#!/usr/bin/env python
# coding: utf-8

# ## Parameter Estimation with AdamW in PyBOP
# 
# In this notebook, we demonstrate an example of parameter estimation for a single-particle model using the AdamW optimiser [1][2]. The AdamW optimiser is an algorithm for gradient-based optimisation, combining the advantages of the Adaptive Gradient Algorithm (AdaGrad) and Root Mean Square Propagation (RMSProp).
# 
# [[1]: Adam: A Method for Stochastic Optimization](https://arxiv.org/abs/1412.6980) 
# 
# [[2]: Decoupled Weight Decay Regularization](https://doi.org/10.48550/arXiv.1711.05101)
# 
# ### Setting up the Environment
# 
# Before we begin, we need to ensure that we have all the necessary tools. We will install PyBOP and upgrade dependencies:

# In[ ]:


get_ipython().run_line_magic('pip', 'install --upgrade pip ipywidgets -q')
get_ipython().run_line_magic('pip', 'install pybop -q')


# ### Importing Libraries
# 
# With the environment set up, we can now import PyBOP alongside other libraries we will need:

# In[ ]:


import numpy as np

import pybop


# Let's fix the random seed in order to generate consistent output during development, although this does not need to be done in practice.

# In[ ]:


np.random.seed(8)


# ### Generate Synthetic Data
# 
# To demonstrate parameter estimation, we first need some data. We will generate synthetic data using the PyBOP forward model, which requires defining a parameter set and the model itself.
# 
# #### Defining Parameters and Model
# 
# We start by creating an example parameter set and then instantiate the single-particle model (SPM):

# In[ ]:


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


# ### Simulating Forward Model
# 
# We can then simulate the model using the `predict` method, with a default constant current to generate voltage data.

# In[ ]:


t_eval = np.arange(0, 900, 2)
values = model.predict(t_eval=t_eval)


# ### Adding Noise to Voltage Data
# 
# To make the parameter estimation more realistic, we add Gaussian noise to the data.

# In[ ]:


sigma = 0.001
corrupt_values = values["Voltage [V]"].data + np.random.normal(0, sigma, len(t_eval))


# ## Identify the Parameters

# We will now set up the parameter estimation process by defining the datasets for optimisation and selecting the model parameters we wish to estimate.

# ### Creating Optimisation Dataset
# 
# The dataset for optimisation is composed of time, current, and the noisy voltage data:

# In[ ]:


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


# ### Defining Parameters to Estimate
# 
# We select the parameters for estimation and set up their prior distributions and bounds:

# In[ ]:


parameters = [
    pybop.Parameter(
        "Negative electrode active material volume fraction",
        prior=pybop.Gaussian(0.6, 0.02),
        bounds=[0.5, 0.8],
    ),
    pybop.Parameter(
        "Positive electrode active material volume fraction",
        prior=pybop.Gaussian(0.48, 0.02),
        bounds=[0.4, 0.7],
    ),
]


# ### Setting up the Optimisation Problem
# 
# With the datasets and parameters defined, we can set up the optimisation problem, its cost function, and the optimiser.

# In[ ]:


problem = pybop.FittingProblem(model, parameters, dataset)
cost = pybop.SumSquaredError(problem)
optim = pybop.Optimisation(cost, optimiser=pybop.AdamW)
optim.set_max_unchanged_iterations(40)
optim.set_max_iterations(150)


# ### Running the Optimisation
# 
# We proceed to run the AdamW optimisation algorithm to estimate the parameters:

# In[ ]:


x, final_cost = optim.run()


# ### Viewing the Estimated Parameters
# 
# After the optimisation, we can examine the estimated parameter values:

# In[ ]:


x  # This will output the estimated parameters


# ## Plotting and Visualisation
# 
# PyBOP provides various plotting utilities to visualise the results of the optimisation.

# ### Comparing System Response
# 
# We can quickly plot the system's response using the estimated parameters compared to the target:

# In[ ]:


pybop.quick_plot(problem, problem_inputs=x, title="Optimised Comparison");


# ### Convergence and Parameter Trajectories
# 
# To assess the optimisation process, we can plot the convergence of the cost function and the trajectories of the parameters:

# In[ ]:


pybop.plot_convergence(optim)
pybop.plot_parameters(optim);


# ### Cost Landscape
# 
# Finally, we can visualise the cost landscape and the path taken by the optimiser:

# In[ ]:


# Plot the cost landscape
pybop.plot2d(cost, steps=15)
# Plot the cost landscape with optimisation path and updated bounds
bounds = np.asarray([[0.6, 0.9], [0.5, 0.8]])
pybop.plot2d(optim, bounds=bounds, steps=15);


# ### Conclusion
# 
# This notebook illustrates how to perform parameter estimation using AdamW in PyBOP, providing insights into the optimisation process through various visualisations.