Functional properties of 2D materials like graphene can be tailored by designing their 3D structure at the Angstrom to nanometer scale. While there are routes to tailoring 3D structure at larger scales, achieving controllable sub-micron 3D deformations has remained an elusive goal since the original discovery of graphene. In this contribution, we summarize the state-of-the-art in controllable 3D structures, and present our perspective on pathways to realizing atomic-scale control. We propose an approach based on strategic application of mechanical load to precisely relocate and position topological defects that give rise to curvature and corrugation to achieve a desired 3D structure. Realizing this approach requires establishing the detailed nature of defect migration and pathways in response to applied load. From a computational perspective, the key needed advances lie in the identification of defect migration mechanisms. These needed advances define new forward and inverse problems: when a fixed stress or strain field is applied, along which pathways will defects migrate?, and vice versa. We provide a formal statement of these forward and inverse problems, and review recent methods that may enable solving them. The forward problem is addressed by determining the potential energy surface of allowable topological configurations through Monte Carlo and Gaussian process models to determine defect migration paths through dynamic programming algorithms or Monte Carlo tree search. Two inverse models are suggested, one based on genetic algorithms and another on convolutional neural networks, to predict the applied loads that induce migration and position defects to achieve desired curvature and corrugation. The realization of controllable 3D structures enables a vast design space at multiple scales to enable new functionality in flexible electronics, soft robotics, biomimetics, optics, and other application areas.

可以通过在Ang至纳米尺度上设计3D结构来定制2D材料（如石墨烯）的功能特性。尽管有大规模定制3D结构的途径，但自最初发现石墨烯以来，实现可控的亚微米3D变形仍然是遥不可及的目标。在此贡献中，我们总结了可控3D结构中的最新技术，并提出了实现原子级控制的途径的观点。我们提出了一种基于机械负载战略应用的方法，以精确地重新定位和定位拓扑缺陷，这些拓扑缺陷会引起曲率和波纹以实现所需的3D结构。要实现此方法，需要建立缺陷迁移的详细性质和响应所施加负载的途径。从计算的角度来看，需要取得进展的关键在于确定缺陷迁移机制。这些需要的进步定义了新的正反问题：当施加固定的应力或应变场时，缺陷将沿着哪些路径迁移？反之亦然。我们提供了这些正反问题的正式陈述，并回顾了可能解决这些问题的最新方法。通过蒙特卡洛和高斯过程模型确定允许的拓扑结构的势能面，以通过动态编程算法或蒙特卡洛树搜索来确定缺陷迁移路径，从而解决了前向问题。建议使用两种逆模型，一种基于遗传算法，另一种基于卷积神经网络，以预测施加的载荷，这些载荷会引起迁移和位置缺陷，以实现所需的曲率和波纹。可控3D结构的实现实现了多个规模的广阔设计空间，从而在柔性电子，软机器人，仿生，光学和其他应用领域中实现了新功能。