In this talk, we discuss the effective geometric motions of parabolic Ginzburg--Landau systems with potentials of high-dimensional wells. Combining modulated energy methods and weak convergence methods, we derive a convergence rate of a phase indicator function to the limiting interface motion (by mean curvature), the limiting harmonic heat flows in the inner and outer bulk regions segregated by the interface, and a non-standard boundary condition of them. These results are valid provided that the initial datum of the system is well-prepared under natural energy assumptions.