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

Vaddireddy, Harsha; Rasheed, Adil; Staples, Anne E.; San, Omer

doi:10.1063/1.5136351

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

Journal Article · 15 January 2020 · Physics of Fluids

DOI: https://doi.org/10.1063/1.5136351 · OSTI ID:1593556

Vaddireddy, Harsha ^[1];

^[2];

^[3];

^[4]

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

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.

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

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

Grant/Contract Number:: SC0019290

OSTI ID:: 1593556

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 1 Vol. 32; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Sub-grid scale model classification and blending through deep learning Maulik, Romit; San, Omer; Jacob, Jamey D. arXiv https://doi.org/10.48550/arxiv.1812.11949	text	January 2018
Deep Learning Ganatra, Sanket Zenodo https://doi.org/10.5281/zenodo.1189359	text	January 2018
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence Holland, John H. The MIT Press https://doi.org/10.7551/mitpress/1090.001.0001	book	January 1992
An Introduction to Genetic Algorithms Mitchell, Melanie MIT Press https://doi.org/10.7551/mitpress/3927.001.0001	book	January 1998

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An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics Pawar, Suraj; Ahmed, Shady E.; San, Omer Mathematics, Vol. 8, Issue 4 https://doi.org/10.3390/math8040570	journal	April 2020

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