1. Linear model: Linear model is one of the simplest mathematical models, which assumes that there is a linear relationship between input and output. For example, a linear regression model can be used to predict the relationship between the dependent variable (output) and the independent variable (input).
2. Nonlinear model: The nonlinear model considers the nonlinear relationship between input and output. For example, polynomial regression model can be used to fit the nonlinear relationship between dependent variable and multiple independent variables.
3. Probability model: Probability model is used to describe the probability of random events. For example, given some prior information, Bayesian theorem can be used to calculate the probability of events.
4. Statistical model: Statistical model is used to describe the overall characteristics and distribution of data. For example, the normal distribution model can be used to describe the mean and variance of a set of data.
5. Differential equation model: Differential equation model is used to describe the dynamic behavior of the system with time. For example, Newton's laws of motion can be expressed by differential equations.
6. Optimization model: the optimization model is used to find the optimal solution, that is, the solution that maximizes or minimizes the objective function under certain conditions. For example, the linear programming model can be used to solve the resource allocation problem.