3 years ago

Variance‐based simplex stochastic collocation with model order reduction for high‐dimensional systems.

D.G. Giovanis, M.D. Shields

Summary

In this work, an adaptive simplex stochastic collocation method is introduced in which sample refinement is informed by variability in the solution of the system. The proposed method is based on the concept of multi‐element stochastic collocation methods and is capable of dealing with very high dimensional models whose solutions are expressed as a vector, a matrix, or a tensor. The method leverages random samples in order to create a multi‐element polynomial chaos surrogate model that incorporates local anisotropy in the refinement, informed by the variance of the estimated solution. blueThis feature makes it beneficial for strongly nonlinear and/or discontinuous problems with correlated non‐Gaussian uncertainties. To solve large systems, a reduced order model (ROM) of the high‐dimensional response is identified using singular value decomposition (higher‐order SVD for matrix/tensor solutions) and polynomial chaos is used to interpolate the ROM. The method is applied to several stochastic systems of varying type of response (scalar/vector/matrix) and it shows considerable improvement in performance compared to existing simplex stochastic collocation methods and adaptive sparse grid collocation methods.

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.