A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material models. An alternate approach is to utilize automatic differentiation (AD). While AD has been around for decades, and has also been applied in TO, wider adoption has largely been absent. In this educational paper, we aim to reintroduce AD for TO, and make it easily accessible through illustrative codes. In particular, we employ JAX, a high-performance Python library for automatically computing sensitivities from a user defined TO problem. The resulting framework, referred to here as AuTO, is illustrated through several examples in compliance minimization, compliant mechanism design and microstructural design.

中文翻译：

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AuTO：拓扑优化中自动区分的框架

拓扑优化（TO）的关键步骤是发现灵敏度。手动推导和实现灵敏度可能非常费力且容易出错，尤其是对于非平凡的目标，约束条件和材料模型而言。另一种方法是利用自动微分（AD）。尽管AD已有数十年的历史，并且也已在TO中得到应用，但在很大程度上却缺乏广泛的采用。在本教育论文中，我们旨在重新引入针对TO的AD，并使其易于通过说明性代码进行访问。特别是，我们采用了高性能的Python库JAX，用于自动计算用户定义的TO问题的敏感度。通过最小化合规性，顺应性机制设计和微结构设计中的几个示例，说明了所得的框架（在此称为AuTO）。