I think most of the classical statistical methods for curve fitting happen to be some kind of variant of using least squares on a manually chosen parameterizable function - you'll have to chose between a linear, polynomial, exponential or some other moire complex forms.

The nice things of using a simple feedforward DNN is that it will automatically infer both the nonlinear function structure and parameters and for simple basic use cases like this that don't require a lot of training it works well and you can even validate the fit visually by looking at the graph output.