Application of the symbolic regression algorithm AI-Feynman to fluid equations.

Abstract

Advances in machine learning have led to the proposal of new symbolic regression methods, such as AI-Feynman, which uses neural networks to find symmetries and divisibility, simplifying the problem and enabling efficient symbolic regression. However, the original AI-Feynman does not deal with equations involving derivatives. Since most physical phenomena are described by differential equations, this poses a major problem, by which most physical phenomena are described. In this study, the symbolic regression by AI-Feynman in fluid-dynamic systems is investigated. For the three initial conditions, the advection equation and the Burgers equation are identified with the given differential equation. For the Navier-Stokes equations, some terms were different from the given differential equations, but equations that could explain the data with a high degree of accuracy were identified. These results strongly support the applicability of the AI-Feynman to physical phenomena that derivatives are included in the equation.