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.
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.
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.
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