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

• Published in: Physics of fluids (1994) Vol. 32; no. 1
• Main Authors: Vaddireddy, Harsha, Rasheed, Adil, Staples, Anne E., San, Omer
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.01.2020
• Subjects: Algorithms; Computational fluid dynamics; Distillation; Error analysis; Evolutionary algorithms; Fluid dynamics; Fluid flow; Gene expression; Machine learning; Physics; Regression analysis; Truncation errors
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5136351

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.