Let's imagine there is a phenomenon I want to understand. I have a few multivariate time series about the phenomenon but not a lot. I don't know how the variables are related to each other but from what I can tell the phenomenon appears to have time delays, feedback and nonlinear interactions between variables over time.
If my goal is to get a better understanding of this phenomenon, with the intent of intervening and changing outcomes in some way, what tools should I try?
My first thought is that statistical modeling and causality for time series are mainly concerned with linear relationships, and would therefore not give me very much information about how to intervene because they don't capture feedback and nonlinearity.
I don't have enough data to try and learn the dynamics of the system with ML.
Creating PDEs/ODEs seems like the classic tool for this kind of thing. That would probably involve making assumptions about the phenomenon and trying to build up a differential equation model from basic principals that captures most of the variance in the time series I have.
But is there anything else that could work?