[DiffEqParamEstim.jl] Add a findfit function

[ChrisRackauckas]

@fdekerme

I had written a Git issue a few months ago ( Add a findfit function · Issue #220 · SciML/DiffEqParamEstim.jl (github.com)) on this subject but having had no response I take the liberty of making a post here.

Sorry, I generally respond to every SciML issue but I don’t have this email in my inbox so I must’ve accidentally deleted it or something. Thanks for getting back in touch.

@fdekerme

Since the package DiffEqParamEstim.jl is defined as "a simple interface for users who want to quickly run standard parameter estimation routines for model calibration ", it would be interesting to add a findfit function on the model of the homonymous functions in Wolfram Mathematica (FindFit: Find parameters to best fit data—Wolfram Documentation ; Fitting system of Differential equations to a dataset - Online Technical Discussion Groups—Wolfram Community) or SageMath (Numerical Root Finding and Optimization - Numerical Optimization) for example. This findfit function would combine a “generic” cost function, the definition of the OptimizationProblem and the solving. It would greatly simplify the use of DiffEqParamEstim.jl, which is certainly very efficient for complex situations, but which is a bit of a gas factory when you only have a small ODE system to fit on dat

Yes, that would be a nice contribution. I don’t plan to work on this but would accept a PR.

@fdekerme

I’m also convinced that the varmap_to_vars function, which is essential for combining ModelingToolkit and DiffEqParamEstim.jl, is extremely unintuitive and could be greatly improved. The documentation (Frequently Asked Questions · ModelingToolkit.jl) alone is confusing. Just one example : unless I’m mistaken, the expression

People shouldn’t be using this so much anymore. remake, prob[p], and sol[p] should be sufficient for what most people need to be doing.