Adding an example of using the package in practice

[matt-graham]

Raising as part of JOSS review openjournals/joss-reviews#6148

The tutorial example in https://github.com/firedrakeproject/checkpoint_schedules/blob/main/docs/notebooks/tutorial.ipynb is great at giving an understanding of the packages's API and an overview of the different checkpoint schedule algorithms implemented, however it would also be useful to have an example of how the package can be used in practice in actual adjoint computation, even if it's for a trivial problem / forward computation.

The paper indicates the package has been incoroporated in to tlm_adjoint (presumably once tlm-adjoint/tlm_adjoint#382 is merged in?) - even just linking to how the package is used there as a 'next steps' tutorial example could be useful.

[Ig-dolci]

@matt-graham We appreciate your suggestion to include an example application in our documentation.

Following your suggestion and seeking to make the usage of checkpoint_schedules more accessible, we have included an example of checkpoint_schedules usage in an adjoint-based gradient problem. You can access it in the following notebook: checkpoint_schedule application: Adjoint-Based Gradient with the Burger's Equation.

We are also pleased to inform you that checkpoint_schedules is now incorporated into the pyadjoint package (PR 121).

[matt-graham]

@Ig-dolci - thanks the new notebook is fantastic!