Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here we provide a detailed analysis of the heterogenous graph structures of spider webs, and use deep learning as a way to model and then synthesize artificial, bio-inspired 3D web structures. The generative AI models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) An analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation, 2) a discrete diffusion model with full neighbor representation, and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bio-inspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles towards integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

翻译：蜘蛛网是令人惊叹的生物结构，由纤细而坚韧的丝状纤维构成，并排列成具有显著力学性能（例如轻质高强、实现多样化力学响应）的复杂分层架构。虽然简单的二维圆形蛛网易于模仿，但基于三维蛛网结构的建模与合成仍具挑战性，部分原因在于其丰富的设计特征。本文对蜘蛛网的异构图结构进行了详细分析，并利用深度学习建模与合成了仿生三维蛛网结构。生成式AI模型基于关键几何参数（包括平均边长、节点数量、平均节点度等）进行条件约束。为识别图的构建原理，我们采用归纳表示采样方法对实验测定的大型蜘蛛网图进行采样，生成数据集用于训练三种条件生成模型：1）受非平衡热力学启发的模拟扩散模型（采用稀疏邻域表示），2）全邻域表示的离散扩散模型，3）全邻域表示的自回归Transformer架构。三种模型均具备可扩展性，可生成复杂的新型仿生蛛网结构，并成功构建满足设计目标的图结构。我们进一步提出算法，基于一系列几何设计目标（包括螺旋形和参数化形状），将生成模型产生的蛛网样本组装为更大尺度结构，模仿并扩展自然设计原理以适配多元工程目标。通过3D打印制造多种蛛网结构，并测试其力学性能。