Exploring approximate analytical expression for magneticskyrmion structure based on symbolic regression method

Magnetic skyrmion is a kind of nontrivial topological magnetic structure, which can exist stably in chiralmagnet with Dzyaloshinskii-Moriya (DM) interaction, and its static and dynamic properties are closely relatedto its structural characteristics. However, there are no general analytical expressions for skyrmion profiles.Therefore, many researchers have provided approximate solutions. In this paper, a new approach to exploringmagnetic skyrmion structures is introduced by using a symbolic regression approach. Considering the influenceof DM interaction and external magnetic field on magnetic skyrmion structure, two suitable approximateexpressions are obtained through symbolic regression algorithms. The applicability of these expressions dependson the dominant interaction. The research results in this work validate the powerful capability of symbolicregression algorithms in exploring the magnetic skyrmion profiles. So, the present study provides a new methodfor finding the analytical expressions for magnetic structure