ICML 2025

Geometry-Informed Neural Networks
Arturs Berzins * 1 2 Andreas Radler * 1 Eric Volkmann * 1
Sebastian Sanokowski 1 Sepp Hochreiter 1 Johannes Brandstetter 1 3
Abstract
Geometry is a ubiquitous tool in computer graph-
ics, 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 frame-
work for training shape-generative neural fields
without data by leveraging user-specified design
requirements in the form of objectives and con-
straints. By adding diversity as an explicit con-
straint, GINNs avoid mode-collapse and can gen-
erate multiple diverse solutions, often required in
geometry tasks. Experimentally, we apply GINNs
to several problems spanning physics, geometry,
and engineering design, showing control over ge-
ometrical and topological properties, such as sur-
face 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.
1. Introduction
Recent advances in deep learning have revolutionized fields
with abundant data, such as computer vision and natural
language processing. However, the scarcity of large datasets
in many other domains, including 3D computer graphics,
design, engineering, and physics, restricts the use of ad-
vanced supervised learning techniques, necessitating the
exploration of alternative learning strategies.
Fortunately, these disciplines are often equipped with formal
*Equal contribution 1LIT AI Lab, Institute for Machine Learn-
ing, JKU Linz, Austria 2Part of this work was done while at SIN-
TEF and Department of Mathematics, University of Oslo, Nor-
way 3Emmi AI GmbH, Linz, Austria. Correspondence to: Arturs
Berzins <berzins@ml.jku.at>.
Proceedings of the 42 nd International Confere...