Discovery of the data-driven differential equation-based models of continuous metocean process

Abstract

Data-driven models are widely used in cases when the model structure is not known a priori. However, most contemporary data-driven modeling methods like neural networks and most types of simple regression cannot be interpreted. Decision trees are on contrary, interpretable, however, the model structure remains simple and thus interpretable complex models are barely obtained with decision trees. The possible tradeoff between the model complexity and interpretability is the data-driven differential equations discovery methods. At the current time, most of the methods are not able to handle the data with a significant noise level. In the paper, a new approach to the problem is proposed. The approach involves evolutionary algorithm and sparse regression and allows one to obtain various forms of equations, defined only by the number of meta-parameters instead of the pre-defined library of terms. The application of PDE discovery tool to obtain continuous metocean process equation is described.