Multi-Objective Discovery of PDE Systems Using Evolutionary Approach

Usually, the data-driven methods of the systems of partial differential equations (PDEs) discovery are limited to the scenarios, when the result can be manifested as the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the external forcing is of interest for the researcher and can not be described by the component of the vector equation. In the paper, a multi-objective co-evolution algorithm is proposed. The single equations within the system and the system itself are evolved simultaneously to obtain the system. This approach allows discovering the systems with the form-independent equations. In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications. The example of the two-dimensional Navier-Stokes equation is considered.