A machine learning approach for efficient uncertainty quantification using multiscale methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:354

Article

Chan, Shing¹  Elsheikh, Ahmed H.¹ 

[1] Heriot Watt Univ, Sch Energy Geosci Infrastruct & Soc, Edinburgh, Midlothian, Scotland

关键词: Machine learning;    Multiscale methods;    Uncertainty quantification;    Porous media flow;    Neural networks;   

DOI  :  10.1016/j.jcp.2017.10.034

来源: Elsevier

【 摘 要 】

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. Weattribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free