Techniques for numerical calculations of phase transformation kinetics have recently become available. These methods are integrated with computational thermodynamics to allow for the description of diffusion-controlled transformations as a function of time. Such calculations have been applied to the modeling of solidification behavior in the current study. Three examples are considered which relate to the prediction of microstructure development and solute redistribution during conditions corresponding to welding conditions. The examples evaluate dendritic growth, planar growth, and competition between alternate solidification modes. It is shown that these techniques are particularly powerful when dealing with multi-component (>2) alloy systems. For such multi-component alloys, new considerations must be taken into account to describe the solute redistribution and the conditions leading to planar front growth. Finally, when studying global behavior covering a wide range of alloy compositions and thermal conditions, individual computations become impractical. For such calculations, neural network analysis may be beneficial and an example is given where such an analysis is shown to be suitable in describing a complex series of phase transformations