There are a few options, but none of them give an "absolute truth" result between 0 and 1. The two common options are AIC and BIC. see here: Model selection with nonlinear fitting? Statistical tests seem ambiguousModel selection with nonlinear fitting? Statistical tests seem ambiguous
Another option is the S measure: http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-to-interpret-s-the-standard-error-of-the-regression
Some thoughts:
- As models become more complex, there are less "absolute truth" answers like R^2 between 0 and 1. With more flexible models, it's easy to get to a 100% fit of training data, and metrics like R^2 are irrelevant.
- Make sure you test your model with some test data. non linear models tend to overfit.