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Robust topology optimization with low rank approximation using artificial neural networks

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Abstract

We present a low rank approximation approach for topology optimization of parametrized linear elastic structures. The parametrization is considered on loading and stiffness of the structure. The low rank approximation is achieved by identifying a parametric connection among coarse finite element models of the structure (associated with different design iterates) and is used to inform the high fidelity finite element analysis. We build an Artificial Neural Network (ANN) map between low resolution design iterates and their corresponding interpolative coefficients (obtained from low rank approximations) and use this surrogate to perform high resolution parametric topology optimization. We demonstrate our approach on robust topology optimization with compliance constraints/objective functions and develop error bounds for the the parametric compliance computations. We verify these parametric computations with more challenging quantities of interest such as the p-norm of von Mises stress. To conclude, we use our approach on a 3D robust topology optimization and show significant reduction in computational cost via quantitative measures.

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Notes

  1. As an example, if \({\varvec{X}}_{in}\) is an image with \(100 \times 100\) pixels (cells) and \(k_n=10\), an arbitrary index set for \(\mathcal {I}\) and \(\mathcal {J}\) could be \(\mathcal {I}=\{1,2,\ldots ,10\}\) and \(\mathcal {J}=\{11,12,\ldots ,20\}\).

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Acknowledgements

This research was sponsored by the Army Research Laboratory (ARL) under Cooperative Agreement Number W911NF-12-2-0023. The first and third authors were partially supported by the Air Force Office of Scientific Research under grant FA9550-20-1-0338. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of ARL or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

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Authors and Affiliations

  1. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA

    Vahid Keshavarzzadeh

  2. Scientific Computing and Imaging Institute, School of Computing, University of Utah, Salt Lake City, USA

    Robert M. Kirby

  3. Department of Mathematics, Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA

    Akil Narayan

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  1. Vahid Keshavarzzadeh
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Correspondence to Vahid Keshavarzzadeh.

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Keshavarzzadeh, V., Kirby, R.M. & Narayan, A. Robust topology optimization with low rank approximation using artificial neural networks. Comput Mech 68, 1297–1323 (2021). https://doi.org/10.1007/s00466-021-02069-3

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