We introduce the first neural optimization framework to solve a classical instance of the tiling problem. Namely, we seek a non-periodic tiling of an arbitrary 2D shape using one or more types of tiles: the tiles maximally fill the shape's interior without overlaps or holes. To start, we reformulate tiling as a graph problem by modeling candidate tile locations in the target shape as graph nodes and connectivity between tile locations as edges. Further, we build a graph convolutional neural network, coined TilinGNN, to progressively propagate and aggregate features over graph edges and predict tile placements. TilinGNN is trained by maximizing the tiling coverage on target shapes, while avoiding overlaps and holes between the tiles. Importantly, our network is self-supervised, as we articulate these criteria as loss terms defined on the network outputs, without the need of ground-truth tiling solutions. After training, the runtime of TilinGNN is roughly linear to the number of candidate tile locations, significantly outperforming traditional combinatorial search. We conducted various experiments on a variety of shapes to showcase the speed and versatility of TilinGNN. We also present comparisons to alternative methods and manual solutions, robustness analysis, and ablation studies to demonstrate the quality of our approach.

中文翻译：

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TilinGNN：学习使用自监督图神经网络平铺

我们引入了第一个神经优化框架来解决平铺问题的经典实例。也就是说，我们寻求使用一种或多种类型的瓷砖对任意 2D 形状进行非周期性平铺：瓷砖最大程度地填充形状的内部而没有重叠或孔洞。首先，我们通过将目标形状中的候选瓦片位置建模为图形节点并将瓦片位置之间的连接性建模为边，将切片重新表述为图形问题。此外，我们构建了一个图卷积神经网络，创造了 TilinGNN，以逐步传播和聚合图边缘上的特征并预测图块放置。TilinGNN 通过最大化目标形状上的平铺覆盖率来训练，同时避免平铺之间的重叠和空洞。重要的是，我们的网络是自我监督的，当我们将这些标准表述为在网络输出上定义的损失项时，不需要地面实况平铺解决方案。经过训练，TilinGNN 的运行时间与候选瓦片位置的数量大致呈线性关系，明显优于传统的组合搜索。我们对各种形状进行了各种实验，以展示 TilinGNN 的速度和多功能性。我们还提供了与替代方法和手动解决方案、稳健性分析和消融研究的比较，以证明我们方法的质量。我们对各种形状进行了各种实验，以展示 TilinGNN 的速度和多功能性。我们还提供了与替代方法和手动解决方案、稳健性分析和消融研究的比较，以证明我们方法的质量。我们对各种形状进行了各种实验，以展示 TilinGNN 的速度和多功能性。我们还提供了与替代方法和手动解决方案、稳健性分析和消融研究的比较，以证明我们方法的质量。