Add design principles page

[sebapersson]

To help understand the format of the spec, I think it would be great to have a page on design principles in the spec.

Overall, I consider the design principles to be:

1. Adhere as close as possible to the PEtab standard. That is, we want to support all PEtab features, and for new things added, we want them to adhere as close as possible to the PEtab logic.
2. Performance. This is why we make the distinction partially on static and dynamic hybridization. Because if the ML model is evaluated pre-simulation, we can make quite a number of optimizations in the code.

@dilpath anything else you think would be worthwhile to include?

[dilpath]

Sounds good. There are other design principles in the spec that I guess we don't need to repeat, e.g. why the NN model YAML is optional.

But there are other choices that are less clear -- i.e., that dynamic hybridization can only be specified via the hybridization table, rather than the condition table. We could primarily state this assumption, and secondarily justify it.
This is because a user might want to specify different input to the NN model in each period of the experiment -- this is not possible in PEtab SciML (unless the user encodes the arrays as time-varying PEtab parameters or mechanistic model parameters...). So we could additionally highlight limitations due to our design choices on this page.

[sebapersson]

But there are other choices that are less clear -- i.e., that dynamic hybridization can only be specified via the hybridization table, rather than the condition table. We could primarily state this assumption, and secondarily justify it.
This is because a user might want to specify different input to the NN model in each period of the experiment -- this is not possible in PEtab SciML (unless the user encodes the arrays as time-varying PEtab parameters or mechanistic model parameters...). So we could additionally highlight limitations due to our design choices on this page.

I agree. I will make a draft PR we can iterate.

[dilpath]

A comparison of NN objects to pre-existing PEtab objects might also be useful, what do you think?

i.e. we designed NN non-mechanistic-model inputs and parameters to be like PEtab fixed parameters (static case). NN outputs are PEtab fixed parameters (static case) or time-varying functions like mechanistic model state variables or PEtab observables (dynamic case).

[sebapersson]

A comparison of NN objects to pre-existing PEtab objects might also be useful, what do you think?

I agree!