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Article

Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

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Submitted:

09 November 2018

Posted:

13 November 2018

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Abstract
This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.
Keywords: 
parameter-dependent model; surrogate modeling; tensor-train decomposition; gappy POD; heterogeneous data; elasto-viscoplasticity
Subject: 
Engineering  -   Mechanical Engineering
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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