Geometry-Informed Neural Networks

2024-02-21

arXiv.org

AI Summary

Controllable geometric generation remains challenging in scenarios lacking large-scale 3D shape datasets. Method: This paper proposes a data-free neural implicit field generation framework that encodes user-specified design objectives—such as smoothness, genus (number of holes), and connectivity—as partial differential equation (PDE) constraints, geometric differential operator regularizers, and a multi-objective Lagrangian optimization objective, all directly embedded into neural field training. Contribution/Results: It establishes the first data-free paradigm for implicit shape generation; introduces explicit diversity constraints to mitigate mode collapse; and enables joint yet disentangled control over geometric and topological attributes. Experiments on multiple benchmarks and real-world engineering design tasks demonstrate precise, stable control over surface smoothness, connectivity, and genus, while consistently producing high-quality, diverse, and feasible shape ensembles.

Technology Category

• Natural Language Processing: Generation
• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Web data generation and simulation

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 validation 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.

Problem

• Overcoming lack of large shape datasets for supervised learning
• Generating diverse geometric solutions without mode-collapse
• Controlling geometric and topological properties in design tasks

Innovation

• Geometry-informed neural networks for shape generation
• Training without data using design objectives
• Diversity constraint prevents mode-collapse