Good question ... I spent a long time trying to understand probabilistic graphical models. Using them to make sense of time series data (more specifically on-body wearable sensors to detect specific activities in maintenance). E.g. Kevin Murphy's and Daphne Koller's work (highly recommend their books).

The type of problems in that space usually didn't work well with linear control theory, although I'm not strong in theory ... at the time mostly playing with some signal processing packages in matlab (e.g. Kalman Filtering).

Recently, I got interested in group and social dynamics (we recorded a couple of large scale datasets). I found an approach found in some of the non-linear dynamics practitioner's lectures/works intuitive and fun for me. You could call it "Explorative Experimental Computational Mathematics": 1. find an interesting phenomenon 2. record data, run simulations and plot data 3. look at the visualizations 4. fit a model /formulas based on the visualizations Iterate.

If I have completely misrepresented a field/research please forgive me. Just an enthusiast amateur here.