Low rank surrogates for fuzzy‐stochastic partial differential equations

We consider a particular fuzzy‐stochastic PDE depending on the interaction of probabilistic and non‐probabilistic (via fuzzy arithmetic in terms of possibility theory) influences. Such a combination is beneficial in an engineering context, where aleatoric and epistemic uncertainties appear simultaneously. The fuzzy‐stochastic dependence is described in a high‐dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To alleviate this severe obstacle, a compressed low‐rank approximation in form of Hierarchical Tucker representation of the desired parametric quantity of interest is derived. The performance of the proposed model order reduction approach is demonstrated.