  Solar flares and plasma eruptions are sudden releases of magnetic energy
stored in the plasma atmosphere. To understand the physical mechanisms
governing their occurrences, three-dimensional magnetic fields from the
photosphere up to the corona must be studied. The solar photospheric magnetic
fields are observable, whereas the coronal magnetic fields cannot be measured.
One method for inferring coronal magnetic fields is performing data-driven
simulations, which involves time-series observational data of the photospheric
magnetic fields with the bottom boundary of magnetohydrodynamic simulations. We
developed a data-driven method in which temporal evolutions of the
observational vector magnetic field can be reproduced at the bottom boundary in
the simulation by introducing an inverted velocity field. This velocity field
is obtained by inversely solving the induction equation and applying an
appropriate gauge transformation. Using this method, we performed a data-driven
simulation of successive small eruptions observed by the Solar Dynamics
Observatory and the Solar Magnetic Activity Telescope in November 2017. The
simulation well reproduced the converging motion between opposite-polarity
magnetic patches, demonstrating successive formation and eruptions of helical
flux ropes.
