I would like to fit a non-linear model by doing nonlinear feature transformation first (e.g. exp, log) and then using linear regression (or regularized linear regression). However, I am stuck at whether to do standardization first before nonlinear transformation or vice versa. I know it doesn't matter for polynomial fitting because your final models will be mathematically equivalent no matter you do z-score before polynomial transformation or later.
But when it comes to other types of nonlinear transformation, I am very confused. Because all my variables have physical meaning and also have different magnitude (e.g. concentration measurements/wave numbers/temperatures/mass....). And I am trying to find a relation between the concentration = f(temperature,mass...). So say my final model is $C = exp (T) + m^2*T... $, centering T or not really makes the model different.