AuTO: a framework for Automatic differentiation in Topology Optimization

A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of 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, its wider adoption has largely been absent. In this educational paper, we aim to reintroduce AD for TO, making it easily accessible through illustrative codes. In particular, we employ JAX, a high-performance Python library for au tomatically 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.