Rediscovery of governing equations from simulation data using Genetic Programming

Abstract

With advances in computers, observation, and simulation technology, it becomes an era when a large amount of data is generated, and it is becoming more important to find out the meaning and knowledge contained in the data. In this paper, we formulated the process of finding the governing equation describing the given data as a symbolic regression problem. In the proposed method, ”partial differential function” is introduced into Genetic Programming to generate partial differential equations automatically, and the generated equations and data are compared and evaluated to automatically distill equations with less error. We conducted numerical experiments to estimate the governing equation from fluid simulation data and evaluated the validity of the proposed method. As a result, the original equation was obtained with high probability, and it was found that the proposed method becomes an effective tool to find useful modeling to represent the data.