کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
497983 | 862959 | 2013 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Non-intrusive low-rank separated approximation of high-dimensional stochastic models Non-intrusive low-rank separated approximation of high-dimensional stochastic models](/preview/png/497983.png)
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.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 263, 15 August 2013, Pages 42–55