Enabling reduced-order data-driven nonlinear identification and modeling through naive elastic net regularization

This work discusses an improved method of reduced-order modeling for existing data-driven nonlinear identification techniques through the incorporation of naïve elastic net regularization. The data-driven methods considered for this study operate using basis functions to represent the observed nonlinearity. Elastic net regularization is used to minimize the number of non-zero coefficients, thus modifying the basis functions and providing a compact representation. The ability of the naïve elastic net to provide reduced-order nonlinear models that can both accurately fit various data sets and computationally simulate new responses is illustrated through studies considering both synthetic data and experimental data. In both cases, the results obtained with the naïve elastic net are shown to match or outperform those from other traditional methods.