Mathematical modeling is the link between mathematics and practical problems and is the medium through which mathematics is widely used in related fields. This paper introduces the definitions of mathematical models in different disciplines and for different practical problems and gives the specific steps of mathematical modeling and the key problems to be solved in each step, the most important of which is nonlinear regression theory. The parameter estimation of the error variance of the nonlinear regression model is performed by the least squares method, and for the problem of poor numerical stability and computational complexity due to the pathological matrix in solving the least squares method, the least squares method is proposed based on adding the edge computing framework. The results show that the system efficiency of the nonlinear regression model based on edge computing is 92%, and the resource utilization is between 80% and 90% on average, which is higher than the two algorithms of RPP and RPA. The nonlinear regression model based on edge computing proposed in this paper organically combines mathematical modeling, which can make mathematical modeling play a greater role in the practical application process and solve more practical problems.