Transformations for varying scale parameters

[BradyPlanden]

Feature description

When optimising parameters of varying scale, we overshoot acceptable parameter ranges during fitting (for non-bounded methods). Transforming / normalising the parameter space on input to the optimiser should solve this issue. An example of this issue is:

import pybop
import numpy as np

parameter_set = pybop.ParameterSet("pybamm", "Chen2020")
model = pybop.lithium_ion.SPMe(parameter_set=parameter_set)

# Fitting parameters
parameters = [
    pybop.Parameter(
        "Positive electrode diffusivity [m2.s-1]",
        prior=pybop.Gaussian(3.43e-15, 1e-15),
        bounds=[1e-15, 5e-15],
    ),
]

sigma = 0.001
t_eval = np.arange(0, 900, 2)
values = model.predict(t_eval=t_eval)
corrupt_voltage = values["Terminal voltage [V]"].data + np.random.normal(
    0, sigma, len(t_eval)
)

dataset = [
    pybop.Dataset("Time [s]", t_eval),
    pybop.Dataset("Current function [A]", values["Current [A]"].data),
    pybop.Dataset("Terminal voltage [V]", corrupt_voltage),
]

# Generate problem, cost function, and optimisation class
problem = pybop.Problem(model, parameters, dataset)
cost = pybop.SumSquaredError(problem)
optim = pybop.Optimisation(cost, optimiser=pybop.GradientDescent)
optim.optimiser.set_learning_rate(0.025)

x, final_cost = optim.run()
print("Estimated parameters:", x)

Our implementation of Gradient Descent (#88) is unbounded and immediately select a candidate solution orders of magnitude higher than an acceptable range.

Motivation

No response

Possible implementation

No response

Additional context

No response

[NicolaCourtier]

This issue seems to have been resolved by PR #213.

In light of API changes, the example is now:

import pybop
import numpy as np

parameter_set = pybop.ParameterSet.pybamm("Chen2020")
model = pybop.lithium_ion.SPMe(parameter_set=parameter_set)

# Fitting parameters
parameters = [
    pybop.Parameter(
        "Positive electrode diffusivity [m2.s-1]",
        prior=pybop.Gaussian(3.43e-15, 1e-15),
        bounds=[1e-15, 5e-15],
    ),
]

sigma = 0.001
t_eval = np.arange(0, 900, 2)
values = model.predict(t_eval=t_eval)
corrupt_voltage = values["Terminal voltage [V]"].data + np.random.normal(
    0, sigma, len(t_eval)
)

dataset = pybop.Dataset(
    {
        "Time [s]": t_eval,
        "Current function [A]": values["Current [A]"].data,
        "Voltage [V]": corrupt_voltage,
    }
)

# Generate problem, cost function, and optimisation class
problem = pybop.FittingProblem(model, parameters, dataset)
cost = pybop.SumSquaredError(problem)
optim = pybop.Optimisation(cost, optimiser=pybop.GradientDescent)
# optim.optimiser.set_learning_rate(0.025)  # replaced by sigma

x, final_cost = optim.run()
print("Estimated parameters:", x)