Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:409

Article

Tang, Kejun^1,2,3  Liao, Qifeng¹ 

[1] ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai, Peoples R China

[2] Chinese Acad Sci, Shanghai Inst Microsyst & Informat Technol, Shanghai, Peoples R China

[3] Univ Chinese Acad Sci, Beijing, Peoples R China

关键词: Tensor recovery;    Model reduction;    PDEs;    Uncertainty quantification;   

DOI  :  10.1016/j.jcp.2020.109326

来源: Elsevier

【 摘 要 】

This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models are discrete solutions on given physical grids which are high-dimensional, we use kernel principal component analysis to construct stochastic collocation approximations in reduced dimensional spaces of the outputs. To address the issue of high-dimensional random inputs, we develop a new efficient rank adaptive tensor recovery approach to compute the collocation coefficients. Novel efficient initialization strategies for non-convex optimization problems involved in tensor recovery are also developed in this work. We present a general mathematical framework of our overall model reduction approach, analyze its stability, and demonstrate its efficiency with numerical experiments. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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