Geometry-Informed Neural Networks
Arturs Berzins Andreas Radler Sebastian Sanokowski Sepp Hochreiter Johannes Brandstetter
We introduce the concept of geometry-informed neural networks (GINNs), which
encompass (i) learning under geometric constraints, (ii) neural fields as a
suitable representation, and (iii) generating diverse solutions to
under-determined systems often encountered in geometric tasks. Notably, the
GINN formulation does not require training data, and as such can be considered
generative modeling driven purely by constraints. We add an explicit diversity
loss to mitigate mode collapse. We consider several constraints, in particular,
the connectedness of components which we convert to a differentiable loss
through Morse theory. Experimentally, we demonstrate the efficacy of the GINN
learning paradigm across a range of two and three-dimensional scenarios with
increasing levels of complexity.