Discovery of Sparse Formula Based on Elastic Network Method and Its Application in Identification of Turbulent Boundary Layer Wall Function

Extracting governing equations from data is a central challenge in diverse areas of science and engineering. Where data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology. A sparse representation algorithm based on elastic network optimization is proposed, which combines the advantages of least squares and Lasso to identify the function form directly from the data. The method designs the candidate function terms according to background knowledge, and uses the elastic network optimization algorithm to identify the unknown coefficients of each term with the model. The approach maintains a balance between accuracy and model complexity, avoiding overfitting. The wall function method is a commonly used for dealing with the turbulent boundary layer, which can accelerate convergence rate compared to the near-wall turbulence modelling with reasonable accuracy. The proposed algorithm is used to derive the wall function from the turbulent wall data. Experimental results show that the proposed algorithm is superior to LASSO and least squares in obtaining the model, and faster than numerical calculation.