  This work proposes a sampling-based (non-intrusive) approach within the
context of low-rank separated representations to tackle the issue of
curse-of-dimensionality associated with the solution of models, e.g.,
PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed
in details, the number of random realizations of the solution, required for a
successful approximation, grows linearly with respect to the number of random
inputs. The construction of the separated representation is achieved via a
regularized alternating least-squares regression, together with an error
indicator to estimate model parameters. The computational complexity of such a
construction is quadratic in the number of random inputs. The performance of
the method is investigated through its application to three numerical examples
including two ODE problems with high-dimensional random inputs.
