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Open AccessArticle

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

1
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
2
Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7465 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 570; https://doi.org/10.3390/math8040570
Received: 8 March 2020 / Revised: 31 March 2020 / Accepted: 8 April 2020 / Published: 11 April 2020
(This article belongs to the Special Issue Machine Learning in Fluid Dynamics: Theory and Applications)
In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then present two variants of correction formula based on the assumption that the observed data are a manifestation of all relevant processes. The first method uses a standard least-squares regression with a quadratic approximation and requires solving a rank-deficient linear system, while the second approach employs a recurrent neural network emulator to account for the correction term. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward real-time simulations, where the full process model is not known a priori. View Full-Text
Keywords: hybrid analysis and modeling; Galerkin projection; proper orthogonal decomposition; long short-term memory; error correction hybrid analysis and modeling; Galerkin projection; proper orthogonal decomposition; long short-term memory; error correction
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Pawar, S.; Ahmed, S.E.; San, O.; Rasheed, A. An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics. Mathematics 2020, 8, 570.

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