Discovery of the data-driven models of continuous metocean process in form of nonlinear ordinary differential equations

Abstract Data-driven surrogate models are widely used when the system dynamics equations and governing models are not known a priori. The form of the differential equation with the constant coefficients is widely used to obtain a data-driven physical process model. However, the physical models’ form is more complex, and the constant coefficients are not the case for most non-linear problems. In the article, the algorithm for the discovery of the ordinary differential equations with variable coefficients is proposed. The algorithm is based on discovering the governing equation’s structure, using a combination of sparse regression and an evolutionary algorithm. The proposed method is tested on the synthetic data, obtained from the solution of known ordinary differential equations, and on metocean data fields.