Geometry is a ubiquitous language of 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) to train shape generative models \emph{without any data}. GINNs combine (i) learning under constraints, (ii) neural fields as a suitable representation, and (iii) generating diverse solutions to under-determined problems. We apply GINNs to several two and three-dimensional problems of increasing levels of complexity. Our results demonstrate the feasibility of training shape generative models in a data-free setting. This new paradigm opens several exciting research directions, expanding the application of generative models into domains where data is sparse.

翻译：几何是计算机图形学、设计与工程领域中无处不在的语言。然而，由于缺乏大规模形状数据集，现有监督学习方法的应用受到限制，这促使我们探索替代的学习策略。为此，我们引入几何感知神经网络（GINNs），以在\emph{无需任何数据}的情况下训练形状生成模型。GINNs融合了以下三个要素：(i) 约束条件下的学习，(ii) 神经场作为一种合适的表示方法，以及 (iii) 为欠定问题生成多样化解。我们将GINNs应用于多个复杂度递增的二维和三维问题。实验结果表明，在无数据条件下训练形状生成模型是可行的。这一新范式开辟了多个令人兴奋的研究方向，将生成模型的应用扩展至数据稀缺的领域。