diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2d258bff..6f905bf2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,8 @@
 
 ## Features
 
+
+- [#316](https://github.com/pybop-team/PyBOP/pull/316) - Adds Adam with weight decay (AdamW) optimiser, adds depreciation warning for pints.Adam implementation.
 - [#271](https://github.com/pybop-team/PyBOP/issues/271) - Aligns the output of the optimisers via a generalisation of Result class.
 - [#315](https://github.com/pybop-team/PyBOP/pull/315) - Updates __init__ structure to remove circular import issues and minimises dependancy imports across codebase for faster PyBOP module import. Adds type-hints to BaseModel and refactors rebuild parameter variables.
 - [#236](https://github.com/pybop-team/PyBOP/issues/236) - Restructures the optimiser classes, adds a new optimisation API through direct construction and keyword arguments, and fixes the setting of `max_iterations`, and `_minimising`. Introduces `pybop.BaseOptimiser`, `pybop.BasePintsOptimiser`, and `pybop.BaseSciPyOptimiser` classes.
diff --git a/README.md b/README.md
index 6ff0af9f..8fd09c0a 100644
--- a/README.md
+++ b/README.md
@@ -85,13 +85,13 @@ The table below lists the currently supported [models](https://github.com/pybop-
 |-----------------------------------------------|-------------------------------------------------------------|------------------------------------------|
 | Single Particle Model (SPM) | Covariance Matrix Adaptation Evolution Strategy (CMA-ES) | Sum of Squared Errors (SSE) <tr></tr> |
 | Single Particle Model with Electrolyte (SPMe) | Particle Swarm Optimization (PSO) | Root Mean Squared Error (RMSE) <tr></tr> |
-| Doyle-Fuller-Newman (DFN) | Adaptive Moment Estimation (Adam) | Maximum Likelihood Estimation (MLE) <tr></tr> |
-| Many Particle Model (MPM) | Improved Resilient Backpropagation (iRProp-) | Maximum a Posteriori (MAP) <tr></tr> |
-| Multi-Species Multi-Reactants (MSMR) | Exponential Natural Evolution Strategy (xNES) | Unscented Kalman Filter (UKF) <tr></tr> |
-| Equivalent Circuit Models (ECM) | Separable Natural Evolution Strategy (sNES) | Gravimetric Energy Density <tr></tr> |
-| | Gradient Descent | Volumetric Energy Density <tr></tr> |
+| Doyle-Fuller-Newman (DFN) | Exponential Natural Evolution Strategy (xNES)  | Gaussian Log Likelihood <tr></tr> |
+| Many Particle Model (MPM) | Separable Natural Evolution Strategy (sNES) | Gaussian Log Likelihood w/ known variance <tr></tr> |
+| Multi-Species Multi-Reactants (MSMR) | Adaptive Moment Estimation with Weight Decay (AdamW) | Maximum a Posteriori (MAP) <tr></tr> |
+| Equivalent Circuit Models (ECM) | Improved Resilient Backpropagation (iRProp-) | Unscented Kalman Filter (UKF) <tr></tr> |
+| | SciPy Minimize & Differential Evolution | Gravimetric Energy Density <tr></tr> |
+| | Gradient Descent| Volumetric Energy Density<tr></tr> |
 | | Nelder-Mead | <tr></tr> |
-| | SciPy Minimize & Differential Evolution | <tr></tr> |
 
 </p>
 
diff --git a/benchmarks/benchmark_parameterisation.py b/benchmarks/benchmark_parameterisation.py
index 8440ba5e..a64116a4 100644
--- a/benchmarks/benchmark_parameterisation.py
+++ b/benchmarks/benchmark_parameterisation.py
@@ -13,7 +13,7 @@ class BenchmarkParameterisation:
         [
             pybop.SciPyMinimize,
             pybop.SciPyDifferentialEvolution,
-            pybop.Adam,
+            pybop.AdamW,
             pybop.CMAES,
             pybop.GradientDescent,
             pybop.IRPropMin,
diff --git a/benchmarks/benchmark_track_parameterisation.py b/benchmarks/benchmark_track_parameterisation.py
index fac2d54a..9180ffec 100644
--- a/benchmarks/benchmark_track_parameterisation.py
+++ b/benchmarks/benchmark_track_parameterisation.py
@@ -13,7 +13,7 @@ class BenchmarkTrackParameterisation:
         [
             pybop.SciPyMinimize,
             pybop.SciPyDifferentialEvolution,
-            pybop.Adam,
+            pybop.AdamW,
             pybop.CMAES,
             pybop.GradientDescent,
             pybop.IRPropMin,
diff --git a/examples/notebooks/multi_optimiser_identification.ipynb b/examples/notebooks/multi_optimiser_identification.ipynb
index 8bb6f353..f85b2609 100644
--- a/examples/notebooks/multi_optimiser_identification.ipynb
+++ b/examples/notebooks/multi_optimiser_identification.ipynb
@@ -279,7 +279,7 @@
    "source": [
     "### Selecting the Optimisers\n",
     "\n",
-    "Now, we can select the optimisers to investigate. The first object is a list of non-gradient-based PINTS's optimisers. The next object comprises the gradient-based PINTS's optimisers (Adam, GradientDescent, IRPropMin). The final object forms the SciPy optimisers which can have gradient and non-gradient-based algorithms."
+    "Now, we can select the optimisers to investigate. The first object is a list of non-gradient-based PINTS's optimisers. The next object comprises the gradient-based PINTS's optimisers (AdamW, GradientDescent, IRPropMin). The final object forms the SciPy optimisers which can have gradient and non-gradient-based algorithms."
    ]
   },
   {
@@ -296,7 +296,7 @@
    "outputs": [],
    "source": [
     "gradient_optimisers = [\n",
-    "    pybop.Adam,\n",
+    "    pybop.AdamW,\n",
     "    pybop.GradientDescent,\n",
     "    pybop.IRPropMin,\n",
     "]\n",
@@ -343,8 +343,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Running Adam\n",
-      "NOTE: Boundaries ignored by Adam\n",
+      "Running AdamW\n",
+      "NOTE: Boundaries ignored by AdamW\n",
       "Running GradientDescent\n",
       "NOTE: Boundaries ignored by Gradient Descent\n",
       "Running IRPropMin\n"
@@ -441,16 +441,16 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "| Optimiser: Adam | Results: [0.7940917  0.66244264] |\n",
-      "| Optimiser: Gradient descent | Results: [0.54971602 0.92692275] |\n",
-      "| Optimiser: iRprop- | Results: [0.72245096 0.67281911] |\n",
-      "| Optimiser: Covariance Matrix Adaptation Evolution Strategy (CMA-ES) | Results: [0.72101083 0.67313135] |\n",
-      "| Optimiser: Seperable Natural Evolution Strategy (SNES) | Results: [0.72082105 0.67317566] |\n",
-      "| Optimiser: Particle Swarm Optimisation (PSO) | Results: [0.71816152 0.6738613 ] |\n",
-      "| Optimiser: Exponential Natural Evolution Strategy (xNES) | Results: [0.72064411 0.67318804] |\n",
-      "| Optimiser: Nelder-Mead | Results: [0.72117726 0.67313287] |\n",
-      "| Optimiser: SciPyMinimize | Results: [0.62747904 0.7       ] |\n",
-      "| Optimiser: SciPyDifferentialEvolution | Results: [0.72103631 0.67312847] |\n"
+      "| Optimiser: AdamW | Results: [0.80186169 0.66943058] |\n",
+      "| Optimiser: Gradient descent | Results: [0.44491146 1.59642543] |\n",
+      "| Optimiser: iRprop- | Results: [0.8        0.66516386] |\n",
+      "| Optimiser: Covariance Matrix Adaptation Evolution Strategy (CMA-ES) | Results: [0.7999994  0.66516056] |\n",
+      "| Optimiser: Seperable Natural Evolution Strategy (SNES) | Results: [0.79672265 0.66566242] |\n",
+      "| Optimiser: Particle Swarm Optimisation (PSO) | Results: [0.79978922 0.66557426] |\n",
+      "| Optimiser: Exponential Natural Evolution Strategy (xNES) | Results: [0.79992605 0.66513294] |\n",
+      "| Optimiser: Nelder-Mead | Results: [0.81389091 0.66318217] |\n",
+      "| Optimiser: SciPyMinimize | Results: [0.63594266 0.7       ] |\n",
+      "| Optimiser: SciPyDifferentialEvolution | Results: [0.79999973 0.6651644 ] |\n"
      ]
     }
    ],
@@ -509,7 +509,7 @@
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diff --git a/examples/notebooks/spm_AdamW.ipynb b/examples/notebooks/spm_AdamW.ipynb
new file mode 100644
index 00000000..20b73330
--- /dev/null
+++ b/examples/notebooks/spm_AdamW.ipynb
@@ -0,0 +1,826 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "expmkveO04pw"
+   },
+   "source": [
+    "## Parameter Estimation with AdamW in PyBOP\n",
+    "\n",
+    "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).\n",
+    "\n",
+    "[[1]: Adam: A Method for Stochastic Optimization](https://arxiv.org/abs/1412.6980) \n",
+    "\n",
+    "[[2]: Decoupled Weight Decay Regularization](https://doi.org/10.48550/arXiv.1711.05101)\n",
+    "\n",
+    "### Setting up the Environment\n",
+    "\n",
+    "Before we begin, we need to ensure that we have all the necessary tools. We will install PyBOP from its development branch and upgrade some dependencies:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
+    },
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:40.337833Z",
+     "iopub.status.busy": "2024-04-04T13:51:40.337689Z",
+     "iopub.status.idle": "2024-04-04T13:51:41.935008Z",
+     "shell.execute_reply": "2024-04-04T13:51:41.934618Z"
+    },
+    "id": "X87NUGPW04py",
+    "outputId": "0d785b07-7cff-4aeb-e60a-4ff5a669afbf"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Requirement already satisfied: pip in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (24.0)\n",
+      "Requirement already satisfied: ipywidgets in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (8.1.2)\n",
+      "Requirement already satisfied: comm>=0.1.3 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipywidgets) (0.2.1)\n",
+      "Requirement already satisfied: ipython>=6.1.0 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipywidgets) (8.22.1)\n",
+      "Requirement already satisfied: traitlets>=4.3.1 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipywidgets) (5.14.1)\n",
+      "Requirement already satisfied: widgetsnbextension~=4.0.10 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipywidgets) (4.0.10)\n",
+      "Requirement already satisfied: jupyterlab-widgets~=3.0.10 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipywidgets) (3.0.10)\n",
+      "Requirement already satisfied: decorator in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (5.1.1)\n",
+      "Requirement already satisfied: jedi>=0.16 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (0.19.1)\n",
+      "Requirement already satisfied: matplotlib-inline in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (0.1.6)\n",
+      "Requirement already satisfied: prompt-toolkit<3.1.0,>=3.0.41 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (3.0.43)\n",
+      "Requirement already satisfied: pygments>=2.4.0 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (2.17.2)\n",
+      "Requirement already satisfied: stack-data in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (0.6.3)\n",
+      "Requirement already satisfied: pexpect>4.3 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from ipython>=6.1.0->ipywidgets) (4.9.0)\n",
+      "Requirement already satisfied: parso<0.9.0,>=0.8.3 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from jedi>=0.16->ipython>=6.1.0->ipywidgets) (0.8.3)\n",
+      "Requirement already satisfied: ptyprocess>=0.5 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from pexpect>4.3->ipython>=6.1.0->ipywidgets) (0.7.0)\n",
+      "Requirement already satisfied: wcwidth in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from prompt-toolkit<3.1.0,>=3.0.41->ipython>=6.1.0->ipywidgets) (0.2.13)\n",
+      "Requirement already satisfied: executing>=1.2.0 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from stack-data->ipython>=6.1.0->ipywidgets) (2.0.1)\n",
+      "Requirement already satisfied: asttokens>=2.1.0 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from stack-data->ipython>=6.1.0->ipywidgets) (2.4.1)\n",
+      "Requirement already satisfied: pure-eval in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from stack-data->ipython>=6.1.0->ipywidgets) (0.2.2)\n",
+      "Requirement already satisfied: six>=1.12.0 in /Users/engs2510/.pyenv/versions/3.11.7/envs/pybop/lib/python3.11/site-packages (from asttokens>=2.1.0->stack-data->ipython>=6.1.0->ipywidgets) (1.16.0)\n",
+      "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\n",
+    "%pip install pybop -q"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "jAvD5fk104p0"
+   },
+   "source": [
+    "### Importing Libraries\n",
+    "\n",
+    "With the environment set up, we can now import PyBOP alongside other libraries we will need:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:41.936561Z",
+     "iopub.status.busy": "2024-04-04T13:51:41.936439Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.508083Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.507654Z"
+    },
+    "id": "SQdt4brD04p1"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "import pybop"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "5XU-dMtU04p2"
+   },
+   "source": [
+    "### Generate Synthetic Data\n",
+    "\n",
+    "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.\n",
+    "\n",
+    "#### Defining Parameters and Model\n",
+    "\n",
+    "We start by creating an example parameter set and then instantiate the single-particle model (SPM):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.509591Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.509437Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.534794Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.534452Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "parameter_set = pybop.ParameterSet.pybamm(\"Chen2020\")\n",
+    "model = pybop.lithium_ion.SPM(parameter_set=parameter_set)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Simulating Forward Model\n",
+    "\n",
+    "We can then simulate the model using the `predict` method, with a default constant current to generate voltage data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.536154Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.536069Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.610305Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.609892Z"
+    },
+    "id": "sBasxv8U04p3"
+   },
+   "outputs": [],
+   "source": [
+    "t_eval = np.arange(0, 900, 2)\n",
+    "values = model.predict(t_eval=t_eval)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Adding Noise to Voltage Data\n",
+    "\n",
+    "To make the parameter estimation more realistic, we add Gaussian noise to the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.611946Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.611728Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.621525Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.621156Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "sigma = 0.001\n",
+    "corrupt_values = values[\"Voltage [V]\"].data + np.random.normal(0, sigma, len(t_eval))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "X8-tubYY04p_"
+   },
+   "source": [
+    "## Identify the Parameters"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "PQqhvSZN04p_"
+   },
+   "source": [
+    "We will now set up the parameter estimation process by defining the datasets for optimisation and selecting the model parameters we wish to estimate."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Creating Optimisation Dataset\n",
+    "\n",
+    "The dataset for optimisation is composed of time, current, and the noisy voltage data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.622671Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.622478Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.628864Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.628519Z"
+    },
+    "id": "zuvGHWID04p_"
+   },
+   "outputs": [],
+   "source": [
+    "dataset = pybop.Dataset(\n",
+    "    {\n",
+    "        \"Time [s]\": t_eval,\n",
+    "        \"Current function [A]\": values[\"Current [A]\"].data,\n",
+    "        \"Voltage [V]\": corrupt_values,\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "ffS3CF_704qA"
+   },
+   "source": [
+    "### Defining Parameters to Estimate\n",
+    "\n",
+    "We select the parameters for estimation and set up their prior distributions and bounds:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.629987Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.629809Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.631895Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.631621Z"
+    },
+    "id": "WPCybXIJ04qA"
+   },
+   "outputs": [],
+   "source": [
+    "parameters = [\n",
+    "    pybop.Parameter(\n",
+    "        \"Negative electrode active material volume fraction\",\n",
+    "        prior=pybop.Gaussian(0.6, 0.02),\n",
+    "        bounds=[0.5, 0.8],\n",
+    "    ),\n",
+    "    pybop.Parameter(\n",
+    "        \"Positive electrode active material volume fraction\",\n",
+    "        prior=pybop.Gaussian(0.48, 0.02),\n",
+    "        bounds=[0.4, 0.7],\n",
+    "    ),\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "n4OHa-aF04qA"
+   },
+   "source": [
+    "### Setting up the Optimisation Problem\n",
+    "\n",
+    "With the datasets and parameters defined, we can set up the optimisation problem, its cost function, and the optimiser."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.632931Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.632782Z",
+     "iopub.status.idle": "2024-04-04T13:51:42.705454Z",
+     "shell.execute_reply": "2024-04-04T13:51:42.705066Z"
+    },
+    "id": "etMzRtx404qA"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "NOTE: Boundaries ignored by AdamW\n"
+     ]
+    }
+   ],
+   "source": [
+    "problem = pybop.FittingProblem(model, parameters, dataset)\n",
+    "cost = pybop.SumSquaredError(problem)\n",
+    "optim = pybop.Optimisation(cost, optimiser=pybop.AdamW)\n",
+    "optim.set_max_unchanged_iterations(40)\n",
+    "optim.set_max_iterations(150)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "caprp-bV04qB"
+   },
+   "source": [
+    "### Running the Optimisation\n",
+    "\n",
+    "We proceed to run the AdamW optimisation algorithm to estimate the parameters:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:42.706564Z",
+     "iopub.status.busy": "2024-04-04T13:51:42.706469Z",
+     "iopub.status.idle": "2024-04-04T13:51:50.537424Z",
+     "shell.execute_reply": "2024-04-04T13:51:50.537032Z"
+    },
+    "id": "-9OVt0EQ04qB"
+   },
+   "outputs": [],
+   "source": [
+    "x, final_cost = optim.run()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "-4pZsDmS04qC"
+   },
+   "source": [
+    "### Viewing the Estimated Parameters\n",
+    "\n",
+    "After the optimisation, we can examine the estimated parameter values:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
+    },
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:50.538815Z",
+     "iopub.status.busy": "2024-04-04T13:51:50.538619Z",
+     "iopub.status.idle": "2024-04-04T13:51:50.541683Z",
+     "shell.execute_reply": "2024-04-04T13:51:50.541465Z"
+    },
+    "id": "Hgz8SV4i04qC",
+    "outputId": "e1e42ae7-5075-4c47-dd68-1b22ecc170f6"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.76334915, 0.66225839])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x  # This will output the estimated parameters"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "KxKURtH704qC"
+   },
+   "source": [
+    "## Plotting and Visualisation\n",
+    "\n",
+    "PyBOP provides various plotting utilities to visualise the results of the optimisation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "-cWCOiqR04qC"
+   },
+   "source": [
+    "### Comparing System Response\n",
+    "\n",
+    "We can quickly plot the system's response using the estimated parameters compared to the target:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 467
+    },
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:50.542618Z",
+     "iopub.status.busy": "2024-04-04T13:51:50.542472Z",
+     "iopub.status.idle": "2024-04-04T13:51:50.986055Z",
+     "shell.execute_reply": "2024-04-04T13:51:50.985844Z"
+    },
+    "id": "tJUJ80Ve04qD",
+    "outputId": "855fbaa2-1e09-4935-eb1a-8caf7f99eb75"
+   },
+   "outputs": [
+    {
+     "data": {
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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pybop.quick_plot(problem, parameter_values=x, title=\"Optimised Comparison\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Convergence and Parameter Trajectories\n",
+    "\n",
+    "To assess the optimisation process, we can plot the convergence of the cost function and the trajectories of the parameters:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:50.987237Z",
+     "iopub.status.busy": "2024-04-04T13:51:50.986963Z",
+     "iopub.status.idle": "2024-04-04T13:51:52.766386Z",
+     "shell.execute_reply": "2024-04-04T13:51:52.766178Z"
+    },
+    "id": "N5XYkevi04qD"
+   },
+   "outputs": [
+    {
+     "data": {
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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pybop.plot_convergence(optim)\n",
+    "pybop.plot_parameters(optim);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Cost Landscape\n",
+    "\n",
+    "Finally, we can visualise the cost landscape and the path taken by the optimiser:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2024-04-04T13:51:52.767346Z",
+     "iopub.status.busy": "2024-04-04T13:51:52.767261Z",
+     "iopub.status.idle": "2024-04-04T13:51:57.666000Z",
+     "shell.execute_reply": "2024-04-04T13:51:57.665745Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Plot the cost landscape\n",
+    "pybop.plot2d(cost, steps=15)\n",
+    "# Plot the cost landscape with optimisation path and updated bounds\n",
+    "bounds = np.array([[0.6, 0.9], [0.5, 0.8]])\n",
+    "pybop.plot2d(optim, bounds=bounds, steps=15);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Conclusion\n",
+    "\n",
+    "This notebook illustrates how to perform parameter estimation using AdamW in PyBOP, providing insights into the optimisation process through various visualisations."
+   ]
+  }
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diff --git a/examples/scripts/spm_adam.py b/examples/scripts/spm_AdamW.py
similarity index 98%
rename from examples/scripts/spm_adam.py
rename to examples/scripts/spm_AdamW.py
index 82f884e2..10351512 100644
--- a/examples/scripts/spm_adam.py
+++ b/examples/scripts/spm_AdamW.py
@@ -54,7 +54,7 @@ def noise(sigma):
     model, parameters, dataset, signal=signal, init_soc=init_soc
 )
 cost = pybop.RootMeanSquaredError(problem)
-optim = pybop.Adam(
+optim = pybop.AdamW(
     cost,
     verbose=True,
     allow_infeasible_solutions=True,
diff --git a/pybop/__init__.py b/pybop/__init__.py
index 6d2c0dbf..61971e95 100644
--- a/pybop/__init__.py
+++ b/pybop/__init__.py
@@ -102,6 +102,8 @@
 #
 # Optimiser class
 #
+
+from .optimisers._adamw import AdamWImpl
 from .optimisers.base_optimiser import BaseOptimiser, Result
 from .optimisers.base_pints_optimiser import BasePintsOptimiser
 from .optimisers.scipy_optimisers import (
@@ -118,6 +120,7 @@
     PSO,
     SNES,
     XNES,
+    AdamW,
 )
 from .optimisers.optimisation import Optimisation
 
diff --git a/pybop/optimisers/_adamw.py b/pybop/optimisers/_adamw.py
new file mode 100644
index 00000000..24e5ec98
--- /dev/null
+++ b/pybop/optimisers/_adamw.py
@@ -0,0 +1,235 @@
+#
+# Extends the Pints' Adam Class with a Weight Decay addition
+#
+
+import numpy as np
+from pints import Optimiser as PintsOptimiser
+
+
+class AdamWImpl(PintsOptimiser):
+    """
+    AdamW optimiser (adaptive moment estimation with weight decay), as described in [1]_.
+
+    This method is an extension of the Adam optimiser that introduces weight decay,
+    which helps to regularise the weights and prevent overfitting.
+
+    This class reimplements the Pints' Adam Optimiser, but with the weight decay
+    functionality mentioned above. Original creation and credit is attributed to Pints.
+
+    Pseudo-code is given below. Here the value of the j-th parameter at
+    iteration i is given as ``p_j[i]`` and the corresponding derivative is
+    denoted ``g_j[i]``::
+
+        m_j[i] = beta1 * m_j[i - 1] + (1 - beta1) * g_j[i]
+        v_j[i] = beta2 * v_j[i - 1] + (1 - beta2) * g_j[i]**2
+
+        m_j' = m_j[i] / (1 - beta1**(1 + i))
+        v_j' = v_j[i] / (1 - beta2**(1 + i))
+
+        p_j[i] = p_j[i - 1] - alpha * (m_j' / (sqrt(v_j') + eps) + lambda * p_j[i - 1])
+
+    The initial values of the moments are ``m_j[0] = v_j[0] = 0``, after which
+    they decay with rates ``beta1`` and ``beta2``. The default values for these are,
+    ``beta1 = 0.9`` and ``beta2 = 0.999``.
+
+    The terms ``m_j'`` and ``v_j'`` are "initialisation bias corrected"
+    versions of ``m_j`` and ``v_j`` (see section 2 of the paper).
+
+    The parameter ``alpha`` is a step size, which is set as ``min(sigma0)`` in
+    this implementation.
+
+    The parameter ``lambda`` is the weight decay rate, which is set to ``0.01``
+    by default in this implementation.
+
+    Finally, ``eps`` is a small constant used to avoid division by zero, set to
+    ``eps = `np.finfo(float).eps` in this implementation.
+
+    This is an unbounded method: Any ``boundaries`` will be ignored.
+
+    References
+    ----------
+    .. [1] Decoupled Weight Decay Regularization
+           Loshchilov and Hutter, 2019, arxiv (version v3)
+           https://doi.org/10.48550/arXiv.1711.05101
+    """
+
+    def __init__(self, x0, sigma0=0.015, boundaries=None):
+        if boundaries is not None:
+            print("NOTE: Boundaries ignored by AdamW")
+
+        self.boundaries = None
+        super().__init__(x0, sigma0, self.boundaries)
+
+        # Set optimiser state
+        self._running = False
+        self._ready_for_tell = False
+
+        # Best solution found
+        self._x_best = self._x0
+        self._f_best = np.inf
+
+        # Current point, score, and gradient
+        self._current = self._x0
+        self._current_f = np.inf
+        self._current_df = None
+
+        # Proposed next point (read-only, so can be passed to user)
+        self._proposed = self._x0
+        self._proposed.setflags(write=False)
+
+        # Moment vectors
+        self._m = np.zeros(self._x0.shape)
+        self._v = np.zeros(self._x0.shape)
+
+        # Exponential decay rates for the moment estimates
+        self._b1 = 0.9
+        self._b2 = 0.999
+
+        # Step size
+        self._alpha = np.min(self._sigma0)
+
+        # Weight decay rate
+        self.set_lambda()
+
+        # Small number added to avoid divide-by-zero
+        self._eps = np.finfo(float).eps
+
+        # Powers of decay rates
+        self._b1t = 1
+        self._b2t = 1
+
+    def ask(self):
+        """
+        Returns a list of next points in the parameter-space
+        to evaluate from the optimiser.
+        """
+
+        # Running, and ready for tell now
+        self._ready_for_tell = True
+        self._running = True
+
+        # Return proposed points (just the one)
+        return [self._proposed]
+
+    def f_best(self):
+        """
+        Returns the best score found so far.
+        """
+        return self._f_best
+
+    def f_guessed(self):
+        """
+        Returns the score of the last guessed point.
+        """
+        return self._current_f
+
+    def name(self):
+        """
+        Returns the name of the optimiser.
+        """
+        return "AdamW"
+
+    def needs_sensitivities(self):
+        """
+        Returns ``False`` if this optimiser does not require gradient,
+        and ``True`` otherwise.
+        """
+        return True
+
+    def n_hyper_parameters(self):
+        """
+        The number of hyper-parameters used by this optimiser.
+        """
+        return 5
+
+    def running(self):
+        """
+        Returns ``True`` if the optimisation is in progress.
+        """
+        return self._running
+
+    def tell(self, reply):
+        """
+        Receives a list of function values from the cost function from points
+        previously specified by `self.ask()`, and updates the optimiser state
+        accordingly.
+        """
+
+        # Check ask-tell pattern
+        if not self._ready_for_tell:
+            raise Exception("ask() not called before tell()")
+        self._ready_for_tell = False
+
+        # Unpack reply
+        fx, dfx = reply[0]
+
+        # Update current point
+        self._current = self._proposed
+        self._current_f = fx
+        self._current_df = dfx
+
+        # Update bx^t
+        self._b1t *= self._b1
+        self._b2t *= self._b2
+
+        # "Update biased first moment estimate"
+        self._m = self._b1 * self._m + (1 - self._b1) * dfx
+
+        # "Update biased second raw moment estimate"
+        self._v = self._b2 * self._v + (1 - self._b2) * dfx**2
+
+        # "Compute bias-corrected first moment estimate"
+        m = self._m / (1 - self._b1t)
+
+        # "Compute bias-corrected second raw moment estimate"
+        v = self._v / (1 - self._b2t)
+
+        # Take step with weight decay
+        self._proposed = self._current - self._alpha * (
+            m / (np.sqrt(v) + self._eps) + self._lambda * self._current
+        )
+
+        # Update x_best and f_best
+        if self._f_best > fx:
+            self._f_best = fx
+            self._x_best = self._current
+
+    def x_best(self):
+        """
+        Returns the best parameter values found so far.
+        """
+        return self._x_best
+
+    def x_guessed(self):
+        """
+        Returns the last guessed parameter values.
+        """
+        return self._current
+
+    def set_lambda(self, lambda_: float = 0.01) -> None:
+        """
+        Sets the lambda_ decay constant. This is the weight decay rate
+        that helps in finding the optimal solution.
+        """
+        if not isinstance(lambda_, (int, float)) or not 0 < lambda_ <= 1:
+            raise ValueError("lambda_ must be a numeric value between 0 and 1.")
+
+        self._lambda = float(lambda_)
+
+    def set_b1(self, b1: float) -> None:
+        """
+        Sets the b1 momentum decay constant.
+        """
+        if not isinstance(b1, (int, float)) or not 0 < b1 <= 1:
+            raise ValueError("b1 must be a numeric value between 0 and 1.")
+
+        self._b1 = float(b1)
+
+    def set_b2(self, b2: float) -> None:
+        """
+        Sets the b2 momentum decay constant.
+        """
+        if not isinstance(b2, (int, float)) or not 0 < b2 <= 1:
+            raise ValueError("b2 must be a numeric value between 0 and 1.")
+
+        self._b2 = float(b2)
diff --git a/pybop/optimisers/pints_optimisers.py b/pybop/optimisers/pints_optimisers.py
index d2e55371..4872973a 100644
--- a/pybop/optimisers/pints_optimisers.py
+++ b/pybop/optimisers/pints_optimisers.py
@@ -1,3 +1,5 @@
+from warnings import warn
+
 from pints import CMAES as PintsCMAES
 from pints import PSO as PintsPSO
 from pints import SNES as PintsSNES
@@ -7,7 +9,7 @@
 from pints import IRPropMin as PintsIRPropMin
 from pints import NelderMead as PintsNelderMead
 
-from pybop import BasePintsOptimiser
+from pybop import AdamWImpl, BasePintsOptimiser
 
 
 class GradientDescent(BasePintsOptimiser):
@@ -60,10 +62,43 @@ class Adam(BasePintsOptimiser):
     pints.Adam : The PINTS implementation this class is based on.
     """
 
+    warn(
+        "Adam is deprecated and will be removed in a future release. Please use AdamW instead.",
+        DeprecationWarning,
+        stacklevel=2,
+    )
+
     def __init__(self, cost, **optimiser_kwargs):
         super().__init__(cost, PintsAdam, **optimiser_kwargs)
 
 
+class AdamW(BasePintsOptimiser):
+    """
+    Implements the AdamW optimisation algorithm in PyBOP.
+
+    This class extends the AdamW optimiser, which is a variant of the Adam
+    optimiser that incorporates weight decay. AdamW is designed to be more
+    robust and stable for training deep neural networks, particularly when
+    using larger learning rates.
+
+    Parameters
+    ----------
+    **optimiser_kwargs : optional
+        Valid PyBOP option keys and their values, for example:
+        x0 : array_like
+            Initial position from which optimisation will start.
+        sigma0 : float
+            Initial step size.
+
+    See Also
+    --------
+    pybop.AdamWImpl : The PyBOP implementation this class is based on.
+    """
+
+    def __init__(self, cost, **optimiser_kwargs):
+        super().__init__(cost, AdamWImpl, **optimiser_kwargs)
+
+
 class IRPropMin(BasePintsOptimiser):
     """
     Implements the iRpropMin optimization algorithm.
diff --git a/tests/integration/test_spm_parameterisations.py b/tests/integration/test_spm_parameterisations.py
index 6e5108d7..9ae2b421 100644
--- a/tests/integration/test_spm_parameterisations.py
+++ b/tests/integration/test_spm_parameterisations.py
@@ -81,7 +81,7 @@ def spm_costs(self, model, parameters, cost_class, init_soc):
         "optimiser",
         [
             pybop.SciPyDifferentialEvolution,
-            pybop.Adam,
+            pybop.AdamW,
             pybop.CMAES,
             pybop.IRPropMin,
             pybop.NelderMead,
diff --git a/tests/unit/test_optimisation.py b/tests/unit/test_optimisation.py
index 2eef89ad..97fe12fc 100644
--- a/tests/unit/test_optimisation.py
+++ b/tests/unit/test_optimisation.py
@@ -73,6 +73,7 @@ def two_param_cost(self, model, two_parameters, dataset):
             (pybop.SciPyDifferentialEvolution, "SciPyDifferentialEvolution"),
             (pybop.GradientDescent, "Gradient descent"),
             (pybop.Adam, "Adam"),
+            (pybop.AdamW, "AdamW"),
             (pybop.CMAES, "Covariance Matrix Adaptation Evolution Strategy (CMA-ES)"),
             (pybop.SNES, "Seperable Natural Evolution Strategy (SNES)"),
             (pybop.XNES, "Exponential Natural Evolution Strategy (xNES)"),
@@ -110,6 +111,7 @@ def test_optimiser_classes(self, two_param_cost, optimiser, expected_name):
             pybop.SciPyDifferentialEvolution,
             pybop.GradientDescent,
             pybop.Adam,
+            pybop.AdamW,
             pybop.SNES,
             pybop.XNES,
             pybop.PSO,
@@ -210,6 +212,39 @@ def test_optimiser_kwargs(self, cost, optimiser):
             ):
                 optimiser(cost=cost, bounds={"upper": [np.inf], "lower": [0.57]})
 
+        # Test AdamW hyperparameters
+        if optimiser in [pybop.AdamW]:
+            optim = optimiser(cost=cost, b1=0.9, b2=0.999, lambda_=0.1)
+            optim.pints_optimiser.set_b1(0.9)
+            optim.pints_optimiser.set_b2(0.9)
+            optim.pints_optimiser.set_lambda(0.1)
+
+            assert optim.pints_optimiser._b1 == 0.9
+            assert optim.pints_optimiser._b2 == 0.9
+            assert optim.pints_optimiser._lambda == 0.1
+
+            # Incorrect values
+            for i, match in (("Value", -1),):
+                with pytest.raises(
+                    Exception, match="must be a numeric value between 0 and 1."
+                ):
+                    optim.pints_optimiser.set_b1(i)
+                with pytest.raises(
+                    Exception, match="must be a numeric value between 0 and 1."
+                ):
+                    optim.pints_optimiser.set_b2(i)
+                with pytest.raises(
+                    Exception, match="must be a numeric value between 0 and 1."
+                ):
+                    optim.pints_optimiser.set_lambda(i)
+
+            # Check defaults
+            assert optim.pints_optimiser.n_hyper_parameters() == 5
+            assert not optim.pints_optimiser.running()
+            assert optim.pints_optimiser.x_guessed() == optim.pints_optimiser._x0
+            with pytest.raises(Exception):
+                optim.pints_optimiser.tell([0.1])
+
         else:
             # Check and update initial values
             assert optim.x0 == cost.x0