Friday, October 5, 2012

1210.1532 (Alireza Doostan et al.)

Non-intrusive Low-Rank Separated Approximation of High-Dimensional
Stochastic Models
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Alireza Doostan, AbdoulAhad Validi, Gianluca Iaccarino
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.
View original: http://arxiv.org/abs/1210.1532

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