AuTO: a framework for Automatic differentiation in Topology Optimization

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 6; pp. 4355 - 4365
• Main Authors: Chandrasekhar, Aaditya, Sridhara, Saketh, Suresh, Krishnan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021; Springer Nature B.V
• Subjects: Algorithms; Codes; Compliance; Computational Mathematics and Numerical Analysis; Constraint modelling; Differentiation; Educational Paper; Engineering; Engineering Design; Finite element analysis; Libraries; Optimization; Sensitivity analysis; Theoretical and Applied Mechanics; Topology optimization; JAX; Topology optimization; Sensitivity analysis; Machine learning; Automatic differentiation; Educational code
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-03025-8

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.