1. From the data to the model, the model is established by fitting. Many problems with obvious scientific background are based on this.

2. From physical background to model, establish the relationship between existing data and model parameters. Similar to the first content above, most ode or pde models with high coercivity are based on this.

3. From data to information to knowledge, the data topics are basically the same. Building a model is equivalent to embedding a multivariate statistical or machine learning method in the data.

4. For the model directly established for industrial problems, the quantification is mostly the solution of the model or the pictures of related variables reflecting the conclusion.

Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include both concrete natural phenomena, such as free fall, and abstract phenomena, such as customers' value tendency to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.

We can also intuitively understand this concept: mathematical modeling is a process that makes pure mathematicians (mathematicians who only study mathematics and don't care about its application in practice) become physicists, biologists, economists and even psychologists.