Geometry-Informed Neural Networks

Arturs Berzins, Andreas Radler, Eric Volkmann, Sebastian Sanokowski, Sepp Hochreiter, Johannes Brandstetter

Keywords: geometry, implicit neural representation, neural fields, theory-informed learning, geometric deep learning, physics-informed neural networks, generative design

TL;DR: We introduce GINN -- a framework for training shape-generative neural fields without data by leveraging design constraints and avoiding mode-collapse using a diversity loss.

Abstract: Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) - a framework for training shape-generative neural fields *without data* by leveraging user-specified design requirements in the form of objectives and constraints. By adding *diversity* as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several introductory problems and a realistic 3D engineering design problem, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 11219