Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 9 November 2018 / Approved: 13 November 2018 / Online: 13 November 2018 (10:08:36 CET)

A peer-reviewed article of this Preprint also exists.

Olivier, C.; Ryckelynck, D.; Cortial, J. Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity. Math. Comput. Appl. 2019, 24, 17. Olivier, C.; Ryckelynck, D.; Cortial, J. Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity. Math. Comput. Appl. 2019, 24, 17.

Journal reference: Math. Comput. Appl. 2019, 24, 17
DOI: 10.3390/mca24010017

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.

Subject Areas

parameter-dependent model; surrogate modeling; tensor-train decomposition; gappy POD; heterogeneous data; elasto-viscoplasticity

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