Thomson coil can generate large forces in a short time and hence finds application in fast acting actuators. Behaviour of Thomson coil actuator depends on multi-physics which involves various fields including electrical, electromagnetic, structural and their interactions. As a result, many design parameters related to the different physical domains are involved in the analysis of Thomson coil. Thus, it becomes complicated to have a closed-form equation which can describe the behaviour of this system. In this paper, we derive dimensionless parameters associated with the variables involved in the design of Thomson coil using Buckingham Pi theorem. These dimensionless parameters are then used to develop data-driven models which help to predict the displacement of Thomson coil disc at a specified time interval and gain insights about the actuator when it is subjected to changes in the design parameters.