Multi-objective discovery of PDE systems using evolutionary approach

TL;DR

This paper introduces a multi-objective co-evolution algorithm for discovering systems of PDEs from data, enabling form-independent, component-wise systems that are more interpretable for real-world applications.

Contribution

The paper presents a novel multi-objective co-evolution approach for discovering PDE systems with component-wise equations, improving interpretability over traditional single vector equation methods.

Findings

Successfully applied to 2D Navier-Stokes equations

Enables discovery of form-independent PDE systems

Improves interpretability of the resulting models

Abstract

Usually, the systems of partial differential equations (PDEs) are discovered from observational data in 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. In the paper, a multi-objective co-evolution algorithm is described. 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.