Although numerical heat transfer and fluid flow models have provided significant insight about fusion welding processes and welded materials in recent years, several model input parameters cannot be easily prescribed from fundamental principles. As a result, the model predictions do not always agree with the experimental results. In order to address this problem, the approach adapted here is to develop and test a model that embodies a heat transfer and fluid flow sub-model and an algorithm for optimizing and learning the values of uncertain process variables from a limited volume of experimental data. The heat transfer and fluid flow sub-model numerically calculates three-dimensional temperature and velocity fields and the weld geometry during gas metal arc (GMA) welding of fillet joints. The proposed model could estimate the unknown values of arc efficiency, effective thermal conductivity and effective viscosity as a function of welding conditions based on only a few experimental measurements. A vorticity-based mixing length hypothesis was also used to independently calculate the values of the effective viscosity and effective thermal conductivity. Good agreement between the experimental and the predicted weld geometry showed that this approach was useful in improving reliability of heat transfer and fluid flow calculations.