Breaking down your research problem

Tolerance for the unknown is par for the course in graduate research, so it was no surprise last night when I found myself daunted by the prospect of the next phase of my PhD, which involves a significant jump in the complexity of my simulations.

Talking it through with my wife, though, I realized I could trace the source of my anxiety to 4 or 5 key elements that I haven’t yet learned how to do in the FEA code I am using. Once I broke it down, I realized that I wasn’t dealing with numerous interdependent unknowns and simultaneous “equations”—I was dealing with 5 essentially unrelated components. A sparse, banded matrix! It suddenly felt so simple.

I’ll point now to a very practical bit of advice from Daniel Lemire on intellectual productivity when overwhelmed:

The secret is this: break down your task into small and easy chunks of work. And just do them! […] Sometimes you do not know how to break down the task. Do not worry so much about it. Break it down in some way and get working.

This advice applies especially well to projects that appear to possess a high level of interrelated, parallel issues. Perhaps the dependencies are real, but here is the news flash: you probably aren’t going to simultaneously solve a massively parallel, underdefined problem in your head. In that case, you discretize the problem into the maximum number of as-independent-as-possible components you can and work on each one at a time, iterating over the bunch until the system starts working.

Don’t miss the trees for the tangled forest.

Obvious. Self-evident. Difficult to actually do.

Now back to learning those 5 things.