New solver mode: only including required variables (don't store entire y)

[martinjrobins]

Description

Provide a mode for the solver so that only a user given list of variables are calculated and stored as part of the solution

Motivation

Remove the need to store the entire y solution and store only the variables given by the user

Possible Implementation

Interface might look like the following:

solver = pybamm.IDAKLUSolver()
sol = solver.solve(model, t_eval, solution_include=['Voltage [V]'])
print(sol['Voltage [V]'].entries)

sol['Negative particle surface concentration']  # gives an exception

Additional context

No response

[valentinsulzer]

Sounds good, though I would prefer output_variables instead of solution_include to match the syntax of QuickPlot

[martinjrobins]

Note that we probably need to do this for the JaxSolver as well, see pybop-team/PyBOP#25

@BradyPlanden

[BradyPlanden]

Just to crosspost, I'll start working on the Jax implementation of this as discussed in the above PyBOP issue.