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Clustering discretization methods for generation of material performance databases in machine learning and design optimization. (English) Zbl 1470.74073

Summary: 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.

MSC:

74S99 Numerical and other methods in solid mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74P15 Topological methods for optimization problems in solid mechanics
68T05 Learning and adaptive systems in artificial intelligence
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