Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization

JOURNAL OF COMPUTATIONAL PHYSICS

卷:348

Article

Pang, Guofei¹  Perdikaris, Paris²  Cai, Wei³  Karniadakis, George Em⁴ 

[1] Beijing Computat Sci Res Ctr, Algorithms Div, Beijing 100193, Peoples R China

[2] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

[3] Southern Methodist Univ, Dept Math, Dallas, TX 75275 USA

[4] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Fractional modeling;    Porous media;    Machine learning;    Inverse problem;    Gaussian process regression;    Uncertainty quantification;    Model uncertainty;   

DOI  :  10.1016/j.jcp.2017.07.052

来源: Elsevier

【 摘 要 】

The fractional advection-dispersion equation (FADE) can describe accurately the solute transport in groundwater but its fractional order has to be determined a priori. Here, we employ multi-fidelity Bayesian optimization to obtain the fractional order under various conditions, and we obtain more accurate results compared to previously published data. Moreover, the present method is very efficient as we use different levels of resolution to construct a stochastic surrogate model and quantify its uncertainty. We consider two different problem set ups. In the first set up, we obtain variable fractional orders of one-dimensional FADE, considering both synthetic and field data. In the second set up, we identify constant fractional orders of two-dimensional FADE using synthetic data. We employ multi-resolution simulations using two-level and three-level Gaussian process regression models to construct the surrogates. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free