The Role of Theory and Data in Model Building: from Richardson to machine learning

The talk is devoted to a discussion of different  typologies of models:

 I-  Oversimplified models;

 II- Models by analogy;

  III- Large scale models;

IV- Models from data. 

In the class  I  there is the celebrated   Lorenz model; the  Lotka-Volterra  system  is in the class  II, and it is at the origin of biomathematics.

Among the  models in the class III  we have the effective equations used, e.g., in meteorology and engineering,  where only "relevant variables" are taken into account.

In the class  IV we find the most interesting (and difficult) problem:the building  of models just from datawithout a reference theoretical framework.