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.
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.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.