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

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.

Keywords

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