Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Zhang, Dongkun¹  Yang, Liu¹  Karniadakis, George Em¹ 

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

关键词: Gaussian process regression;    Domain decomposition;    Multi-fidelity;    Machine learning;   

DOI  :  10.1016/j.jcp.2018.07.039

来源: Elsevier

【 摘 要 】

We consider a new prototype problem in domain decomposition with the solution in one domain governed by a known partial differential equation (PDE) whereas the solution in an adjacent domain is reconstructed by information gathered from distributed sensors (data) of variable fidelity. The PDE-domain and the Data-domain are tightly coupled, as the PDE solution is driven by the collected data, while the information gathered from its associated sensors is influenced by the PDE solution. Our overall methodology is based on the Schwarz alternating method and on recent advances in Gaussian process regression (GPR) using multi-fidelity data. The effectiveness of the proposed domain decomposition algorithm is demonstrated by examples of Helmholtz equations in both one-dimensional (1D) and two-dimensional (2D) domains. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free