  The challenges for non-intrusive methods for Polynomial Chaos modeling lie in
the computational efficiency and accuracy under a limited number of model
simulations. These challenges can be addressed by enforcing sparsity in the
series representation through retaining only the most important basis terms. In
this work, we present a novel sparse Bayesian learning technique for obtaining
sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine
model and is trained using Variational Inference. The methodology shows great
potential in high-dimensional data-driven settings using relatively few data
points and achieves user-controlled sparse levels that are comparable to other
methods such as compressive sensing. The proposed approach is illustrated on
two numerical examples, a synthetic response function that is explored for
validation purposes and a low-carbon steel plate with random Young's modulus
and random loading, which is modeled by stochastic finite element with 38 input
random variables.
