Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges is an expensive iterative process. Existing techniques for solving such inverse mechanical problems rely on traditional direct optimization methods, which are slow and computationally expensive, limiting iteration speed and design exploration. Neural networks would seem to offer a solution, via data-driven amortized optimization for specific design tasks, but they often require extensive fine-tuning and cannot ensure that important design criteria, such as mechanical integrity, are met. In this work, we combine neural networks with a differentiable mechanics simulator to develop a model that accelerates the solution of shape approximation problems for architectural structures modeled as bar systems. As a result, our model offers explicit guarantees to satisfy mechanical constraints while generating designs that match target geometries. We validate our model in two tasks, the design of masonry shells and cable-net towers. Our model achieves better accuracy and generalization than fully neural alternatives, and comparable accuracy to direct optimization but in real time, enabling fast and sound design exploration. We further demonstrate the real-world potential of our trained model by deploying it in 3D modeling software and by fabricating a physical prototype. Our work opens up new opportunities for accelerated physical design enhanced by neural networks for the built environment.

翻译：为壳体、塔楼和桥梁等建筑结构设计具有力学效率的几何形状是一个昂贵且迭代的过程。解决此类力学逆问题的现有技术依赖于传统的直接优化方法，这些方法速度慢、计算成本高，限制了迭代速度与设计探索。神经网络似乎通过针对特定设计任务的数据驱动摊销优化提供了一种解决方案，但它们通常需要大量微调，且无法确保满足如力学完整性等重要设计标准。在本工作中，我们将神经网络与可微分力学模拟器相结合，开发了一个加速求解以杆系建模的建筑结构形状逼近问题的模型。因此，我们的模型在生成符合目标几何形状的设计的同时，提供了满足力学约束的明确保证。我们在两个任务中验证了模型：砌体壳体设计与索网塔楼设计。相较于完全基于神经网络的方案，我们的模型实现了更高的精度与泛化能力；相较于直接优化方法，在保持相当精度的同时实现了实时计算，从而支持快速且可靠的设计探索。我们进一步通过将训练模型部署至三维建模软件并制作物理原型，展示了其实际应用潜力。本研究为神经网络增强的建筑环境加速物理设计开辟了新的机遇。