Allow linked design parameters

[NicolaCourtier]

Description

Enables relations to be enforced between the optimisation parameters and other model parameters for the purpose of design optimisation. Adds an example showing how to link the porosity to the active material volume fraction.

Issue reference

Fixes #532

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.08%. Comparing base (c8b00e6) to head (bdd8a12).
Report is 2 commits behind head on develop.

Additional details and impacted files

@@           Coverage Diff            @@
##           develop     #533   +/-   ##
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  Coverage    99.08%   99.08%           
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  Files           52       52           
  Lines         3605     3622   +17     
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+ Hits          3572     3589   +17     
  Misses          33       33           

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[NicolaCourtier]

This is not the neatest implementation and only works for design problems, but it's functionality that I would like to use!

[martinjrobins]

I'm not sure this is such a good idea. I'm not a fan of monkeypatching functions on a method (it can lead to some very confusing debugging later down the line), and its probably going to be confusing for users if they have to replace a function with signature def update_linked_parameters(self, parameter_set: None): with one that has a different signature def update_linked_parameters(parameter_set: Inputs):.

In the example given, you are effectivly removing the "Positive electrode porosity" parameter from the model, but not really because this parameter still exists in the underlying pybamm model. If the model is used in a design problem it won't have this parameter because your custom function is overwriting it every time, but if it is used in a fitting problem it will have this parameter. Worse yet, if the user accidiently tries to add "Positive electrode porosity" to the list of fitted parameters in a design problem, pybop will happily accept this, even through the model doesn't have this parameter in it anymore. I think this will lead to all sorts of confusions

[NicolaCourtier]

These are all good points... Let's find another way to implement this. I would like to be able to run this example and also change/add parameter relations to test different design assumptions.

[martinjrobins]

I would do something like this to alter the underlying pybamm model:

import pybop
import pybamm

# The aim of this script is to show how to systematically update
# design parameters which depend on the optimisation parameters.

# Define parameter set and model
parameter_set = pybop.ParameterSet.pybamm("Chen2020", formation_concentrations=True)
model = pybop.lithium_ion.SPMe(parameter_set=parameter_set)

parameter_to_replace = pybamm.Parameter("Positive electrode porosity")
replacement_symbol = 1 - pybamm.Parameter("Positive electrode active material volume fraction")

def replace_parameter(symbol):
    if symbol == parameter_to_replace:
        return replacement_symbol
    else:
        return symbol.create_copy(symbol.children)

def replace_dict(dictionary):
    return {key: replace_parameter(value) for key, value in dictionary.items()}

def replace_list(lst):
    return [replace_parameter(item) for item in lst]


new_model = model.pybamm_model.new_copy()
new_model.rhs = replace_dict(new_model.rhs)
new_model.algebraic = replace_dict(new_model.algebraic)
new_model.initial_conditions = replace_dict(new_model.initial_conditions)
new_model.boundary_conditions = replace_dict(new_model.boundary_conditions)
new_model.variables = replace_dict(new_model.variables)
new_model.events = replace_list(new_model.events)

model.pybamm_model = new_model


# Fitting parameters
parameters = pybop.Parameters(
    pybop.Parameter(
        "Positive electrode thickness [m]",
        prior=pybop.Gaussian(7.56e-05, 0.1e-05),
        bounds=[65e-06, 10e-05],
    ),
    pybop.Parameter(
        "Positive electrode active material volume fraction",
        prior=pybop.Gaussian(0.6, 0.15),
        bounds=[0.1, 0.9],
    ),
)

# Define test protocol
experiment = pybop.Experiment(
    [
        "Discharge at 1C until 2.5 V (5 seconds period)",
        "Hold at 2.5 V for 30 minutes or until 10 mA (5 seconds period)",
    ],
)
signal = ["Voltage [V]", "Current [A]"]

# Generate problem
problem = pybop.DesignProblem(
    model,
    parameters,
    experiment,
    signal=signal,
    initial_state={"Initial SoC": 1.0},
    update_capacity=True,
)

# Define the cost
cost = pybop.GravimetricEnergyDensity(problem)

# Run optimisation
optim = pybop.XNES(
    cost, verbose=True, allow_infeasible_solutions=False, max_iterations=10
)
x, final_cost = optim.run()
print("Estimated parameters:", x)
print(f"Initial gravimetric energy density: {cost(optim.x0):.2f} Wh.kg-1")
print(f"Optimised gravimetric energy density: {cost(x):.2f} Wh.kg-1")

# Plot the timeseries output
pybop.quick_plot(problem, problem_inputs=x, title="Optimised Comparison")

# Plot the cost landscape with optimisation path
pybop.plot2d(optim, steps=5)

[martinjrobins]

You could hide all the messing around with the pybamm model in a replace function on the pybop model

[NicolaCourtier]

This is very nice, thanks @martinjrobins!

[martinjrobins]

looks great @NicolaCourtier. I've made a few suggestions to improve the test on evaluate_symbol

[martinjrobins]

looks good to me!

[BradyPlanden]

Looks good, nice one!