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

1
Safran Tech, Modelling & Simulation, Rue des Jeunes Bois, Châteaufort, 78114 Magny-Les-Hameaux, France
2
MAT-Centre des Matériaux, MINES ParisTech, PSL Research University, CNRS UMR 7633, 10 rue Desbruères, 91003 Evry, France
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 17; https://doi.org/10.3390/mca24010017
Received: 9 November 2018 / Revised: 11 January 2019 / Accepted: 23 January 2019 / Published: 28 January 2019
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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 of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating 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. View Full-Text
Keywords: parameter-dependent model; surrogate modeling; tensor-train decomposition; gappy POD; heterogeneous data; elasto-viscoplasticity parameter-dependent model; surrogate modeling; tensor-train decomposition; gappy POD; heterogeneous data; elasto-viscoplasticity
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Olivier, C.; Ryckelynck, D.; Cortial, J. Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity. Math. Comput. Appl. 2019, 24, 17.

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