates that the NeuroNURBS performs comparably and, in some cases, superior to UV-grids, but with a significantly improved efficiency: for training the surface autoencoder, GPU consumption is reduced by 86.7%; memory requirement drops by 79.9% for storing 3D solids. Moreover, adapting BrepGen for solid generation with our NeuroNURBS improves the FID from 30.04 to 27.24, and resolves the undulating issue in generated surfaces.

On the Hyperparameters influencing a PINN's generalization beyond the training domain

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we analyze the performance of PINNs for various architectural hyperparameters and algorithmic settings based on a novel error metric and other factors such as training time. The proposed metric and approach are tailored to evaluate how well a PINN generalizes to points outside its training domain. Besides, we investigate the effect of the algorithmic setup on the outcome prediction of a PINN, inside and outside its training domain, to explore the effect of each hyperparameter. Through our study, we assess how the algorithmic setup of PINNs influences their potential for generalization and deduce the settings which maximize the potential of a PINN for accurate generalization. The study that we present returns insightful and at times counterintuitive results on PINNs. These results can be useful in PINN applications when defining the model and evaluating it.