Add creating_a_problem example

examples/notebooks/creating_a_problem.ipynb

@@ -0,0 +1,194 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "expmkveO04pw"
+   },
+   "source": [
+    "## Creating a Problem\n",
+    "\n",
+    "In this notebook, we create and solve a single particle model (SPM). This is achieved using a predefined parameter set introduced in Marquis et al. [[1]](https://doi.org/10.1149/1945-7111/abbce4) \n",
+    "\n",
+    "Before we begin, we need to ensure that we have all the necessary tools. We will install PyBOP and upgrade dependencies."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
+    },
+    "id": "X87NUGPW04py",
+    "outputId": "0d785b07-7cff-4aeb-e60a-4ff5a669afbf"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n",
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip install --upgrade pip ipywidgets -q\n",
+    "%pip install pybop -q\n",
+    "\n",
+    "import numpy as np\n",
+    "\n",
+    "import pybop\n",
+    "\n",
+    "pybop.PlotlyManager().pio.renderers.default = \"notebook_connected\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "5XU-dMtU04p2"
+   },
+   "source": [
+    "### Creating a Model\n",
+    "\n",
+    "A fitting problem consists of three parts: An experimental dataset that is used for fitting, a model that the dataset should be fit to, and the parameters that should be fit. To obtain a problem we therefore first need to create a model. This has been explained in detail in the creating_a_model example. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_set = pybop.ParameterSet.pybamm(\"Marquis2019\")\n",
+    "model = pybop.lithium_ion.SPM(parameter_set=parameter_set)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Next, the parameters. All parameters of the problem are contained in pybop.Parameters(). Each of the variable to fit is defined as a pybop.Parameter() separated by commas inside pybop.Parameters(). In this example, we have two parameters, the positive electrode thickness and the positive particle radius:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameters = pybop.Parameters(\n",
+    "    pybop.Parameter(\n",
+    "        \"Positive electrode thickness [m]\",\n",
+    "        prior=pybop.Gaussian(7.56e-05, 0.05e-05),\n",
+    "        bounds=[65e-06, 10e-05],\n",
+    "    ),\n",
+    "    pybop.Parameter(\n",
+    "        \"Positive particle radius [m]\",\n",
+    "        prior=pybop.Gaussian(5.22e-06, 0.05e-06),\n",
+    "        bounds=[2e-06, 9e-06],\n",
+    "    ),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The third component is the dataset. This could be an experimental dataset or a simulation. In this example, we just use simulation data by running model.predict() for a 1C discharge, similar to the creating_a_problem example. To pass it to the problem, we need to extract the voltage, time and current data from the simulation results and define it as the dataset:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_eval = np.arange(0, 3700, 1)\n",
+    "solution = model.predict([], t_eval)  # No inputs i.e []\n",
+    "dataset = pybop.Dataset(\n",
+    "    {\n",
+    "        \"Time [s]\": np.arange(0, len(solution[\"Voltage [V]\"].data), 1),\n",
+    "        \"Current function [A]\": solution[\"Current [A]\"].data,\n",
+    "        \"Voltage [V]\": solution[\"Voltage [V]\"].data,\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Setting up the problem\n",
+    "With all parts setup, we can now make a problem. Therefore, we use pybop.FittingProblem() to define a simple fitting problem and the model, parameters and dataset defined before as inputs."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "problem = pybop.FittingProblem(model, parameters, dataset)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Testing the problem\n",
+    "To verify our problem, we solve assign a sum of squared error cost function to it and solve it. \n",
+    "The solution can be compared to the values in the parameter_set defined in the beginning."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(array([7.62324125e-05, 5.20703504e-06]), inf)\n",
+      "7.67500163945363e-05\n",
+      "5.310487559937693e-06\n"
+     ]
+    }
+   ],
+   "source": [
+    "cost = pybop.SumSquaredError(problem)\n",
+    "optim = pybop.Optimisation(cost)\n",
+    "result = optim.run()\n",
+    "print(result)\n",
+    "print(parameter_set[\"Positive electrode thickness [m]\"])\n",
+    "print(parameter_set[\"Positive particle radius [m]\"])"
+   ]
+  }
+ ],
+ "metadata": {
+  "colab": {
+   "provenance": []
+  },
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}