Connecting ML model to nonlinear system model?

How can we combine a data-driven (machine learning) model of hair growth (for example) with a nonlinear system model to improve accuracy?

And a more complex case is, what concepts should I look into to connect a ML hair treatment model (not just hair growth) to the nonlinear system of hair growth?

Sorry if my question is vague. The goal is to understand what treatments work better. relying on both mathematical modeling and on ML models.