Geometry-Informed Neural Networks

arXiv:2402.14009v1 Announce Type: new
Abstract: 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 …

abstract arxiv concept constraints cs.cv cs.lg data diverse fields generative geometry iii networks neural networks representation solutions systems tasks training training data type