Yep, this is why I talk about the virtuous feedback loop between these two modes. Empirical methods feed theory which feeds empirical methods ad infinitum.

In the field of ML, a concrete example might be the tool Xgboost (#1) and the original work that led to and developed Gradient Boosting itself (#2), of which Xgboost is an implementation, and probably one that has helped refine the underlying theory as well.

ML has lots of examples where the researcher(s) for #2 were also doing #1. A famous paper in NLP comes to mind as an excellent example of this overlap (PDF: https://www.csie.ntu.edu.tw/~b92b02053/print/good-turing-smo...)

> I understand the separation between physics. But most structural analysis methods are discovered by professors of structural engineering and not physicists(and much of it is empirical).

You're confusing the occupation with the role. Just because your job title is professor of structural engineering it doesn't mean that you are not studying "matter, its motion and behavior through space and time, and the related entities of energy and force."

https://en.wikipedia.org/wiki/Physics