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In this study we put forth a modular approach for distilling hidden flowphysics in discrete and sparse observations. To address functionalexpressiblity, a key limitation of the black-box machine learning methods, wehave exploited the use of symbolic regression as a principle for identifyingrelations and operators that are related to the underlying processes. Thisapproach combines evolutionary computation with feature engineering to providea tool to discover hidden parameterizations embedded in the trajectory of fluidflows in the Eulerian frame of reference. Our approach in this study mainlyinvolves gene expression programming (GEP) and sequential threshold ridgeregression (STRidge) algorithms. We demonstrate our results in three differentapplications: (i) equation discovery, (ii) truncation error analysis, and (iii)hidden physics discovery, for which we include both predicting unknown sourceterms from a set of sparse observations and discovering subgrid scale closuremodels. We illustrate that both GEP and STRidge algorithms are able to distillthe Smagorinsky model from an array of tailored features in solving theKraichnan turbulence problem. Our results demonstrate the huge potential ofthese techniques in complex physics problems, and reveal the importance offeature selection and feature engineering in model discovery approaches.

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors