从生物力学到工程刺激-响应系统的范畴论框架
A Category-Theoretic Framework from Biological Mechanics to Engineered Stimulus-Response Systems
AI总结：
本文提出一种范畴论框架，用于将生物材料的自适应行为转化为工程系统，通过保持各抽象层次的物理一致性，实现生物设计逻辑的工程实现。
摘要：
自然材料通过层次组织和跨尺度耦合机制实现自适应行为。然而，将其转化为工程仍 largely 假设性。本文提出一个范畴论的组合框架，用于验证源自自然的设计。该框架定义了刺激-响应动态系统的范畴及其自然和人工子范畴。它引入了一个从生物力学到工程系统的结构保持实现函子。同时，它正式化了一个机器无关的规范层，将行为意图与可执行的制造程序联系起来。该框架以松果的湿度响应层次结构作为生物案例进行实例化。在Grasshopper中实现了完整流程，将形式规范转化为模块化参数化脚本，保持模型的组合结构。生成的设计通过熔融沉积制造进行制造，经实验评估并测试与从流程中导出的模型预测。当前实现生成了四个执行器类别，涵盖两种刺激类型和两种运动响应。其中一个执行器纯通过组合来自已验证组件，无需额外手动推导。结果表明，组合性不仅作为描述语言，还可作为生成和系统层面可验证的方法用于机械材料设计。更广泛地说，这项工作为在日益计算化、生成化和物理驱动的设计流程中嵌入形式多尺度推理提供了具体途径。
英文摘要：
Natural materials achieve adaptive behavior through hierarchical organization and coupled mechanisms across scales. Their translation into engineering, however, remains largely heuristic. What is missing is a formal translation framework that carries biological design logic into engineered realization while preserving physical consistency across levels of abstraction. Here we present a category theoretic compositional framework for verified nature-derived design. The framework defines a category of stimulus response dynamical systems with natural and artificial subcategories. It introduces a structure preserving implementation functor from biological mechanics to engineered systems. It also formalizes a machine agnostic specification layer that links behavioral intent to executable fabrication programs. We instantiate the framework on the hygromorphic pinecone hierarchy as a representative biological case. We implement the full pipeline in Grasshopper, where formal specifications are translated into modular parametric scripts that preserve the compositional structure of the model. The resulting designs are fabricated by fused filament fabrication, evaluated experimentally, and tested against model predictions derived from the pipeline. The current implementation generates four actuator classes spanning two stimulus types and two kinematic responses. One actuator arises purely through composition from previously validated components, without additional manual derivation. The results show that compositionality can function not just as a descriptive language, but as a generative and system level verifiable method for mechanical material design. More broadly, the work provides a concrete route for embedding formal multiscale reasoning within increasingly computational, generative, and physics-driven design workflows.
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