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A manifold learning approach for integrated computational materials engineering. (English) Zbl 1390.74196
Summary: Image-based simulation is becoming an appealing technique to homogenize properties of real microstructures of heterogeneous materials. However fast computation techniques are needed to take decisions in a limited time-scale. Techniques based on standard computational homogenization are seriously compromised by the real-time constraint. The combination of model reduction techniques and high performance computing contribute to alleviate such a constraint but the amount of computation remains excessive in many cases. In this paper we consider an alternative route that makes use of techniques traditionally considered for machine learning purposes in order to extract the manifold in which data and fields can be interpolated accurately and in real-time and with minimum amount of online computation. Locallly Linear Embedding is considered in this work for the real-time thermal homogenization of heterogeneous microstructures.

MSC:
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
68T05 Learning and adaptive systems in artificial intelligence
74Q05 Homogenization in equilibrium problems of solid mechanics
62H35 Image analysis in multivariate analysis
62P35 Applications of statistics to physics
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