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arXiv · 1210.1532

Non-intrusive Low-Rank Separated Approximation of High-Dimensional Stochastic Models

Alireza Doostan·AbdoulAhad Validi·Gianluca Iaccarino
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Abstract

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.

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Alireza Doostan, AbdoulAhad Validi, Gianluca Iaccarino. 2012-10-04. Non-intrusive Low-Rank Separated Approximation of High-Dimensional Stochastic Models. https://doi.org/10.1016/j.cma.2013.04.003

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