Recent breakthroughs in artificial intelligence (AI) afford opportunities for new paradigms for material design and optimization. For modeling-driven design approaches, the optimization of mechanical properties, in general, requires boundary value problems (BVPs) to be solved. Machine learning (ML) models, trained on high-throughput labeled data obtained from the solution of BVPs, are able to explore and exploit vast design spaces. Nevertheless, prior to the implementation of those methods, applied load and displacement constraints have to be known beforehand. Here, we present a semi-supervised approach to design topological structures of architected materials based on the load levels of only 1% of nodes, along with the connectivity and mechanical properties of the architected materials. Graph neural networks (GNNs), which can learn graph embeddings and show outstanding performance on semi-supervised classification tasks using small amount of data, have been used to predict the distribution of the load levels of the remaining 99%. The integration of the network with an algorithm to redistribute truss thickness enables us to perform multiscale design of architected materials under various geometries and loads. This work reveals the potential of a novel paradigm to design architected materials via semi-supervised learning, and inspires applications such as using sparse sensors in truss designs in additive manufacturing, architectures and civil infrastructure under complex loading conditions.

人工智能（AI）的最新突破为材料设计和优化的新范例提供了机会。对于建模驱动的设计方法，机械性能的优化通常需要解决边值问题（BVP）。机器学习（ML）模型经过从BVP解决方案中获得的高通量标记数据的训练，能够探索和利用广阔的设计空间。但是，在实施这些方法之前，必须事先知道施加的载荷和位移约束。在这里，我们提出了一种基于结构的半监督方法，该方法仅基于节点的1％的负载水平以及结构化材料的连接性和机械性能来设计结构化材料的拓扑结构。图神经网络（GNN），它可以学习图形嵌入并使用少量数据在半监督分类任务中显示出出色的性能，已用于预测其余99％的负载水平的分布。网络与重新分配桁架厚度的算法的集成使我们能够在各种几何形状和载荷下执行建筑材料的多尺度设计。这项工作揭示了一种通过半监督学习来设计建筑材料的新颖范例的潜力，并激发了诸如在复杂负载条件下在增材制造，建筑和民用基础设施的桁架设计中使用稀疏传感器的应用程序。已被用来预测其余99％的负载水平的分布。网络与重新分配桁架厚度的算法的集成使我们能够在各种几何形状和载荷下执行建筑材料的多尺度设计。这项工作揭示了一种通过半监督学习来设计建筑材料的新颖范例的潜力，并激发了诸如在复杂负载条件下在增材制造，建筑和民用基础设施的桁架设计中使用稀疏传感器的应用程序。已被用来预测其余99％的负载水平的分布。网络与重新分配桁架厚度的算法的集成使我们能够在各种几何形状和载荷下执行建筑材料的多尺度设计。这项工作揭示了一种通过半监督学习来设计建筑材料的新颖范例的潜力，并激发了诸如在复杂负载条件下在增材制造，建筑和民用基础设施的桁架设计中使用稀疏传感器的应用程序。