Fifth Generation models make a serious effort to include a model of the arc in the heat source model. This adds the equations of magneto - hydrodynamics to the equations in the previous models. Although these Fifth Generation models are very general, they face even more serious mathematical difficulties than the Fourth Generation Weld Heat Source Models. Often existence and uniqueness cannot be proven. The numerical methods face very serious difficulties.

This is not to argue that computer simulations of Fourth and Fifth Generation models are not useful. It is to argue that to date (2003) their usefulness for predicting the geometry of the weld pool in high power industrial welds has been limited.