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Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows

Wu, Jin-Long and Michelén-Ströfer, Carlos and Xiao, Heng (2019) Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows. Computers & Fluids, 193 . Art. No. 104292. ISSN 0045-7930. https://resolver.caltech.edu/CaltechAUTHORS:20191205-092446923

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Abstract

In uncertainty quantification of computational models (e.g., turbulence modeling) with Bayesian inferences, Gaussian processes are commonly used as the prior for model discrepancies. However, constructing the covariance kernel is a challenging task that requires significant physical knowledge of the problem. On the other hand, often the model discrepancies are described by partial differential equations (PDEs) of known structures (e.g. Reynolds stress transport equations for turbulent flows), albeit with unclosed terms (e.g, velocity triple correlation and press–strain-rate correlation). In this work, we utilize such PDEs to construct physics-informed covariance kernels by exploiting the fundamental connection between PDEs and covariance functions. We demonstrate the merits of the physics-informed covariance kernel with the application to turbulent flows over periodic hills. The covariance kernel and the modes (eigenfunctions) obtained from the physics-informed approach are physically more realistic than those obtained with commonly used squared exponential kernels. This method also has the potential of improving the performance of Bayesian model-form uncertainty quantification in applications beyond turbulent flows.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.compfluid.2019.104292DOIArticle
ORCID:
AuthorORCID
Michelén-Ströfer, Carlos0000-0001-6274-7271
Xiao, Heng0000-0002-3323-4028
Additional Information:© 2019 Elsevier Ltd. Received 11 May 2019, Revised 15 August 2019, Accepted 11 September 2019, Available online 12 September 2019.
Record Number:CaltechAUTHORS:20191205-092446923
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191205-092446923
Official Citation:Jin-Long Wu, Carlos Michelén-Ströfer, Heng Xiao, Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows, Computers & Fluids, Volume 193, 2019, 104292, ISSN 0045-7930, https://doi.org/10.1016/j.compfluid.2019.104292. (http://www.sciencedirect.com/science/article/pii/S0045793019302555)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100199
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Dec 2019 18:38
Last Modified:05 Dec 2019 18:38

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