There are hundreds of data-driven machine learning models. It is easy to name a few: neural networks, linear regression, SVM, etc etc... but what is model-driven (or non data-driven) modelling and what are famous and useable examples for e.g. regression tasks?
If the model is not derived from the data then it must be built manually, so non data driven means rule based.
This was the big trend in AI in the 80s before Machine Learning, these pre-ML automatic prediction systems were called expert systems and they were quite successful at the time in industry (here are some examples of applications).
The way one would build a system for a regression task is essentially this: do the whole regression analysis manually, find the parameters and hard-code them in the prediction system.
As far as I know Machine Learning has pretty much made this kind of rule-based systems obsolete, due to their total lack of flexibility and the very high cost in manual labor to build one.