AuTO: A Framework for Automatic differentiation in Topology 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.

References in corpus (2)

• Array Programming with NumPy
• Topology optimization under thermo-elastic buckling

Cited by in corpus (3)

• JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science
• Deep energy method in topology optimization applications
• A framework for structural shape optimization based on automatic differentiation, the adjoint method and accelerated linear algebra