Geometry-Informed Neural Networks

TL;DR

This paper introduces geometry-informed neural networks (GINNs), a novel framework that enables shape generation without large datasets by incorporating user-defined objectives and constraints, allowing for diverse and controlled geometric outputs.

Contribution

The paper presents GINNs, a new data-free training approach for shape-generative neural fields that uses explicit constraints to control geometry and diversity, avoiding mode-collapse.

Findings

GINNs can generate multiple diverse shapes without data.

They effectively control geometric properties like smoothness and topology.

Demonstrated across physics, geometry, and engineering design tasks.

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 problems spanning physics, geometry, and engineering design, 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.