when to specify parameter mappings and using default values

[isaacsas]

Right now it appears that default values for parameters get ignored during discretize. Similarly, one currently has to pass a parameter mapping to PDESystem giving the parameter values, which is not consistent with other ModelingToolkit system types (where such mappings are not required until problem creation time). I would propose making discretize require passing the parameter mapping, and for parameters not included in the mapping it should check if they have default values available (as done for other system/problem types).

[xtalax]

@ChrisRackauckas @zoemcc Thoughts?

[isaacsas]

As an alternative, perhaps structural simplification could be moved into symbolic_discretize, since that is still a symbolic component, and then users could be pointed to using that function that to get back an ODESystem or NonlinearSystem. That would give a closer workflow to other system types, as users could then directly pass these to ODEProblem / NonlinearProblem with ICs and/or parameter mappings as needed.