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AuTO: a framework for Automatic differentiation in Topology Optimization

Structural and Multidisciplinary Optimization volume 64, pages 4355–4365 (2021)Cite this article

Abstract

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 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.

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Acknowledgements

The authors would like to thank the support of National Science Foundation through grant CMMI 1561899.

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Author notes

  1. Aaditya Chandrasekhar and Saketh Sridhara contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, USA

    Aaditya Chandrasekhar, Saketh Sridhara & Krishnan Suresh

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  1. Aaditya Chandrasekhar
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  2. Saketh Sridhara
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  3. Krishnan Suresh
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Correspondence to Krishnan Suresh.

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Replication of results

The Python code pertinent to this paper is available at https://github.com/UW-ERSL/AuTO.

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Chandrasekhar, A., Sridhara, S. & Suresh, K. AuTO: a framework for Automatic differentiation in Topology Optimization. Struct Multidisc Optim 64, 4355–4365 (2021). https://doi.org/10.1007/s00158-021-03025-8

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  • DOI: https://doi.org/10.1007/s00158-021-03025-8

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