Title: Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data

Abstract

Here we put forth a modular approach for distilling hidden flow physics from discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use of symbolic regression as a principle for identifying relations and operators that are related to the underlying processes. This approach combines evolutionary computation with feature engineering to provide a tool for discovering hidden parameterizations embedded in the trajectory of fluid flows in the Eulerian frame of reference. Our approach in this study mainly involves gene expression programming (GEP) and sequential threshold ridge regression (STRidge) algorithms. We demonstrate our results in three different applications: (i) equation discovery, (ii) truncation error analysis, and (iii) hidden physics discovery, for which we include both predicting unknown source terms from a set of sparse observations and discovering subgrid scale closure models. We illustrate that both GEP and STRidge algorithms are able to distill the Smagorinsky model from an array of tailored features in solving the Kraichnan turbulence problem. Our results demonstrate the huge potential of these techniques in complex physics problems, and reveal the importance of feature selection and feature engineering in model discovery approaches.

Authors:

Vaddireddy, Harsha ^[1]; Rasheed, Adil  ^[2];

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• Search DOE PAGES for ORCID "0000-0003-2690-983X"
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Staples, Anne E.  ^[3];

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• Search DOE PAGES for ORCID "0000-0003-4823-8184"
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San, Omer  ^[1]

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• Search DOE PAGES for ORCID "0000-0002-2241-4648"
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+ Show Author Affiliations

1. Oklahoma State Univ., Stillwater, OK (United States)
2. Norwegian Univ. of Science and Technology, Trondheim (Norway)
3. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:

2020-01-16

Research Org.:

Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

OSTI Identifier:

1593556

Alternate Identifier(s):

OSTI ID: 1591974

Grant/Contract Number:  

SC0019290

Resource Type:

Accepted Manuscript

Journal Name:

Physics of Fluids

Additional Journal Information:

Journal Volume: 32; Journal Issue: 1; Journal ID: ISSN 1070-6631

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING