Sampling and resolution characteristics in reduced order models of shallow water equations: Intrusive vs nonintrusive

Ahmed, Shady E.; San, Omer; Bistrian, Diana A.; Navon, Ionel M.

doi:10.1002/fld.4815

Title: Sampling and resolution characteristics in reduced order models of shallow water equations: Intrusive vs nonintrusive

Journal Article · 23 January 2020 · International Journal for Numerical Methods in Fluids

DOI: https://doi.org/10.1002/fld.4815 · OSTI ID:1737500

^[1];

^[2]; Bistrian, Diana A. ^[3];

^[4]

Oklahoma State Univ., Stillwater, OK (United States); Oklahoma State University Stillwater
Oklahoma State Univ., Stillwater, OK (United States)
Univ. “Politechnica” of Timisoara, Hunedoara (Romania)
Florida State Univ., Tallahassee, FL (United States)

We investigate the sensitivity of reduced order models (ROMs) to training data spatial resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive reduced order modeling technique. For non-intrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with sorted bases selection. Also, we highlight the differences between mean-subtracting the data (centering) and using the data without mean-subtraction. We tested these ROMs using a system of 2D shallow water equations for four different numerical experiments, adopting combinations of sampling rates and spatial resolutions. For these cases, we found that the DMD basis obtained with hard threshodling is sensitive to sampling rate. The sorted DMD algorithm helps to mitigate this problem and yields more stabilized and converging solution. Furthermore, we demonstrate that both DMD approaches without mean subtraction provide significantly more accurate results than DMD with mean-subtracting the data. On the other hand, POD is relatively insensitive to sampling rate and yields better representation of the flow field. Meanwhile, spatial resolution has little effect on both POD and DMD performances. Here, the numerical results reveal that an ANN on POD subspace (POD-ANN) performs remarkably better than POD-GP and DMD in capturing system dynamics, even with a small number of modes.

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Research Organization:: Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0019290

OSTI ID:: 1737500

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 8 Vol. 92; ISSN 0271-2091

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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