A numerical magneto-thermo-hydrodynamic (MTHD) model coupled with an inverse optimization method is developed for the identification of heat flux parameters for the Gas Tungsten Arc Welding (GTAW) process. The MTHD model is based on the four conservation equations of mass, momentum (Navier-Stokes equations), energy (heat transfer) and electric potential. The stated MTHD includes the force term due to magnetic field in the momentum equation (Lorentz force). The transport phenomena and the heat transfer from the electrical arc plasma to the weld pool determine the weld penetration and the weld pool shape. In the current study an attempt has been made to replace the argon electrical arc plasma effect with a heat flux modelled by a Gaussian function on the anode surface. The major parameters that influence the formation of weld pool shape were identified using a parametric study and are welding efficiency and base radius of the Gaussian distribution. A multivariable optimization algorithm based on Levenberg-Marquardt Method is used for the inverse problem. It is concluded that algorithm developed were able to predict the reference numerical model and demonstrated the stability and robustness of the algorithm using a noised input data.