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An adaptiveANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient

Zhiwen Zhang Xin Hu Thomas Y. Hou Guang Lin Mike Yan

Numerical Analysis and Scientific Computing mathscidoc:1912.431040

Communications in Computational Physics, 2014.4
In this paper, we present an adaptive, analysis of variance (ANOVA)-based data-driven stochastic method (ANOVA-DSM) to study the stochastic partial differential equations (SPDEs) in the multi-query setting. Our new method integrates the advantages of both the adaptive ANOVA decomposition technique and the data-driven stochastic method. To handle high-dimensional stochastic problems, we investigate the use of adaptive ANOVA decomposition in the stochastic space as an effective dimension-reduction technique. To improve the slow convergence of the generalized polynomial chaos (gPC) method or stochastic collocation (SC) method, we adopt the data-driven stochastic method (DSM) for speed up. An essential ingredient of the DSM is to construct a set of stochastic basis under which the stochastic solutions enjoy a compact representation for a broad range of forcing functions and/or boundary conditions
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@inproceedings{zhiwen2014an,
  title={An adaptiveANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient},
  author={Zhiwen Zhang, Xin Hu, Thomas Y. Hou, Guang Lin, and Mike Yan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211421474847604},
  booktitle={Communications in Computational Physics},
  year={2014},
}
Zhiwen Zhang, Xin Hu, Thomas Y. Hou, Guang Lin, and Mike Yan. An adaptiveANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. 2014. In Communications in Computational Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211421474847604.
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