AuTO: A Framework for Automatic differentiation in Topology Optimization

TL;DR

AuTO introduces an accessible framework using automatic differentiation via JAX to simplify and improve sensitivity analysis in topology optimization, demonstrated through various design examples.

Contribution

The paper reintroduces AD for TO, providing an easy-to-use Python framework with illustrative codes to enhance sensitivity computation in complex optimization problems.

Findings

AuTO effectively computes sensitivities for diverse TO problems.

The framework simplifies implementation and reduces errors in sensitivity derivation.

Demonstrations include compliance minimization, mechanism design, and microstructural optimization.

Abstract

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.