Mathematical modeling of physical systems are commonly faced situations. Solution depends on the quality of the modeling directly. Among the many techniques, High Dimensional Model Representation (HDMR) is a new method that brings great efficiency to the modeling of a system. Although Interpolation, Splines, Finite differences etc. are useful methods, they do not often give as good results as HDMR does. These methods need more reference points or nodes and higher order polynomials for better results, and this means higher cost calculations. However, HDMR offers new expansions, truncation of intended order, needed for less sample points etc.. Since HDMR is a modeling method based on optimization and projection operator theory, solving problems with differential equations, input - output systems require less calculations with high effectiveness. In addition, HDMR contains analysis of variance calculations. Hence, HDMR is also an effective method for statistics.