  The ultimate goal of studying the magnetopause position is to accurately
determine its location. Both traditional empirical computation methods and the
currently popular machine learning approaches have shown promising results. In
this study, we propose a Regression-based Physics-Informed Neural Networks
(Reg-PINNs) that combines physics-based numerical computation with vanilla
machine learning. This new generation of Physics Informed Neural Networks
overcomes the limitations of previous methods restricted to solving ordinary
and partial differential equations by incorporating conventional empirical
models to aid the convergence and enhance the generalization capability of the
neural network. Compared to Shue et al. [1998], our model achieves a reduction
of approximately 30% in root mean square error. The methodology presented in
this study is not only applicable to space research but can also be referenced
in studies across various fields, particularly those involving empirical
models.
