Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning

JOURNAL OF COMPUTATIONAL PHYSICS

卷:395

Article

Carlberg, Kevin T.^1,4  Jameson, Antony^3,5  Kochenderfer, Mykel J.²  Morton, Jeremy²  Peng, Liqian¹  Witherden, Freddie D.² 

[1] Sandia Natl Labs, Livermore, CA 94550 USA

[2] Stanford Univ, Durand Bldg,496 Lomita Mall, Stanford, CA 94305 USA

[3] Texas A&M Univ, College Stn, TX 77843 USA

[4] 7011 East Ave,MS 9159, Livermore, MS 94550 USA

[5] 701 HR Bright Bldg, College Stn, TX 77843 USA

关键词: CFD;    High-order schemes;    Deep learning;    Autoencoders;    Dynamics learning;    Machine learning;   

DOI  :  10.1016/j.jcp.2019.05.041

来源: Elsevier

【 摘 要 】

Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any time instance) a posteriori. The objective of this work is therefore to accurately recover missing CFD data a posteriori at any time instance, given that the solution has been written to disk at only a relatively small number of time instances. We consider in particular high-order discretizations (e.g., discontinuous Galerkin), as such techniques are becoming increasingly popular for the simulation of highly separated flows. To satisfy this objective, this work proposes a methodology consisting of two stages: 1) dimensionality reduction and 2) dynamics learning. For dimensionality reduction, we propose a novel hierarchical approach. First, the method reduces the number of degrees of freedom within each element of the high-order discretization by applying autoencoders from deep learning. Second, the methodology applies principal component analysis to compress the global vector of encodings. This leads to a low-dimensional state, which associates with a nonlinear embedding of the original CFD data. For dynamics learning, we propose to apply regression techniques (e.g., kernel methods) to learn the discrete-time velocity characterizing the time evolution of this low-dimensional state. A numerical example on a large-scale CFD example characterized by nearly 13 million degrees of freedom illustrates the suitability of the proposed method in an industrial setting. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free