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Clustering discretization methods for generation of material performance databases in machine learning and design optimization

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Abstract

Mechanical science and engineering can use machine learning. However, data sets have remained relatively scarce; fortunately, known governing equations can supplement these data. This paper summarizes and generalizes three reduced order methods: self-consistent clustering analysis, virtual clustering analysis, and FEM-clustering analysis. These approaches have two-stage structures: unsupervised learning facilitates model complexity reduction and mechanistic equations provide predictions. These predictions define databases appropriate for training neural networks. The feed forward neural network solves forward problems, e.g., replacing constitutive laws or homogenization routines. The convolutional neural network solves inverse problems or is a classifier, e.g., extracting boundary conditions or determining if damage occurs. We will explain how these networks are applied, then provide a practical exercise: topology optimization of a structure (a) with non-linear elastic material behavior and (b) under a microstructural damage constraint. This results in microstructure-sensitive designs with computational effort only slightly more than for a conventional linear elastic analysis.

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Notes

  1. A 5% deviation from the reference solution (DNS) is indicated by the blue shaded region in Figs. 6 and 7.

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Acknowledgements

The authors thank Sourav Saha and Satyajit Mojumder for their helpful suggestions during the writing process. W.K.L. acknowledges the support of the National Science Foundation under Grant No. MOMS/CMMI-1762035. O.L.K. thanks the United States National Science Foundation (NSF) for their support through the NSF Graduate Research Fellowship Program under financial award number DGE-1324585. H. L. acknowledges the support by the Northwestern University Data Science Initiative (DSI) under Grant No. 171 4745002 10043324. L.Z. and SQ.T. were supported partially by the National Science Foundation of China under Grant numbers 11832001, 11521202, and 11890681.

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Author notes

  1. Hengyang Li, Orion L. Kafka and Jiaying Gao have contributed equally to this work.

Authors and Affiliations

  1. Northwestern University, 2145 Sheridan Road, Tech B224, Evanston, IL, 60208-3109, USA

    Hengyang Li, Orion L. Kafka, Jiaying Gao, Cheng Yu, Mahsa Tajdari & Wing Kam Liu

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

    Yinghao Nie, Shan Tang, Xu Guo, Gang Li & Gengdong Cheng

  3. HEDPS and LTCS, College of Engineering, Peking University, Beijing, China

    Lei Zhang & Shaoqiang Tang

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  1. Hengyang Li
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Correspondence to Wing Kam Liu.

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Li, H., Kafka, O.L., Gao, J. et al. Clustering discretization methods for generation of material performance databases in machine learning and design optimization. Comput Mech 64, 281–305 (2019). https://doi.org/10.1007/s00466-019-01716-0

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