In STEM (In USA), the coursework duration of the PhD typically lasts about 1-2 years beyond that, students take 0 (or in certain cases, very few) courses in their subsequent PhD years. I work in applied math with a lot of applications in every field imaginable : Finance, Economics, Energy, Healthcare, Services etc.
During my coursework phase (owing to the breadth requirement), I was made to take courses in different departments and each time I attended a course in a new department I would think "Wow, this field could really benefit from extensions of my research". I would chalk out a few ideas and read up a few papers, find out that it's already done but be glad that I generated a new idea nonetheless.
Now, I am nearing the end of my coursework phase and I am wondering : How do I keep my ability to "see" applications in fields other than mine alive?
Global Question : After a student's coursework phase, how does he stay aware of applications of his research field besides the ones discussed in papers?
My advisor encourages me to attend as many seminar talks as possible (in all allied fields) which I do but it's not the same level of enjoyment.