Evo-SINDy: Universal Discovery of Partial Differential Equations Using Cooperative Evolutionary Computation

The discovery of the mathematical form of partial differential equations (PDEs) from data has broad applications and significant implications in many fields. Existing data-driven methods such as the well-known SINDy method, however, struggle to identify arbitrary forms of PDEs with minimal prior knowledge. In this paper, we propose a data-driven method for PDE identification, named Evo-SINDy, which leverages a multi-population co-evolutionary algorithm to address the limitations of SINDy. This method is able to efficiently identify PDEs from a sufficiently large search space that best match data characteristics, ensuring minimal reliance on prior knowledge. Experimental results demonstrate that Evo-SINDy can identify more numbers of one-dimensional PDEs within a unified framework than the other known methods, and outperforms two recently-proposed methods that use open libraries in terms of computational efficiency.